├── chapters
    ├── __init__.py
    ├── chapter9.py
    ├── chapter7.py
    ├── chapter10.py
    └── chapter8.py
├── data
    ├── ch10q11.csv
    ├── lsat_efron.csv
    ├── ch09q03.csv
    ├── snodgrass.csv
    ├── cloud_seeding.csv
    ├── geysers.csv
    ├── nerve.csv
    └── fijiquakes.csv
├── README.md
├── .gitignore
├── solutions
    ├── ch07q03.ipynb
    ├── ch9q02.ipynb
    ├── ch07q10.ipynb
    ├── ch09q07.ipynb
    ├── ch07q08.ipynb
    ├── ch08q01.ipynb
    ├── ch08q03.ipynb
    ├── ch10q11.ipynb
    ├── ch09q03.ipynb
    ├── ch10q07.ipynb
    └── ch08q07.ipynb
└── images
    └── ch09q09_boxplot.svg


/chapters/__init__.py:
--------------------------------------------------------------------------------
1 | 


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/data/ch10q11.csv:
--------------------------------------------------------------------------------
1 | drug,total,nausea
2 | placebo,80,45
3 | chlorpromazine,75,26
4 | dimenhydrinate,85,52
5 | pentobarbital100,67,35
6 | pentobarbital150,85,37
7 | 


--------------------------------------------------------------------------------
/data/lsat_efron.csv:
--------------------------------------------------------------------------------
 1 | lsat,gpa
 2 | 576,3.39
 3 | 635,3.30
 4 | 558,2.81
 5 | 578,3.03
 6 | 666,3.44
 7 | 580,3.07
 8 | 555,3.00
 9 | 661,3.43
10 | 651,3.36
11 | 605,3.13
12 | 653,3.12
13 | 575,2.74
14 | 545,2.76
15 | 572,2.88
16 | 594,3.96
17 | 


--------------------------------------------------------------------------------
/data/ch09q03.csv:
--------------------------------------------------------------------------------
 1 | value
 2 | 3.23
 3 | -2.5
 4 | 1.88
 5 | -0.68
 6 | 4.43
 7 | 0.17
 8 | 1.03
 9 | -0.07
10 | -0.01
11 | 0.76
12 | 1.76
13 | 3.18
14 | 0.33
15 | -0.31
16 | 0.30
17 | -0.61
18 | 1.52
19 | 5.43
20 | 1.54
21 | 2.28
22 | 0.42
23 | 2.33
24 | -1.03
25 | 4.00
26 | 0.39
27 | 


--------------------------------------------------------------------------------
/data/snodgrass.csv:
--------------------------------------------------------------------------------
 1 | author,total
 2 | twain,.225
 3 | twain,.262
 4 | twain,.217
 5 | twain,.240
 6 | twain,.230
 7 | twain,.229
 8 | twain,.235
 9 | twain,.217
10 | snodgrass,.209
11 | snodgrass,.205
12 | snodgrass,.196
13 | snodgrass,.210
14 | snodgrass,.202
15 | snodgrass,.207
16 | snodgrass,.224
17 | snodgrass,.223
18 | snodgrass,.220
19 | snodgrass,.201
20 | 


--------------------------------------------------------------------------------
/data/cloud_seeding.csv:
--------------------------------------------------------------------------------
 1 | Unseeded_Clouds,Seeded_Clouds
 2 | 1202.6,2745.6
 3 | 830.1,1697.8
 4 | 372.4,1656.0
 5 | 345.5,978.0
 6 | 321.2,703.4
 7 | 244.3,489.1
 8 | 163.0,430.0
 9 | 147.8,334.1
10 | 95.0,302.8
11 | 87.0,274.7
12 | 81.2,274.7
13 | 68.5,255.0
14 | 47.3,242.5
15 | 41.1,200.7
16 | 36.6,198.6
17 | 29.0,129.6
18 | 28.6,119.0
19 | 26.3,118.3
20 | 26.1,115.3
21 | 24.4,92.4
22 | 21.7,40.6
23 | 17.3,32.7
24 | 11.5,31.4
25 | 4.9,17.5
26 | 4.9,7.7
27 | 1.0,4.1
28 | 


--------------------------------------------------------------------------------
/chapters/chapter9.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | from scipy.stats import norm
 3 | from .chapter7 import CI
 4 | 
 5 | 
 6 | def parametric_bootstrap(dist, n, statistic, iters, random_state=0):
 7 |     for i in range(iters):
 8 |         yield statistic(dist.rvs(n, random_state=random_state+i))
 9 | 
10 | 
11 | def parametric_bootstrap_variance(dist, n, statistic, iters, random_state=0):
12 |     boots = list(parametric_bootstrap(dist, n, statistic, iters, random_state=random_state))
13 |     vboot = np.var(boots, axis=0)
14 |     return vboot
15 | 


--------------------------------------------------------------------------------
/chapters/chapter7.py:
--------------------------------------------------------------------------------
 1 | import math
 2 | from collections import namedtuple
 3 | 
 4 | 
 5 | CI = namedtuple('CI', ('lower', 'upper'))
 6 | 
 7 | 
 8 | class ECDF(object):
 9 | 
10 |     def __init__(self, obs):
11 |         self.observations = obs
12 | 
13 |     def __call__(self, x):
14 |         return sum(1 for ob in self.observations if ob <= x) / len(self.observations)
15 | 
16 |     def error(self, a):
17 |         n = len(self.observations)
18 |         return math.sqrt(math.log(2 / a) / (2*n))
19 | 
20 |     def ci(self, x, a=0.05):
21 |         e = self.error(a)
22 |         y = self(x)
23 |         l = max(y - e, 0)
24 |         u = min(y + e, 1)
25 |         return CI(l, u)
26 | 


--------------------------------------------------------------------------------
/chapters/chapter10.py:
--------------------------------------------------------------------------------
 1 | def bonferroni(ps, alpha):
 2 |     """
 3 |     Return a p-value for multiple tests using Bonferroni.
 4 | 
 5 |     See page 166.
 6 |     """
 7 |     return alpha / len(ps)
 8 | 
 9 | 
10 | def benjamini_hochberg(ps, alpha, independent=True):
11 |     """
12 |     Return a p-value for multiple tests using the Benjamini-Hochberg method.
13 | 
14 |     See page 167.
15 |     """
16 | 
17 |     m = len(ps)
18 |     ps = sorted(ps)
19 | 
20 |     if independent:
21 |         c = 1
22 |     else:
23 |         c = sum(1 / i for i in range(1, m + 1))
24 | 
25 |     ls = [i * alpha / (c * m) for i in range(1, m + 1)]
26 |     r = max(i for i in range(m) if ps[i] < ls[i])
27 | 
28 |     return ps[r]
29 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # All of Statistics
 2 | 
 3 | Solutions to [Wasserman's 'All Of Statistics'](https://link.springer.com/book/10.1007/978-0-387-21736-9), using the 2005 corrected second printing, ISBN 0-387-40272-1.
 4 | 
 5 | ## Organisation
 6 | 
 7 | Please follow these guidelines:
 8 | 
 9 | * Solutions go in [solutions](/solutions) as markdown or notebook (ipynb). They should be labelled `chXXqYY` where `XX` is the (0 padded) chapter number and `YY` is the (0 padded) question number.  For example, question 3 from chapter 7 should be labelled `ch07q03`.
10 | * Anything useful/reusable/more involved should go in [chapters](/chapters).
11 | * Datasets go in [data](/data).
12 | * Use python 3, not python 2.
13 | 
14 | Some more mathematical solutions may be found [on the blog](https://stappit.github.io/categories/allofstatistics.html).
15 | 


--------------------------------------------------------------------------------
/.gitignore:
--------------------------------------------------------------------------------
 1 | # Byte-compiled / optimized / DLL files
 2 | __pycache__/
 3 | *.py[cod]
 4 | *$py.class
 5 | 
 6 | # C extensions
 7 | *.so
 8 | 
 9 | # Distribution / packaging
10 | .Python
11 | env/
12 | build/
13 | develop-eggs/
14 | dist/
15 | downloads/
16 | eggs/
17 | .eggs/
18 | lib/
19 | lib64/
20 | parts/
21 | sdist/
22 | var/
23 | *.egg-info/
24 | .installed.cfg
25 | *.egg
26 | 
27 | # PyInstaller
28 | #  Usually these files are written by a python script from a template
29 | #  before PyInstaller builds the exe, so as to inject date/other infos into it.
30 | *.manifest
31 | *.spec
32 | 
33 | # Installer logs
34 | pip-log.txt
35 | pip-delete-this-directory.txt
36 | 
37 | # Unit test / coverage reports
38 | htmlcov/
39 | .tox/
40 | .coverage
41 | .coverage.*
42 | .cache
43 | nosetests.xml
44 | coverage.xml
45 | *,cover
46 | .hypothesis/
47 | 
48 | # Translations
49 | *.mo
50 | *.pot
51 | 
52 | # Django stuff:
53 | *.log
54 | local_settings.py
55 | 
56 | # Flask stuff:
57 | instance/
58 | .webassets-cache
59 | 
60 | # Scrapy stuff:
61 | .scrapy
62 | 
63 | # Sphinx documentation
64 | docs/_build/
65 | 
66 | # PyBuilder
67 | target/
68 | 
69 | # IPython Notebook
70 | .ipynb_checkpoints
71 | 
72 | # pyenv
73 | .python-version
74 | 
75 | # celery beat schedule file
76 | celerybeat-schedule
77 | 
78 | # dotenv
79 | .env
80 | 
81 | # virtualenv
82 | venv/
83 | ENV/
84 | 
85 | # Spyder project settings
86 | .spyderproject
87 | 
88 | # Rope project settings
89 | .ropeproject
90 | 


--------------------------------------------------------------------------------
/chapters/chapter8.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | from scipy.stats import norm
 3 | from .chapter7 import CI
 4 | 
 5 | 
 6 | def bootstrap(observations, statistic, iters, random_state=0):
 7 |     """
 8 |     Yield the statistic applied to bootstapped samples.
 9 | 
10 |     :observations: DataFrame,
11 |         cols are random variables
12 |         rows are observations
13 | 
14 |     :statistic: the statistic to be calculated on each sample
15 |     :iters: int, the number of iterations
16 |     """
17 | 
18 |     n = len(observations)
19 |     for i in range(iters):
20 |         yield statistic(observations.sample(n, replace=True,
21 |                                             random_state=random_state+i))
22 | 
23 | 
24 | def bootstrap_variance(observations, statistic, iters, random_state=0):
25 |     boots = list(bootstrap(observations, statistic, iters,
26 |                            random_state=random_state))
27 |     vboot = np.var(boots, axis=0)
28 |     return vboot
29 | 
30 | 
31 | def bootstrap_ci_normal(observations, statistic, iters, a, random_state=0):
32 |     t = statistic(observations)
33 |     vboot = bootstrap_variance(observations, statistic, iters,
34 |                                random_state=random_state)
35 |     seboot = np.sqrt(vboot)
36 |     z = np.abs(norm.ppf(a / 2))
37 |     return CI(t - z*seboot, t + z*seboot)
38 | 
39 | 
40 | def bootstrap_ci_pivot(observations, statistic, iters, a, random_state=0):
41 |     theta = statistic(observations)
42 |     boots = list(bootstrap(observations, statistic, iters, random_state=random_state))
43 |     theta_l = np.percentile(boots, 100 - 100*a / 2)
44 |     theta_r = np.percentile(boots, 100*a / 2)
45 |     return CI(2*theta - theta_l, 2*theta - theta_r)
46 | 
47 | 
48 | def bootstrap_ci_percentile(observations, statistic, iters, a, random_state=0):
49 |     boots = list(bootstrap(observations, statistic, iters, random_state=random_state))
50 |     theta_l = np.percentile(boots, 100*a / 2, axis=0)
51 |     theta_r = np.percentile(boots, 100 - 100*a / 2, axis=0)
52 |     return CI(theta_l, theta_r)
53 | 


--------------------------------------------------------------------------------
/solutions/ch07q03.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 4,
  6 |    "metadata": {},
  7 |    "outputs": [
  8 |     {
  9 |      "name": "stdout",
 10 |      "output_type": "stream",
 11 |      "text": [
 12 |       "The autoreload extension is already loaded. To reload it, use:\n",
 13 |       "  %reload_ext autoreload\n"
 14 |      ]
 15 |     }
 16 |    ],
 17 |    "source": [
 18 |     "import sys\n",
 19 |     "sys.path.append('..')\n",
 20 |     "\n",
 21 |     "from scipy.stats import norm, cauchy\n",
 22 |     "\n",
 23 |     "%load_ext autoreload\n",
 24 |     "%autoreload 2\n",
 25 |     "\n",
 26 |     "from chapters.chapter7 import ECDF"
 27 |    ]
 28 |   },
 29 |   {
 30 |    "cell_type": "code",
 31 |    "execution_count": 5,
 32 |    "metadata": {},
 33 |    "outputs": [
 34 |     {
 35 |      "data": {
 36 |       "text/plain": [
 37 |        "0.959"
 38 |       ]
 39 |      },
 40 |      "execution_count": 5,
 41 |      "metadata": {},
 42 |      "output_type": "execute_result"
 43 |     }
 44 |    ],
 45 |    "source": [
 46 |     "def experiment(dist, iters=1000, size=100):\n",
 47 |     "    correct = 0\n",
 48 |     "    for _ in range(iters):\n",
 49 |     "        xs = dist.rvs(size=size)\n",
 50 |     "        F = ECDF(xs)\n",
 51 |     "        c = sum(1 for x in xs if F.ci(x).lower <= dist.cdf(x) <= F.ci(x).upper) == len(xs)\n",
 52 |     "        correct += c\n",
 53 |     "        \n",
 54 |     "    return correct / iters\n",
 55 |     "\n",
 56 |     "experiment(norm)"
 57 |    ]
 58 |   },
 59 |   {
 60 |    "cell_type": "code",
 61 |    "execution_count": 6,
 62 |    "metadata": {},
 63 |    "outputs": [
 64 |     {
 65 |      "data": {
 66 |       "text/plain": [
 67 |        "0.964"
 68 |       ]
 69 |      },
 70 |      "execution_count": 6,
 71 |      "metadata": {},
 72 |      "output_type": "execute_result"
 73 |     }
 74 |    ],
 75 |    "source": [
 76 |     "experiment(cauchy)"
 77 |    ]
 78 |   },
 79 |   {
 80 |    "cell_type": "code",
 81 |    "execution_count": null,
 82 |    "metadata": {
 83 |     "collapsed": true
 84 |    },
 85 |    "outputs": [],
 86 |    "source": []
 87 |   }
 88 |  ],
 89 |  "metadata": {
 90 |   "kernelspec": {
 91 |    "display_name": "Python 3",
 92 |    "language": "python",
 93 |    "name": "python3"
 94 |   },
 95 |   "language_info": {
 96 |    "codemirror_mode": {
 97 |     "name": "ipython",
 98 |     "version": 3
 99 |    },
100 |    "file_extension": ".py",
101 |    "mimetype": "text/x-python",
102 |    "name": "python",
103 |    "nbconvert_exporter": "python",
104 |    "pygments_lexer": "ipython3",
105 |    "version": "3.4.3"
106 |   }
107 |  },
108 |  "nbformat": 4,
109 |  "nbformat_minor": 2
110 | }
111 | 


--------------------------------------------------------------------------------
/solutions/ch9q02.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "import numpy as np"
 12 |    ]
 13 |   },
 14 |   {
 15 |    "cell_type": "code",
 16 |    "execution_count": 2,
 17 |    "metadata": {
 18 |     "collapsed": true
 19 |    },
 20 |    "outputs": [],
 21 |    "source": [
 22 |     "a = 1\n",
 23 |     "b = 3\n",
 24 |     "n = 10"
 25 |    ]
 26 |   },
 27 |   {
 28 |    "cell_type": "code",
 29 |    "execution_count": 3,
 30 |    "metadata": {
 31 |     "collapsed": true
 32 |    },
 33 |    "outputs": [],
 34 |    "source": [
 35 |     "a_n = []\n",
 36 |     "b_n = []\n",
 37 |     "\n",
 38 |     "for i in range(1000):\n",
 39 |     "    sample = np.random.uniform(low=a, high=b, size=n)\n",
 40 |     "    a_n.append(np.min(sample))\n",
 41 |     "    b_n.append(np.max(sample))\n",
 42 |     "    "
 43 |    ]
 44 |   },
 45 |   {
 46 |    "cell_type": "code",
 47 |    "execution_count": 7,
 48 |    "metadata": {
 49 |     "collapsed": true
 50 |    },
 51 |    "outputs": [],
 52 |    "source": [
 53 |     "a_hat = np.mean(a_n)\n",
 54 |     "a_se = np.std(a_n)\n",
 55 |     "b_hat = np.mean(b_n)\n",
 56 |     "b_se = np.std(b_n)"
 57 |    ]
 58 |   },
 59 |   {
 60 |    "cell_type": "code",
 61 |    "execution_count": 8,
 62 |    "metadata": {},
 63 |    "outputs": [
 64 |     {
 65 |      "data": {
 66 |       "text/plain": [
 67 |        "(1.1941042516407383, 0.84548759286368136, 1.5427209104177952)"
 68 |       ]
 69 |      },
 70 |      "execution_count": 8,
 71 |      "metadata": {},
 72 |      "output_type": "execute_result"
 73 |     }
 74 |    ],
 75 |    "source": [
 76 |     "a_hat, a_hat-1.96*a_se, a_hat+1.96*a_se"
 77 |    ]
 78 |   },
 79 |   {
 80 |    "cell_type": "code",
 81 |    "execution_count": 9,
 82 |    "metadata": {},
 83 |    "outputs": [
 84 |     {
 85 |      "data": {
 86 |       "text/plain": [
 87 |        "(2.8130740778803318, 2.46884620062258, 3.1573019551380836)"
 88 |       ]
 89 |      },
 90 |      "execution_count": 9,
 91 |      "metadata": {},
 92 |      "output_type": "execute_result"
 93 |     }
 94 |    ],
 95 |    "source": [
 96 |     "b_hat, b_hat-1.96*b_se, b_hat+1.96*b_se"
 97 |    ]
 98 |   },
 99 |   {
100 |    "cell_type": "markdown",
101 |    "metadata": {},
102 |    "source": [
103 |     "Bootstrap method fails here ^^ "
104 |    ]
105 |   },
106 |   {
107 |    "cell_type": "code",
108 |    "execution_count": null,
109 |    "metadata": {
110 |     "collapsed": true
111 |    },
112 |    "outputs": [],
113 |    "source": []
114 |   }
115 |  ],
116 |  "metadata": {
117 |   "kernelspec": {
118 |    "display_name": "Python 3",
119 |    "language": "python",
120 |    "name": "python3"
121 |   },
122 |   "language_info": {
123 |    "codemirror_mode": {
124 |     "name": "ipython",
125 |     "version": 3
126 |    },
127 |    "file_extension": ".py",
128 |    "mimetype": "text/x-python",
129 |    "name": "python",
130 |    "nbconvert_exporter": "python",
131 |    "pygments_lexer": "ipython3",
132 |    "version": "3.5.1"
133 |   }
134 |  },
135 |  "nbformat": 4,
136 |  "nbformat_minor": 2
137 | }
138 | 


--------------------------------------------------------------------------------
/data/geysers.csv:
--------------------------------------------------------------------------------
  1 | index,eruptions,waiting
  2 | 1, 3.600,79
  3 | 2, 1.800,54
  4 | 3, 3.333,74
  5 | 4, 2.283,62
  6 | 5, 4.533,85
  7 | 6, 2.883,55
  8 | 7, 4.700,88
  9 | 8, 3.600,85
 10 | 9, 1.950,51
 11 | 10,4.350,85
 12 | 11,1.833,54
 13 | 12,3.917,84
 14 | 13,4.200,78
 15 | 14,1.750,47
 16 | 15,4.700,83
 17 | 16,2.167,52
 18 | 17,1.750,62
 19 | 18,4.800,84
 20 | 19,1.600,52
 21 | 20,4.250,79
 22 | 21,1.800,51
 23 | 22,1.750,47
 24 | 23,3.450,78
 25 | 24,3.067,69
 26 | 25,4.533,74
 27 | 26,3.600,83
 28 | 27,1.967,55
 29 | 28,4.083,76
 30 | 29,3.850,78
 31 | 30,4.433,79
 32 | 31,4.300,73
 33 | 32,4.467,77
 34 | 33,3.367,66
 35 | 34,4.033,80
 36 | 35,3.833,74
 37 | 36,2.017,52
 38 | 37,1.867,48
 39 | 38,4.833,80
 40 | 39,1.833,59
 41 | 40,4.783,90
 42 | 41,4.350,80
 43 | 42,1.883,58
 44 | 43,4.567,84
 45 | 44,1.750,58
 46 | 45,4.533,73
 47 | 46,3.317,83
 48 | 47,3.833,64
 49 | 48,2.100,53
 50 | 49,4.633,82
 51 | 50,2.000,59
 52 | 51,4.800,75
 53 | 52,4.716,90
 54 | 53,1.833,54
 55 | 54,4.833,80
 56 | 55,1.733,54
 57 | 56,4.883,83
 58 | 57,3.717,71
 59 | 58,1.667,64
 60 | 59,4.567,77
 61 | 60,4.317,81
 62 | 61,2.233,59
 63 | 62,4.500,84
 64 | 63,1.750,48
 65 | 64,4.800,82
 66 | 65,1.817,60
 67 | 66,4.400,92
 68 | 67,4.167,78
 69 | 68,4.700,78
 70 | 69,2.067,65
 71 | 70,4.700,73
 72 | 71,4.033,82
 73 | 72,1.967,56
 74 | 73,4.500,79
 75 | 74,4.000,71
 76 | 75,1.983,62
 77 | 76,5.067,76
 78 | 77,2.017,60
 79 | 78,4.567,78
 80 | 79,3.883,76
 81 | 80,3.600,83
 82 | 81,4.133,75
 83 | 82,4.333,82
 84 | 83,4.100,70
 85 | 84,2.633,65
 86 | 85,4.067,73
 87 | 86,4.933,88
 88 | 87,3.950,76
 89 | 88,4.517,80
 90 | 89,2.167,48
 91 | 90,4.000,86
 92 | 91,2.200,60
 93 | 92,4.333,90
 94 | 93,1.867,50
 95 | 94,4.817,78
 96 | 95,1.833,63
 97 | 96,4.300,72
 98 | 97,4.667,84
 99 | 98,3.750,75
100 | 99,1.867,51
101 | 100,4.900,82
102 | 101,2.483,62
103 | 102,4.367,88
104 | 103,2.100,49
105 | 104,4.500,83
106 | 105,4.050,81
107 | 106,1.867,47
108 | 107,4.700,84
109 | 108,1.783,52
110 | 109,4.850,86
111 | 110,3.683,81
112 | 111,4.733,75
113 | 112,2.300,59
114 | 113,4.900,89
115 | 114,4.417,79
116 | 115,1.700,59
117 | 116,4.633,81
118 | 117,2.317,50
119 | 118,4.600,85
120 | 119,1.817,59
121 | 120,4.417,87
122 | 121,2.617,53
123 | 122,4.067,69
124 | 123,4.250,77
125 | 124,1.967,56
126 | 125,4.600,88
127 | 126,3.767,81
128 | 127,1.917,45
129 | 128,4.500,82
130 | 129,2.267,55
131 | 130,4.650,90
132 | 131,1.867,45
133 | 132,4.167,83
134 | 133,2.800,56
135 | 134,4.333,89
136 | 135,1.833,46
137 | 136,4.383,82
138 | 137,1.883,51
139 | 138,4.933,86
140 | 139,2.033,53
141 | 140,3.733,79
142 | 141,4.233,81
143 | 142,2.233,60
144 | 143,4.533,82
145 | 144,4.817,77
146 | 145,4.333,76
147 | 146,1.983,59
148 | 147,4.633,80
149 | 148,2.017,49
150 | 149,5.100,96
151 | 150,1.800,53
152 | 151,5.033,77
153 | 152,4.000,77
154 | 153,2.400,65
155 | 154,4.600,81
156 | 155,3.567,71
157 | 156,4.000,70
158 | 157,4.500,81
159 | 158,4.083,93
160 | 159,1.800,53
161 | 160,3.967,89
162 | 161,2.200,45
163 | 162,4.150,86
164 | 163,2.000,58
165 | 164,3.833,78
166 | 165,3.500,66
167 | 166,4.583,76
168 | 167,2.367,63
169 | 168,5.000,88
170 | 169,1.933,52
171 | 170,4.617,93
172 | 171,1.917,49
173 | 172,2.083,57
174 | 173,4.583,77
175 | 174,3.333,68
176 | 175,4.167,81
177 | 176,4.333,81
178 | 177,4.500,73
179 | 178,2.417,50
180 | 179,4.000,85
181 | 180,4.167,74
182 | 181,1.883,55
183 | 182,4.583,77
184 | 183,4.250,83
185 | 184,3.767,83
186 | 185,2.033,51
187 | 186,4.433,78
188 | 187,4.083,84
189 | 188,1.833,46
190 | 189,4.417,83
191 | 190,2.183,55
192 | 191,4.800,81
193 | 192,1.833,57
194 | 193,4.800,76
195 | 194,4.100,84
196 | 195,3.966,77
197 | 196,4.233,81
198 | 197,3.500,87
199 | 198,4.366,77
200 | 199,2.250,51
201 | 200,4.667,78
202 | 201,2.100,60
203 | 202,4.350,82
204 | 203,4.133,91
205 | 204,1.867,53
206 | 205,4.600,78
207 | 206,1.783,46
208 | 207,4.367,77
209 | 208,3.850,84
210 | 209,1.933,49
211 | 210,4.500,83
212 | 211,2.383,71
213 | 212,4.700,80
214 | 213,1.867,49
215 | 214,3.833,75
216 | 215,3.417,64
217 | 216,4.233,76
218 | 217,2.400,53
219 | 218,4.800,94
220 | 219,2.000,55
221 | 220,4.150,76
222 | 221,1.867,50
223 | 222,4.267,82
224 | 223,1.750,54
225 | 224,4.483,75
226 | 225,4.000,78
227 | 226,4.117,79
228 | 227,4.083,78
229 | 228,4.267,78
230 | 229,3.917,70
231 | 230,4.550,79
232 | 231,4.083,70
233 | 232,2.417,54
234 | 233,4.183,86
235 | 234,2.217,50
236 | 235,4.450,90
237 | 236,1.883,54
238 | 237,1.850,54
239 | 238,4.283,77
240 | 239,3.950,79
241 | 240,2.333,64
242 | 241,4.150,75
243 | 242,2.350,47
244 | 243,4.933,86
245 | 244,2.900,63
246 | 245,4.583,85
247 | 246,3.833,82
248 | 247,2.083,57
249 | 248,4.367,82
250 | 249,2.133,67
251 | 250,4.350,74
252 | 251,2.200,54
253 | 252,4.450,83
254 | 253,3.567,73
255 | 254,4.500,73
256 | 255,4.150,88
257 | 256,3.817,80
258 | 257,3.917,71
259 | 258,4.450,83
260 | 259,2.000,56
261 | 260,4.283,79
262 | 261,4.767,78
263 | 262,4.533,84
264 | 263,1.850,58
265 | 264,4.250,83
266 | 265,1.983,43
267 | 266,2.250,60
268 | 267,4.750,75
269 | 268,4.117,81
270 | 269,2.150,46
271 | 270,4.417,90
272 | 271,1.817,46
273 | 272,4.467,74
274 | 


--------------------------------------------------------------------------------
/solutions/ch07q10.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {},
  7 |    "outputs": [
  8 |     {
  9 |      "name": "stdout",
 10 |      "output_type": "stream",
 11 |      "text": [
 12 |       "/Users/Steve/aos\n"
 13 |      ]
 14 |     }
 15 |    ],
 16 |    "source": [
 17 |     "cd ../.."
 18 |    ]
 19 |   },
 20 |   {
 21 |    "cell_type": "code",
 22 |    "execution_count": 2,
 23 |    "metadata": {
 24 |     "collapsed": true
 25 |    },
 26 |    "outputs": [
 27 |     {
 28 |      "name": "stderr",
 29 |      "output_type": "stream",
 30 |      "text": [
 31 |       "/home/brian/.virtualenvs/this/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
 32 |       "  return f(*args, **kwds)\n"
 33 |      ]
 34 |     }
 35 |    ],
 36 |    "source": [
 37 |     "import pandas as pd\n",
 38 |     "import numpy as np"
 39 |    ]
 40 |   },
 41 |   {
 42 |    "cell_type": "code",
 43 |    "execution_count": 3,
 44 |    "metadata": {
 45 |     "collapsed": true
 46 |    },
 47 |    "outputs": [],
 48 |    "source": [
 49 |     "clouds = pd.read_csv('../data/cloud_seeding.csv')"
 50 |    ]
 51 |   },
 52 |   {
 53 |    "cell_type": "code",
 54 |    "execution_count": 9,
 55 |    "metadata": {
 56 |     "collapsed": true
 57 |    },
 58 |    "outputs": [],
 59 |    "source": [
 60 |     "seeded = clouds['Seeded_Clouds']\n",
 61 |     "unseeded = clouds['Unseeded_Clouds']"
 62 |    ]
 63 |   },
 64 |   {
 65 |    "cell_type": "markdown",
 66 |    "metadata": {},
 67 |    "source": [
 68 |     "We have the following parameter:\n",
 69 |     "\n",
 70 |     "$\\theta = T(F_2) - T(F_1)$\n",
 71 |     "\n",
 72 |     "With the following estimator:\n",
 73 |     "\n",
 74 |     "$\\hat{\\theta} = \\hat{\\mu_2} - \\hat{\\mu_1}$\n",
 75 |     "\n",
 76 |     "The variance is given by:\n",
 77 |     "\n",
 78 |     "$V(\\hat{\\theta}) = V(\\hat{\\mu_2} - \\hat{\\mu_1})$\n",
 79 |     "\n",
 80 |     "$ = V(\\hat{\\mu_2}) + V(\\hat{\\mu_1})$\n",
 81 |     "\n",
 82 |     "And the standard error is:\n",
 83 |     "\n",
 84 |     "$se(\\hat{\\theta}) = \\sqrt{V(\\hat{\\theta})}$"
 85 |    ]
 86 |   },
 87 |   {
 88 |    "cell_type": "code",
 89 |    "execution_count": 10,
 90 |    "metadata": {
 91 |     "collapsed": true
 92 |    },
 93 |    "outputs": [],
 94 |    "source": [
 95 |     "# n obs\n",
 96 |     "n_s = len(seeded)\n",
 97 |     "n_u = len(unseeded)"
 98 |    ]
 99 |   },
100 |   {
101 |    "cell_type": "code",
102 |    "execution_count": 11,
103 |    "metadata": {
104 |     "collapsed": true
105 |    },
106 |    "outputs": [],
107 |    "source": [
108 |     "mu_s = np.mean(seeded)\n",
109 |     "mu_u = np.mean(unseeded)"
110 |    ]
111 |   },
112 |   {
113 |    "cell_type": "code",
114 |    "execution_count": 12,
115 |    "metadata": {
116 |     "collapsed": true
117 |    },
118 |    "outputs": [],
119 |    "source": [
120 |     "mu_theta = mu_s - mu_u"
121 |    ]
122 |   },
123 |   {
124 |    "cell_type": "code",
125 |    "execution_count": 13,
126 |    "metadata": {
127 |     "collapsed": true
128 |    },
129 |    "outputs": [],
130 |    "source": [
131 |     "se_theta = np.sqrt(np.var(seeded) / n_s + np.var(unseeded) / n_u)"
132 |    ]
133 |   },
134 |   {
135 |    "cell_type": "code",
136 |    "execution_count": 14,
137 |    "metadata": {
138 |     "collapsed": true
139 |    },
140 |    "outputs": [
141 |     {
142 |      "data": {
143 |       "text/plain": [
144 |        "136.124128223444"
145 |       ]
146 |      },
147 |      "execution_count": 14,
148 |      "metadata": {},
149 |      "output_type": "execute_result"
150 |     }
151 |    ],
152 |    "source": [
153 |     "se_theta"
154 |    ]
155 |   },
156 |   {
157 |    "cell_type": "code",
158 |    "execution_count": 17,
159 |    "metadata": {
160 |     "collapsed": true
161 |    },
162 |    "outputs": [],
163 |    "source": [
164 |     "# confidence interval (.95)\n",
165 |     "z = 1.96\n",
166 |     "U = mu_theta + z*se_theta\n",
167 |     "L = mu_theta - z*se_theta"
168 |    ]
169 |   },
170 |   {
171 |    "cell_type": "code",
172 |    "execution_count": 18,
173 |    "metadata": {},
174 |    "outputs": [
175 |     {
176 |      "data": {
177 |       "text/plain": [
178 |        "(544.1994451641041, 10.592862528203682)"
179 |       ]
180 |      },
181 |      "execution_count": 18,
182 |      "metadata": {},
183 |      "output_type": "execute_result"
184 |     }
185 |    ],
186 |    "source": [
187 |     "# not significant @ .95\n",
188 |     "U, L"
189 |    ]
190 |   },
191 |   {
192 |    "cell_type": "code",
193 |    "execution_count": null,
194 |    "metadata": {},
195 |    "outputs": [],
196 |    "source": []
197 |   }
198 |  ],
199 |  "metadata": {
200 |   "kernelspec": {
201 |    "display_name": "Python 3",
202 |    "language": "python",
203 |    "name": "python3"
204 |   },
205 |   "language_info": {
206 |    "codemirror_mode": {
207 |     "name": "ipython",
208 |     "version": 3
209 |    },
210 |    "file_extension": ".py",
211 |    "mimetype": "text/x-python",
212 |    "name": "python",
213 |    "nbconvert_exporter": "python",
214 |    "pygments_lexer": "ipython3",
215 |    "version": "3.5.2"
216 |   }
217 |  },
218 |  "nbformat": 4,
219 |  "nbformat_minor": 2
220 | }
221 | 


--------------------------------------------------------------------------------
/solutions/ch09q07.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 17,
  6 |    "metadata": {},
  7 |    "outputs": [
  8 |     {
  9 |      "name": "stdout",
 10 |      "output_type": "stream",
 11 |      "text": [
 12 |       "The autoreload extension is already loaded. To reload it, use:\n",
 13 |       "  %reload_ext autoreload\n"
 14 |      ]
 15 |     }
 16 |    ],
 17 |    "source": [
 18 |     "import sys\n",
 19 |     "sys.path.append('..')\n",
 20 |     "\n",
 21 |     "from scipy.stats import binom, norm\n",
 22 |     "import pandas as pd\n",
 23 |     "import numpy as np\n",
 24 |     "import seaborn as sns\n",
 25 |     "import matplotlib.pyplot as plt\n",
 26 |     "\n",
 27 |     "from chapters.chapter7 import CI\n",
 28 |     "from chapters.chapter8 import bootstrap, bootstrap_variance\n",
 29 |     "from chapters.chapter9 import parametric_bootstrap, parametric_bootstrap_variance\n",
 30 |     "\n",
 31 |     "%load_ext autoreload\n",
 32 |     "%autoreload 2\n",
 33 |     "\n",
 34 |     "%matplotlib inline\n",
 35 |     "plt.style.use('ggplot')"
 36 |    ]
 37 |   },
 38 |   {
 39 |    "cell_type": "markdown",
 40 |    "metadata": {},
 41 |    "source": [
 42 |     "## MLE"
 43 |    ]
 44 |   },
 45 |   {
 46 |    "cell_type": "markdown",
 47 |    "metadata": {},
 48 |    "source": [
 49 |     "The MLE for $\\psi$ is $\\hat \\psi = \\hat p_1 - \\hat p_2$."
 50 |    ]
 51 |   },
 52 |   {
 53 |    "cell_type": "markdown",
 54 |    "metadata": {},
 55 |    "source": [
 56 |     "The Fisher information matrix is\n",
 57 |     "$$\n",
 58 |     "\\begin{pmatrix}\n",
 59 |     "    \\frac{n1}{p_1 (1-p_1)} & 0 \\\\\n",
 60 |     "    0 & \\frac{n1}{p_1 (1-p_1)}\n",
 61 |     "\\end{pmatrix}\n",
 62 |     "$$"
 63 |    ]
 64 |   },
 65 |   {
 66 |    "cell_type": "markdown",
 67 |    "metadata": {},
 68 |    "source": [
 69 |     "The delta method standard error is $\\sqrt{\\frac{p_1 (1 - p_1)}{n_1} + \\frac{p_2 (1 - p_2)}{n_2}}$"
 70 |    ]
 71 |   },
 72 |   {
 73 |    "cell_type": "code",
 74 |    "execution_count": 26,
 75 |    "metadata": {},
 76 |    "outputs": [
 77 |     {
 78 |      "data": {
 79 |       "text/plain": [
 80 |        "0.06000000000000005"
 81 |       ]
 82 |      },
 83 |      "execution_count": 26,
 84 |      "metadata": {},
 85 |      "output_type": "execute_result"
 86 |     }
 87 |    ],
 88 |    "source": [
 89 |     "n1 = 200\n",
 90 |     "n2 = n1\n",
 91 |     "x1 = 160\n",
 92 |     "x2 = 148\n",
 93 |     "p1_hat = x1 / n1\n",
 94 |     "p2_hat = x2 / n2\n",
 95 |     "\n",
 96 |     "psi_hat = p1_hat - p2_hat\n",
 97 |     "mle = psi_hat\n",
 98 |     "psi_hat"
 99 |    ]
100 |   },
101 |   {
102 |    "cell_type": "code",
103 |    "execution_count": 29,
104 |    "metadata": {},
105 |    "outputs": [
106 |     {
107 |      "data": {
108 |       "text/plain": [
109 |        "0.041976183723630711"
110 |       ]
111 |      },
112 |      "execution_count": 29,
113 |      "metadata": {},
114 |      "output_type": "execute_result"
115 |     }
116 |    ],
117 |    "source": [
118 |     "se_delta = np.sqrt((p1_hat * (1 - p1_hat)) / n1 + (p2_hat * (1 - p2_hat)) / n2)\n",
119 |     "se_delta"
120 |    ]
121 |   },
122 |   {
123 |    "cell_type": "code",
124 |    "execution_count": 30,
125 |    "metadata": {},
126 |    "outputs": [
127 |     {
128 |      "data": {
129 |       "text/plain": [
130 |        "1.6448536269514722"
131 |       ]
132 |      },
133 |      "execution_count": 30,
134 |      "metadata": {},
135 |      "output_type": "execute_result"
136 |     }
137 |    ],
138 |    "source": [
139 |     "alpha = 0.05\n",
140 |     "z_alpha = norm.ppf(1 - alpha)\n",
141 |     "z_alpha"
142 |    ]
143 |   },
144 |   {
145 |    "cell_type": "code",
146 |    "execution_count": 31,
147 |    "metadata": {},
148 |    "outputs": [
149 |     {
150 |      "data": {
151 |       "text/plain": [
152 |        "CI(lower=-0.0090446780433952739, upper=0.12904467804339537)"
153 |       ]
154 |      },
155 |      "execution_count": 31,
156 |      "metadata": {},
157 |      "output_type": "execute_result"
158 |     }
159 |    ],
160 |    "source": [
161 |     "ci_delta = CI(mle - z_alpha * se_delta, mle + z_alpha * se_delta)\n",
162 |     "ci_delta"
163 |    ]
164 |   },
165 |   {
166 |    "cell_type": "markdown",
167 |    "metadata": {},
168 |    "source": [
169 |     "## Parametric Bootstrap"
170 |    ]
171 |   },
172 |   {
173 |    "cell_type": "code",
174 |    "execution_count": 28,
175 |    "metadata": {},
176 |    "outputs": [
177 |     {
178 |      "data": {
179 |       "text/plain": [
180 |        "0.0017500987677499999"
181 |       ]
182 |      },
183 |      "execution_count": 28,
184 |      "metadata": {},
185 |      "output_type": "execute_result"
186 |     }
187 |    ],
188 |    "source": [
189 |     "dist1 = binom(n1, p1_hat)\n",
190 |     "dist2 = binom(n2, p2_hat)\n",
191 |     "\n",
192 |     "statistic = np.mean\n",
193 |     "\n",
194 |     "seed1 = 121111\n",
195 |     "seed2 = 951\n",
196 |     "\n",
197 |     "iters = 10000\n",
198 |     "\n",
199 |     "boots1 = parametric_bootstrap(dist1, 1, statistic, iters, random_state=seed1)\n",
200 |     "boots2 = parametric_bootstrap(dist2, 1, statistic, iters, random_state=seed2)\n",
201 |     "\n",
202 |     "boots = (xx1/n1 - xx2/n2 for xx1, xx2 in zip(boots1, boots2))\n",
203 |     "se_boot = np.var(list(boots))\n",
204 |     "se_boot"
205 |    ]
206 |   },
207 |   {
208 |    "cell_type": "code",
209 |    "execution_count": 32,
210 |    "metadata": {},
211 |    "outputs": [
212 |     {
213 |      "data": {
214 |       "text/plain": [
215 |        "CI(lower=0.057121343694343164, upper=0.062878656305656949)"
216 |       ]
217 |      },
218 |      "execution_count": 32,
219 |      "metadata": {},
220 |      "output_type": "execute_result"
221 |     }
222 |    ],
223 |    "source": [
224 |     "ci_boot = CI(psi_hat - z_alpha * se_boot, psi_hat + z_alpha * se_boot)\n",
225 |     "ci_boot"
226 |    ]
227 |   },
228 |   {
229 |    "cell_type": "code",
230 |    "execution_count": null,
231 |    "metadata": {
232 |     "collapsed": true
233 |    },
234 |    "outputs": [],
235 |    "source": []
236 |   }
237 |  ],
238 |  "metadata": {
239 |   "kernelspec": {
240 |    "display_name": "Python 3",
241 |    "language": "python",
242 |    "name": "python3"
243 |   },
244 |   "language_info": {
245 |    "codemirror_mode": {
246 |     "name": "ipython",
247 |     "version": 3
248 |    },
249 |    "file_extension": ".py",
250 |    "mimetype": "text/x-python",
251 |    "name": "python",
252 |    "nbconvert_exporter": "python",
253 |    "pygments_lexer": "ipython3",
254 |    "version": "3.5.2"
255 |   }
256 |  },
257 |  "nbformat": 4,
258 |  "nbformat_minor": 2
259 | }
260 | 


--------------------------------------------------------------------------------
/solutions/ch07q08.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {},
  7 |    "outputs": [
  8 |     {
  9 |      "name": "stdout",
 10 |      "output_type": "stream",
 11 |      "text": [
 12 |       "/Users/Steve/aos\n"
 13 |      ]
 14 |     }
 15 |    ],
 16 |    "source": [
 17 |     "cd ../.."
 18 |    ]
 19 |   },
 20 |   {
 21 |    "cell_type": "code",
 22 |    "execution_count": 1,
 23 |    "metadata": {
 24 |     "collapsed": true
 25 |    },
 26 |    "outputs": [
 27 |     {
 28 |      "name": "stderr",
 29 |      "output_type": "stream",
 30 |      "text": [
 31 |       "/home/brian/.virtualenvs/this/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
 32 |       "  return f(*args, **kwds)\n"
 33 |      ]
 34 |     }
 35 |    ],
 36 |    "source": [
 37 |     "import pandas as pd"
 38 |    ]
 39 |   },
 40 |   {
 41 |    "cell_type": "code",
 42 |    "execution_count": 3,
 43 |    "metadata": {
 44 |     "collapsed": true
 45 |    },
 46 |    "outputs": [],
 47 |    "source": [
 48 |     "geysers = pd.read_csv('../data/geysers.csv')"
 49 |    ]
 50 |   },
 51 |   {
 52 |    "cell_type": "code",
 53 |    "execution_count": 4,
 54 |    "metadata": {},
 55 |    "outputs": [
 56 |     {
 57 |      "data": {
 58 |       "text/plain": [
 59 |        "(272, 3)"
 60 |       ]
 61 |      },
 62 |      "execution_count": 4,
 63 |      "metadata": {},
 64 |      "output_type": "execute_result"
 65 |     }
 66 |    ],
 67 |    "source": [
 68 |     "geysers.shape"
 69 |    ]
 70 |   },
 71 |   {
 72 |    "cell_type": "code",
 73 |    "execution_count": 5,
 74 |    "metadata": {
 75 |     "collapsed": true
 76 |    },
 77 |    "outputs": [],
 78 |    "source": [
 79 |     "import numpy as np"
 80 |    ]
 81 |   },
 82 |   {
 83 |    "cell_type": "code",
 84 |    "execution_count": 6,
 85 |    "metadata": {},
 86 |    "outputs": [
 87 |     {
 88 |      "data": {
 89 |       "text/plain": [
 90 |        "70.8970588235294"
 91 |       ]
 92 |      },
 93 |      "execution_count": 6,
 94 |      "metadata": {},
 95 |      "output_type": "execute_result"
 96 |     }
 97 |    ],
 98 |    "source": [
 99 |     "np.mean(geysers['waiting'])"
100 |    ]
101 |   },
102 |   {
103 |    "cell_type": "code",
104 |    "execution_count": 7,
105 |    "metadata": {},
106 |    "outputs": [
107 |     {
108 |      "data": {
109 |       "text/plain": [
110 |        "13.569960017586371"
111 |       ]
112 |      },
113 |      "execution_count": 7,
114 |      "metadata": {},
115 |      "output_type": "execute_result"
116 |     }
117 |    ],
118 |    "source": [
119 |     "np.std(geysers['waiting'])"
120 |    ]
121 |   },
122 |   {
123 |    "cell_type": "code",
124 |    "execution_count": 8,
125 |    "metadata": {},
126 |    "outputs": [
127 |     {
128 |      "data": {
129 |       "text/plain": [
130 |        "76.0"
131 |       ]
132 |      },
133 |      "execution_count": 8,
134 |      "metadata": {},
135 |      "output_type": "execute_result"
136 |     }
137 |    ],
138 |    "source": [
139 |     "np.median(geysers['waiting'])"
140 |    ]
141 |   },
142 |   {
143 |    "cell_type": "markdown",
144 |    "metadata": {},
145 |    "source": [
146 |     "## Doing it manually"
147 |    ]
148 |   },
149 |   {
150 |    "cell_type": "markdown",
151 |    "metadata": {},
152 |    "source": [
153 |     "Plug-in estimators:\n",
154 |     "\n",
155 |     "Mean:\n",
156 |     "$\\hat{\\mu} = \\frac{1}{n} \\sum_{i=1}^{n} X_i$\n",
157 |     "\n",
158 |     "Variance:\n",
159 |     "$\\hat{\\sigma}^2 = \\frac{1}{n} \\sum_{i=1}^{n} (X_i - \\hat{\\mu})^2$\n",
160 |     "\n",
161 |     "Standard error:\n",
162 |     "$\\hat{\\sigma} = \\sqrt{\\hat{\\sigma}^2}$ "
163 |    ]
164 |   },
165 |   {
166 |    "cell_type": "code",
167 |    "execution_count": 9,
168 |    "metadata": {
169 |     "collapsed": true
170 |    },
171 |    "outputs": [],
172 |    "source": [
173 |     "x = geysers['waiting']"
174 |    ]
175 |   },
176 |   {
177 |    "cell_type": "code",
178 |    "execution_count": 10,
179 |    "metadata": {},
180 |    "outputs": [],
181 |    "source": [
182 |     "n = len(x)"
183 |    ]
184 |   },
185 |   {
186 |    "cell_type": "code",
187 |    "execution_count": 11,
188 |    "metadata": {
189 |     "collapsed": true
190 |    },
191 |    "outputs": [],
192 |    "source": [
193 |     "mean = np.sum(x) / n"
194 |    ]
195 |   },
196 |   {
197 |    "cell_type": "code",
198 |    "execution_count": 12,
199 |    "metadata": {
200 |     "collapsed": true
201 |    },
202 |    "outputs": [],
203 |    "source": [
204 |     "var = np.sum((x - mean)**2) / n"
205 |    ]
206 |   },
207 |   {
208 |    "cell_type": "code",
209 |    "execution_count": 13,
210 |    "metadata": {},
211 |    "outputs": [],
212 |    "source": [
213 |     "std = np.sqrt(var)"
214 |    ]
215 |   },
216 |   {
217 |    "cell_type": "code",
218 |    "execution_count": 17,
219 |    "metadata": {},
220 |    "outputs": [],
221 |    "source": [
222 |     "se = std / np.sqrt(n)"
223 |    ]
224 |   },
225 |   {
226 |    "cell_type": "code",
227 |    "execution_count": 18,
228 |    "metadata": {},
229 |    "outputs": [
230 |     {
231 |      "data": {
232 |       "text/plain": [
233 |        "(70.8970588235294, 0.8227996836458397)"
234 |       ]
235 |      },
236 |      "execution_count": 18,
237 |      "metadata": {},
238 |      "output_type": "execute_result"
239 |     }
240 |    ],
241 |    "source": [
242 |     "mean, se"
243 |    ]
244 |   },
245 |   {
246 |    "cell_type": "code",
247 |    "execution_count": 21,
248 |    "metadata": {
249 |     "collapsed": true
250 |    },
251 |    "outputs": [],
252 |    "source": [
253 |     "# confidence intervals\n",
254 |     "z = 1.64 # critical value for \\alpha = .1\n",
255 |     "U = mean + z*se\n",
256 |     "L = mean - z*se"
257 |    ]
258 |   },
259 |   {
260 |    "cell_type": "code",
261 |    "execution_count": 23,
262 |    "metadata": {},
263 |    "outputs": [
264 |     {
265 |      "data": {
266 |       "text/plain": [
267 |        "(93.15179325237105, 48.642324394687762)"
268 |       ]
269 |      },
270 |      "execution_count": 23,
271 |      "metadata": {},
272 |      "output_type": "execute_result"
273 |     }
274 |    ],
275 |    "source": [
276 |     "U, L"
277 |    ]
278 |   }
279 |  ],
280 |  "metadata": {
281 |   "kernelspec": {
282 |    "display_name": "Python 3",
283 |    "language": "python",
284 |    "name": "python3"
285 |   },
286 |   "language_info": {
287 |    "codemirror_mode": {
288 |     "name": "ipython",
289 |     "version": 3
290 |    },
291 |    "file_extension": ".py",
292 |    "mimetype": "text/x-python",
293 |    "name": "python",
294 |    "nbconvert_exporter": "python",
295 |    "pygments_lexer": "ipython3",
296 |    "version": "3.5.2"
297 |   }
298 |  },
299 |  "nbformat": 4,
300 |  "nbformat_minor": 2
301 | }
302 | 


--------------------------------------------------------------------------------
/solutions/ch08q01.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 69,
  6 |    "metadata": {},
  7 |    "outputs": [
  8 |     {
  9 |      "name": "stdout",
 10 |      "output_type": "stream",
 11 |      "text": [
 12 |       "The autoreload extension is already loaded. To reload it, use:\n",
 13 |       "  %reload_ext autoreload\n"
 14 |      ]
 15 |     }
 16 |    ],
 17 |    "source": [
 18 |     "import sys\n",
 19 |     "sys.path.append('..')\n",
 20 |     "\n",
 21 |     "import pandas as pd\n",
 22 |     "import numpy as np\n",
 23 |     "import seaborn as sns\n",
 24 |     "import re\n",
 25 |     "import matplotlib as mpl\n",
 26 |     "import matplotlib.pyplot as plt\n",
 27 |     "%matplotlib inline\n",
 28 |     "%load_ext autoreload\n",
 29 |     "%autoreload 2\n",
 30 |     "\n",
 31 |     "from chapters.chapter8 import *"
 32 |    ]
 33 |   },
 34 |   {
 35 |    "cell_type": "code",
 36 |    "execution_count": 77,
 37 |    "metadata": {
 38 |     "collapsed": true
 39 |    },
 40 |    "outputs": [],
 41 |    "source": [
 42 |     "# numpy assumes columns are observations, so we have to transpose our data\n",
 43 |     "corr = lambda df: np.corrcoef(df.T)"
 44 |    ]
 45 |   },
 46 |   {
 47 |    "cell_type": "code",
 48 |    "execution_count": 70,
 49 |    "metadata": {},
 50 |    "outputs": [
 51 |     {
 52 |      "data": {
 53 |       "text/html": [
 54 |        "<div>\n",
 55 |        "<table border=\"1\" class=\"dataframe\">\n",
 56 |        "  <thead>\n",
 57 |        "    <tr style=\"text-align: right;\">\n",
 58 |        "      <th></th>\n",
 59 |        "      <th>lsat</th>\n",
 60 |        "      <th>gpa</th>\n",
 61 |        "    </tr>\n",
 62 |        "  </thead>\n",
 63 |        "  <tbody>\n",
 64 |        "    <tr>\n",
 65 |        "      <th>0</th>\n",
 66 |        "      <td>576</td>\n",
 67 |        "      <td>3.39</td>\n",
 68 |        "    </tr>\n",
 69 |        "    <tr>\n",
 70 |        "      <th>1</th>\n",
 71 |        "      <td>635</td>\n",
 72 |        "      <td>3.30</td>\n",
 73 |        "    </tr>\n",
 74 |        "    <tr>\n",
 75 |        "      <th>2</th>\n",
 76 |        "      <td>558</td>\n",
 77 |        "      <td>2.81</td>\n",
 78 |        "    </tr>\n",
 79 |        "    <tr>\n",
 80 |        "      <th>3</th>\n",
 81 |        "      <td>578</td>\n",
 82 |        "      <td>3.03</td>\n",
 83 |        "    </tr>\n",
 84 |        "    <tr>\n",
 85 |        "      <th>4</th>\n",
 86 |        "      <td>666</td>\n",
 87 |        "      <td>3.44</td>\n",
 88 |        "    </tr>\n",
 89 |        "  </tbody>\n",
 90 |        "</table>\n",
 91 |        "</div>"
 92 |       ],
 93 |       "text/plain": [
 94 |        "   lsat   gpa\n",
 95 |        "0   576  3.39\n",
 96 |        "1   635  3.30\n",
 97 |        "2   558  2.81\n",
 98 |        "3   578  3.03\n",
 99 |        "4   666  3.44"
100 |       ]
101 |      },
102 |      "execution_count": 70,
103 |      "metadata": {},
104 |      "output_type": "execute_result"
105 |     }
106 |    ],
107 |    "source": [
108 |     "df = pd.read_csv('../data/lsat_efron.csv')\n",
109 |     "df.head()"
110 |    ]
111 |   },
112 |   {
113 |    "cell_type": "code",
114 |    "execution_count": 75,
115 |    "metadata": {},
116 |    "outputs": [
117 |     {
118 |      "data": {
119 |       "text/plain": [
120 |        "array([[ 1.        ,  0.54591892],\n",
121 |        "       [ 0.54591892,  1.        ]])"
122 |       ]
123 |      },
124 |      "execution_count": 75,
125 |      "metadata": {},
126 |      "output_type": "execute_result"
127 |     }
128 |    ],
129 |    "source": [
130 |     "c = corr(df)\n",
131 |     "c"
132 |    ]
133 |   },
134 |   {
135 |    "cell_type": "code",
136 |    "execution_count": 76,
137 |    "metadata": {},
138 |    "outputs": [
139 |     {
140 |      "data": {
141 |       "text/plain": [
142 |        "array([[  9.41793757e-17,   1.96841299e-01],\n",
143 |        "       [  1.96841299e-01,   8.26799418e-17]])"
144 |       ]
145 |      },
146 |      "execution_count": 76,
147 |      "metadata": {},
148 |      "output_type": "execute_result"
149 |     }
150 |    ],
151 |    "source": [
152 |     "se = np.sqrt(bootstrap_variance(df, corr, 10000))\n",
153 |     "se"
154 |    ]
155 |   },
156 |   {
157 |    "cell_type": "code",
158 |    "execution_count": 72,
159 |    "metadata": {},
160 |    "outputs": [
161 |     {
162 |      "data": {
163 |       "text/plain": [
164 |        "CI(lower=array([[ 1.        ,  0.16371497],\n",
165 |        "       [ 0.16371497,  1.        ]]), upper=array([[ 1.        ,  0.92812286],\n",
166 |        "       [ 0.92812286,  1.        ]]))"
167 |       ]
168 |      },
169 |      "execution_count": 72,
170 |      "metadata": {},
171 |      "output_type": "execute_result"
172 |     }
173 |    ],
174 |    "source": [
175 |     "bootstrap_ci_normal(df, corr, 10000, 0.05)"
176 |    ]
177 |   },
178 |   {
179 |    "cell_type": "code",
180 |    "execution_count": 74,
181 |    "metadata": {},
182 |    "outputs": [
183 |     {
184 |      "data": {
185 |       "text/plain": [
186 |        "CI(lower=array([[ 1.        ,  0.09183783],\n",
187 |        "       [ 0.09183783,  1.        ]]), upper=array([[ 1.72633836,  0.8181762 ],\n",
188 |        "       [ 0.8181762 ,  1.72633836]]))"
189 |       ]
190 |      },
191 |      "execution_count": 74,
192 |      "metadata": {},
193 |      "output_type": "execute_result"
194 |     }
195 |    ],
196 |    "source": [
197 |     "bootstrap_ci_pivot(df, corr, 10000, 0.05)"
198 |    ]
199 |   },
200 |   {
201 |    "cell_type": "code",
202 |    "execution_count": 73,
203 |    "metadata": {},
204 |    "outputs": [
205 |     {
206 |      "data": {
207 |       "text/plain": [
208 |        "CI(lower=array([[ 1.        ,  0.20647611],\n",
209 |        "       [ 0.20647611,  1.        ]]), upper=array([[ 1.        ,  0.93652281],\n",
210 |        "       [ 0.93652281,  1.        ]]))"
211 |       ]
212 |      },
213 |      "execution_count": 73,
214 |      "metadata": {},
215 |      "output_type": "execute_result"
216 |     }
217 |    ],
218 |    "source": [
219 |     "bootstrap_ci_percentile(df, corr, 10000, 0.05)"
220 |    ]
221 |   },
222 |   {
223 |    "cell_type": "code",
224 |    "execution_count": null,
225 |    "metadata": {
226 |     "collapsed": true
227 |    },
228 |    "outputs": [],
229 |    "source": []
230 |   }
231 |  ],
232 |  "metadata": {
233 |   "kernelspec": {
234 |    "display_name": "Python 3",
235 |    "language": "python",
236 |    "name": "python3"
237 |   },
238 |   "language_info": {
239 |    "codemirror_mode": {
240 |     "name": "ipython",
241 |     "version": 3
242 |    },
243 |    "file_extension": ".py",
244 |    "mimetype": "text/x-python",
245 |    "name": "python",
246 |    "nbconvert_exporter": "python",
247 |    "pygments_lexer": "ipython3",
248 |    "version": "3.5.2"
249 |   }
250 |  },
251 |  "nbformat": 4,
252 |  "nbformat_minor": 2
253 | }
254 | 


--------------------------------------------------------------------------------
/data/nerve.csv:
--------------------------------------------------------------------------------
  1 | duration
  2 | 0.21
  3 | 0.03
  4 | 0.05
  5 | 0.11
  6 | 0.59
  7 | 0.06
  8 | 0.18
  9 | 0.55
 10 | 0.37
 11 | 0.09
 12 | 0.14
 13 | 0.19
 14 | 0.02
 15 | 0.14
 16 | 0.09
 17 | 0.05
 18 | 0.15
 19 | 0.23
 20 | 0.15
 21 | 0.08
 22 | 0.24
 23 | 0.16
 24 | 0.06
 25 | 0.11
 26 | 0.15
 27 | 0.09
 28 | 0.03
 29 | 0.21
 30 | 0.02
 31 | 0.14
 32 | 0.24
 33 | 0.29
 34 | 0.16
 35 | 0.07
 36 | 0.07
 37 | 0.04
 38 | 0.02
 39 | 0.15
 40 | 0.12
 41 | 0.26
 42 | 0.15
 43 | 0.33
 44 | 0.06
 45 | 0.51
 46 | 0.11
 47 | 0.28
 48 | 0.36
 49 | 0.14
 50 | 0.55
 51 | 0.28
 52 | 0.04
 53 | 0.01
 54 | 0.94
 55 | 0.73
 56 | 0.05
 57 | 0.07
 58 | 0.11
 59 | 0.38
 60 | 0.21
 61 | 0.49
 62 | 0.38
 63 | 0.38
 64 | 0.01
 65 | 0.06
 66 | 0.13
 67 | 0.06
 68 | 0.01
 69 | 0.16
 70 | 0.05
 71 | 0.10
 72 | 0.16
 73 | 0.06
 74 | 0.06
 75 | 0.06
 76 | 0.06
 77 | 0.11
 78 | 0.44
 79 | 0.05
 80 | 0.09
 81 | 0.04
 82 | 0.27
 83 | 0.50
 84 | 0.25
 85 | 0.25
 86 | 0.08
 87 | 0.01
 88 | 0.70
 89 | 0.04
 90 | 0.08
 91 | 0.16
 92 | 0.38
 93 | 0.08
 94 | 0.32
 95 | 0.39
 96 | 0.58
 97 | 0.56
 98 | 0.74
 99 | 0.15
100 | 0.07
101 | 0.26
102 | 0.25
103 | 0.01
104 | 0.17
105 | 0.64
106 | 0.61
107 | 0.15
108 | 0.26
109 | 0.03
110 | 0.05
111 | 0.34
112 | 0.07
113 | 0.10
114 | 0.09
115 | 0.02
116 | 0.30
117 | 0.07
118 | 0.12
119 | 0.01
120 | 0.16
121 | 0.14
122 | 0.49
123 | 0.07
124 | 0.11
125 | 0.35
126 | 1.21
127 | 0.17
128 | 0.01
129 | 0.35
130 | 0.45
131 | 0.07
132 | 0.93
133 | 0.04
134 | 0.96
135 | 0.14
136 | 1.38
137 | 0.15
138 | 0.01
139 | 0.05
140 | 0.23
141 | 0.31
142 | 0.05
143 | 0.05
144 | 0.29
145 | 0.01
146 | 0.74
147 | 0.30
148 | 0.09
149 | 0.02
150 | 0.19
151 | 0.47
152 | 0.01
153 | 0.51
154 | 0.12
155 | 0.12
156 | 0.43
157 | 0.32
158 | 0.09
159 | 0.20
160 | 0.03
161 | 0.05
162 | 0.13
163 | 0.15
164 | 0.05
165 | 0.08
166 | 0.04
167 | 0.09
168 | 0.10
169 | 0.10
170 | 0.26
171 | 0.07
172 | 0.68
173 | 0.15
174 | 0.01
175 | 0.27
176 | 0.05
177 | 0.03
178 | 0.40
179 | 0.04
180 | 0.21
181 | 0.29
182 | 0.24
183 | 0.08
184 | 0.23
185 | 0.10
186 | 0.19
187 | 0.20
188 | 0.26
189 | 0.06
190 | 0.40
191 | 0.51
192 | 0.15
193 | 1.10
194 | 0.16
195 | 0.78
196 | 0.04
197 | 0.27
198 | 0.35
199 | 0.71
200 | 0.15
201 | 0.29
202 | 0.04
203 | 0.01
204 | 0.28
205 | 0.21
206 | 0.09
207 | 0.17
208 | 0.09
209 | 0.17
210 | 0.15
211 | 0.62
212 | 0.50
213 | 0.07
214 | 0.39
215 | 0.28
216 | 0.20
217 | 0.34
218 | 0.16
219 | 0.65
220 | 0.04
221 | 0.67
222 | 0.10
223 | 0.51
224 | 0.26
225 | 0.07
226 | 0.71
227 | 0.11
228 | 0.47
229 | 0.02
230 | 0.38
231 | 0.04
232 | 0.43
233 | 0.11
234 | 0.23
235 | 0.14
236 | 0.08
237 | 1.12
238 | 0.50
239 | 0.25
240 | 0.18
241 | 0.12
242 | 0.02
243 | 0.15
244 | 0.12
245 | 0.08
246 | 0.38
247 | 0.22
248 | 0.16
249 | 0.04
250 | 0.58
251 | 0.05
252 | 0.07
253 | 0.28
254 | 0.27
255 | 0.24
256 | 0.07
257 | 0.02
258 | 0.27
259 | 0.27
260 | 0.16
261 | 0.05
262 | 0.34
263 | 0.10
264 | 0.02
265 | 0.04
266 | 0.10
267 | 0.22
268 | 0.24
269 | 0.04
270 | 0.28
271 | 0.10
272 | 0.23
273 | 0.03
274 | 0.34
275 | 0.21
276 | 0.41
277 | 0.15
278 | 0.05
279 | 0.17
280 | 0.53
281 | 0.30
282 | 0.15
283 | 0.19
284 | 0.07
285 | 0.83
286 | 0.04
287 | 0.04
288 | 0.14
289 | 0.34
290 | 0.10
291 | 0.15
292 | 0.05
293 | 0.04
294 | 0.05
295 | 0.65
296 | 0.16
297 | 0.32
298 | 0.87
299 | 0.07
300 | 0.17
301 | 0.10
302 | 0.03
303 | 0.17
304 | 0.38
305 | 0.28
306 | 0.14
307 | 0.07
308 | 0.14
309 | 0.03
310 | 0.21
311 | 0.40
312 | 0.04
313 | 0.11
314 | 0.44
315 | 0.90
316 | 0.10
317 | 0.49
318 | 0.09
319 | 0.01
320 | 0.08
321 | 0.06
322 | 0.08
323 | 0.01
324 | 0.15
325 | 0.50
326 | 0.36
327 | 0.08
328 | 0.34
329 | 0.02
330 | 0.21
331 | 0.32
332 | 0.22
333 | 0.51
334 | 0.12
335 | 0.16
336 | 0.52
337 | 0.21
338 | 0.05
339 | 0.46
340 | 0.44
341 | 0.04
342 | 0.05
343 | 0.04
344 | 0.14
345 | 0.08
346 | 0.21
347 | 0.02
348 | 0.63
349 | 0.35
350 | 0.01
351 | 0.38
352 | 0.43
353 | 0.03
354 | 0.39
355 | 0.04
356 | 0.17
357 | 0.23
358 | 0.78
359 | 0.14
360 | 0.08
361 | 0.11
362 | 0.07
363 | 0.45
364 | 0.46
365 | 0.20
366 | 0.19
367 | 0.50
368 | 0.09
369 | 0.22
370 | 0.29
371 | 0.01
372 | 0.19
373 | 0.06
374 | 0.39
375 | 0.08
376 | 0.03
377 | 0.28
378 | 0.09
379 | 0.17
380 | 0.45
381 | 0.40
382 | 0.07
383 | 0.30
384 | 0.16
385 | 0.24
386 | 0.81
387 | 1.35
388 | 0.01
389 | 0.02
390 | 0.03
391 | 0.06
392 | 0.12
393 | 0.31
394 | 0.64
395 | 0.08
396 | 0.15
397 | 0.06
398 | 0.06
399 | 0.15
400 | 0.68
401 | 0.30
402 | 0.02
403 | 0.04
404 | 0.02
405 | 0.81
406 | 0.09
407 | 0.19
408 | 0.14
409 | 0.12
410 | 0.36
411 | 0.02
412 | 0.11
413 | 0.04
414 | 0.08
415 | 0.17
416 | 0.04
417 | 0.05
418 | 0.14
419 | 0.07
420 | 0.39
421 | 0.13
422 | 0.56
423 | 0.12
424 | 0.31
425 | 0.05
426 | 0.10
427 | 0.13
428 | 0.05
429 | 0.01
430 | 0.09
431 | 0.03
432 | 0.27
433 | 0.17
434 | 0.03
435 | 0.05
436 | 0.26
437 | 0.23
438 | 0.20
439 | 0.76
440 | 0.05
441 | 0.02
442 | 0.01
443 | 0.20
444 | 0.21
445 | 0.02
446 | 0.04
447 | 0.16
448 | 0.32
449 | 0.43
450 | 0.20
451 | 0.13
452 | 0.10
453 | 0.20
454 | 0.08
455 | 0.81
456 | 0.11
457 | 0.09
458 | 0.26
459 | 0.15
460 | 0.36
461 | 0.18
462 | 0.10
463 | 0.34
464 | 0.56
465 | 0.09
466 | 0.15
467 | 0.14
468 | 0.15
469 | 0.22
470 | 0.33
471 | 0.04
472 | 0.07
473 | 0.09
474 | 0.18
475 | 0.08
476 | 0.07
477 | 0.07
478 | 0.68
479 | 0.27
480 | 0.21
481 | 0.11
482 | 0.07
483 | 0.44
484 | 0.13
485 | 0.04
486 | 0.39
487 | 0.14
488 | 0.10
489 | 0.08
490 | 0.02
491 | 0.57
492 | 0.35
493 | 0.17
494 | 0.21
495 | 0.14
496 | 0.77
497 | 0.06
498 | 0.34
499 | 0.15
500 | 0.29
501 | 0.08
502 | 0.72
503 | 0.31
504 | 0.20
505 | 0.10
506 | 0.01
507 | 0.24
508 | 0.07
509 | 0.22
510 | 0.49
511 | 0.03
512 | 0.18
513 | 0.47
514 | 0.37
515 | 0.17
516 | 0.42
517 | 0.02
518 | 0.22
519 | 0.12
520 | 0.01
521 | 0.34
522 | 0.41
523 | 0.27
524 | 0.07
525 | 0.30
526 | 0.09
527 | 0.27
528 | 0.28
529 | 0.15
530 | 0.26
531 | 0.01
532 | 0.06
533 | 0.35
534 | 0.03
535 | 0.26
536 | 0.05
537 | 0.18
538 | 0.46
539 | 0.12
540 | 0.23
541 | 0.32
542 | 0.08
543 | 0.26
544 | 0.82
545 | 0.10
546 | 0.69
547 | 0.15
548 | 0.01
549 | 0.39
550 | 0.04
551 | 0.13
552 | 0.34
553 | 0.13
554 | 0.13
555 | 0.30
556 | 0.29
557 | 0.23
558 | 0.01
559 | 0.38
560 | 0.04
561 | 0.08
562 | 0.15
563 | 0.10
564 | 0.62
565 | 0.83
566 | 0.11
567 | 0.71
568 | 0.08
569 | 0.61
570 | 0.18
571 | 0.05
572 | 0.20
573 | 0.12
574 | 0.10
575 | 0.03
576 | 0.11
577 | 0.20
578 | 0.16
579 | 0.10
580 | 0.03
581 | 0.23
582 | 0.12
583 | 0.01
584 | 0.12
585 | 0.17
586 | 0.14
587 | 0.10
588 | 0.02
589 | 0.13
590 | 0.06
591 | 0.21
592 | 0.50
593 | 0.04
594 | 0.42
595 | 0.29
596 | 0.08
597 | 0.01
598 | 0.30
599 | 0.45
600 | 0.06
601 | 0.25
602 | 0.02
603 | 0.06
604 | 0.02
605 | 0.17
606 | 0.10
607 | 0.28
608 | 0.21
609 | 0.28
610 | 0.30
611 | 0.02
612 | 0.02
613 | 0.28
614 | 0.09
615 | 0.71
616 | 0.06
617 | 0.12
618 | 0.29
619 | 0.05
620 | 0.27
621 | 0.25
622 | 0.10
623 | 0.16
624 | 0.08
625 | 0.52
626 | 0.44
627 | 0.19
628 | 0.72
629 | 0.12
630 | 0.30
631 | 0.14
632 | 0.45
633 | 0.42
634 | 0.09
635 | 0.07
636 | 0.62
637 | 0.51
638 | 0.50
639 | 0.47
640 | 0.28
641 | 0.04
642 | 0.66
643 | 0.08
644 | 0.11
645 | 0.03
646 | 0.32
647 | 0.16
648 | 0.11
649 | 0.26
650 | 0.05
651 | 0.07
652 | 0.04
653 | 0.22
654 | 0.08
655 | 0.08
656 | 0.01
657 | 0.06
658 | 0.05
659 | 0.05
660 | 0.16
661 | 0.05
662 | 0.13
663 | 0.42
664 | 0.21
665 | 0.36
666 | 0.05
667 | 0.01
668 | 0.44
669 | 0.14
670 | 0.14
671 | 0.14
672 | 0.08
673 | 0.51
674 | 0.18
675 | 0.02
676 | 0.51
677 | 0.06
678 | 0.22
679 | 0.01
680 | 0.09
681 | 0.22
682 | 0.59
683 | 0.03
684 | 0.71
685 | 0.14
686 | 0.02
687 | 0.51
688 | 0.03
689 | 0.41
690 | 0.17
691 | 0.37
692 | 0.39
693 | 0.82
694 | 0.81
695 | 0.24
696 | 0.52
697 | 0.40
698 | 0.24
699 | 0.06
700 | 0.73
701 | 0.27
702 | 0.18
703 | 0.01
704 | 0.17
705 | 0.02
706 | 0.11
707 | 0.26
708 | 0.13
709 | 0.68
710 | 0.13
711 | 0.08
712 | 0.71
713 | 0.04
714 | 0.11
715 | 0.13
716 | 0.17
717 | 0.34
718 | 0.23
719 | 0.08
720 | 0.26
721 | 0.03
722 | 0.21
723 | 0.45
724 | 0.40
725 | 0.03
726 | 0.16
727 | 0.06
728 | 0.29
729 | 0.43
730 | 0.03
731 | 0.10
732 | 0.10
733 | 0.31
734 | 0.27
735 | 0.27
736 | 0.33
737 | 0.14
738 | 0.09
739 | 0.27
740 | 0.14
741 | 0.09
742 | 0.08
743 | 0.06
744 | 0.16
745 | 0.02
746 | 0.07
747 | 0.19
748 | 0.11
749 | 0.10
750 | 0.17
751 | 0.24
752 | 0.01
753 | 0.13
754 | 0.21
755 | 0.03
756 | 0.39
757 | 0.01
758 | 0.27
759 | 0.19
760 | 0.02
761 | 0.21
762 | 0.04
763 | 0.10
764 | 0.06
765 | 0.48
766 | 0.12
767 | 0.15
768 | 0.12
769 | 0.52
770 | 0.48
771 | 0.29
772 | 0.57
773 | 0.22
774 | 0.01
775 | 0.44
776 | 0.05
777 | 0.49
778 | 0.10
779 | 0.19
780 | 0.44
781 | 0.02
782 | 0.72
783 | 0.09
784 | 0.04
785 | 0.02
786 | 0.02
787 | 0.06
788 | 0.22
789 | 0.53
790 | 0.18
791 | 0.10
792 | 0.10
793 | 0.03
794 | 0.08
795 | 0.15
796 | 0.05
797 | 0.13
798 | 0.02
799 | 0.10
800 | 0.51
801 | 


--------------------------------------------------------------------------------
/solutions/ch08q03.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 2,
  6 |    "metadata": {},
  7 |    "outputs": [
  8 |     {
  9 |      "name": "stdout",
 10 |      "output_type": "stream",
 11 |      "text": [
 12 |       "The autoreload extension is already loaded. To reload it, use:\n",
 13 |       "  %reload_ext autoreload\n"
 14 |      ]
 15 |     }
 16 |    ],
 17 |    "source": [
 18 |     "import sys\n",
 19 |     "sys.path.append('..')\n",
 20 |     "\n",
 21 |     "import pandas as pd\n",
 22 |     "import numpy as np\n",
 23 |     "import seaborn as sns\n",
 24 |     "import re\n",
 25 |     "import matplotlib as mpl\n",
 26 |     "import matplotlib.pyplot as plt\n",
 27 |     "%matplotlib inline\n",
 28 |     "%load_ext autoreload\n",
 29 |     "%autoreload 2\n",
 30 |     "from scipy.stats import t\n",
 31 |     "\n",
 32 |     "from chapters.chapter8 import *"
 33 |    ]
 34 |   },
 35 |   {
 36 |    "cell_type": "code",
 37 |    "execution_count": 8,
 38 |    "metadata": {},
 39 |    "outputs": [
 40 |     {
 41 |      "data": {
 42 |       "text/plain": [
 43 |        "1.1416303404192403"
 44 |       ]
 45 |      },
 46 |      "execution_count": 8,
 47 |      "metadata": {},
 48 |      "output_type": "execute_result"
 49 |     }
 50 |    ],
 51 |    "source": [
 52 |     "theta = (t.ppf(0.75, 3) - t.ppf(0.25, 3)) / 1.34\n",
 53 |     "theta"
 54 |    ]
 55 |   },
 56 |   {
 57 |    "cell_type": "code",
 58 |    "execution_count": 4,
 59 |    "metadata": {},
 60 |    "outputs": [
 61 |     {
 62 |      "data": {
 63 |       "text/plain": [
 64 |        "array([ 0.97442783, -0.37559688,  4.67457867,  0.93902427, -0.28586191,\n",
 65 |        "        0.02619128, -0.37147975, -1.0917111 ,  1.48828415,  0.5258335 ,\n",
 66 |        "       -0.40666186, -0.78900618,  0.02991144, -0.81607991, -0.38627618,\n",
 67 |        "       -1.19756689,  0.73345944,  0.51085135, -4.08510571, -1.05274502,\n",
 68 |        "       -0.2053558 ,  3.8510504 ,  2.1216446 , -0.26205937,  1.17686852])"
 69 |       ]
 70 |      },
 71 |      "execution_count": 4,
 72 |      "metadata": {},
 73 |      "output_type": "execute_result"
 74 |     }
 75 |    ],
 76 |    "source": [
 77 |     "obs = t.rvs(3, size=25)\n",
 78 |     "obs"
 79 |    ]
 80 |   },
 81 |   {
 82 |    "cell_type": "code",
 83 |    "execution_count": 5,
 84 |    "metadata": {},
 85 |    "outputs": [
 86 |     {
 87 |      "data": {
 88 |       "text/plain": [
 89 |        "1.0042433830474906"
 90 |       ]
 91 |      },
 92 |      "execution_count": 5,
 93 |      "metadata": {},
 94 |      "output_type": "execute_result"
 95 |     }
 96 |    ],
 97 |    "source": [
 98 |     "statistic = lambda obs: (np.percentile(obs, 75) - np.percentile(obs, 25)) / 1.34\n",
 99 |     "statistic(obs)"
100 |    ]
101 |   },
102 |   {
103 |    "cell_type": "code",
104 |    "execution_count": 11,
105 |    "metadata": {},
106 |    "outputs": [
107 |     {
108 |      "name": "stdout",
109 |      "output_type": "stream",
110 |      "text": [
111 |       "CI(lower=0.5156639919152145, upper=1.7167599516444088) CI(lower=0.50928145601241681, upper=1.6958873701224797) CI(lower=0.60911819752546137, upper=1.7146732401098512)\n",
112 |       "CI(lower=0.45410857167372232, upper=1.6607720152176646) CI(lower=0.57279572848059956, upper=1.4535995749343953) CI(lower=0.54014743080611638, upper=1.7647738255667409)\n",
113 |       "CI(lower=0.60385196439111488, upper=2.0267615846572715) CI(lower=0.44406337611351798, upper=1.8036941670598468) CI(lower=0.82691938198853987, upper=1.8807297349587597)\n",
114 |       "CI(lower=0.31543281539107648, upper=1.4306422972329282) CI(lower=0.1446363178002632, upper=1.3344638907117967) CI(lower=0.43377991400451787, upper=1.7456737845072383)\n",
115 |       "CI(lower=-0.25938356924185846, upper=1.6910671291441635) CI(lower=-1.0234556540551818, upper=0.99568040971998006) CI(lower=0.42373786678618308, upper=2.4053288178856)\n",
116 |       "CI(lower=0.10557971324865545, upper=1.3203010453574411) CI(lower=-0.032268548076881842, upper=1.0878079996932903) CI(lower=0.22435652777561224, upper=1.2158881102202943)\n",
117 |       "CI(lower=0.47411736314091735, upper=1.826586770390362) CI(lower=0.33436244724671127, upper=1.7140877732572941) CI(lower=0.58245133819019856, upper=1.9663416862845682)\n",
118 |       "CI(lower=0.1836046052137208, upper=1.4113921561374028) CI(lower=0.28458763548838117, upper=1.312634799769854) CI(lower=0.28457029357400565, upper=1.515986612833125)\n",
119 |       "CI(lower=0.16132369600150859, upper=0.86191509422873924) CI(lower=0.040998096999688594, upper=0.72749954271236239) CI(lower=0.23448210361764971, upper=0.99972066471347398)\n",
120 |       "CI(lower=0.31210619888957303, upper=1.4773828596406258) CI(lower=0.13890777617025574, upper=1.3084174464066127) CI(lower=0.47375910748953726, upper=1.5802200336176546)\n"
121 |      ]
122 |     },
123 |     {
124 |      "data": {
125 |       "text/html": [
126 |        "<div>\n",
127 |        "<table border=\"1\" class=\"dataframe\">\n",
128 |        "  <thead>\n",
129 |        "    <tr style=\"text-align: right;\">\n",
130 |        "      <th></th>\n",
131 |        "      <th>lower</th>\n",
132 |        "      <th>type</th>\n",
133 |        "      <th>upper</th>\n",
134 |        "    </tr>\n",
135 |        "  </thead>\n",
136 |        "  <tbody>\n",
137 |        "    <tr>\n",
138 |        "      <th>0</th>\n",
139 |        "      <td>0.515664</td>\n",
140 |        "      <td>normal</td>\n",
141 |        "      <td>1.716760</td>\n",
142 |        "    </tr>\n",
143 |        "    <tr>\n",
144 |        "      <th>1</th>\n",
145 |        "      <td>0.509281</td>\n",
146 |        "      <td>pivot</td>\n",
147 |        "      <td>1.695887</td>\n",
148 |        "    </tr>\n",
149 |        "    <tr>\n",
150 |        "      <th>2</th>\n",
151 |        "      <td>0.609118</td>\n",
152 |        "      <td>percentile</td>\n",
153 |        "      <td>1.714673</td>\n",
154 |        "    </tr>\n",
155 |        "    <tr>\n",
156 |        "      <th>3</th>\n",
157 |        "      <td>0.783856</td>\n",
158 |        "      <td>normal</td>\n",
159 |        "      <td>1.865298</td>\n",
160 |        "    </tr>\n",
161 |        "    <tr>\n",
162 |        "      <th>4</th>\n",
163 |        "      <td>0.613448</td>\n",
164 |        "      <td>pivot</td>\n",
165 |        "      <td>1.934928</td>\n",
166 |        "    </tr>\n",
167 |        "  </tbody>\n",
168 |        "</table>\n",
169 |        "</div>"
170 |       ],
171 |       "text/plain": [
172 |        "      lower        type     upper\n",
173 |        "0  0.515664      normal  1.716760\n",
174 |        "1  0.509281       pivot  1.695887\n",
175 |        "2  0.609118  percentile  1.714673\n",
176 |        "3  0.783856      normal  1.865298\n",
177 |        "4  0.613448       pivot  1.934928"
178 |       ]
179 |      },
180 |      "execution_count": 11,
181 |      "metadata": {},
182 |      "output_type": "execute_result"
183 |     }
184 |    ],
185 |    "source": [
186 |     "data = {'lower': [], 'upper': [], 'type': []}\n",
187 |     "\n",
188 |     "for i in range(1000):\n",
189 |     "    \n",
190 |     "    obs = pd.Series(t.rvs(3, size=25))\n",
191 |     "    \n",
192 |     "    nci = bootstrap_ci_normal(obs, statistic, 100, 0.05)    \n",
193 |     "    pivci = bootstrap_ci_pivot(obs, statistic, 100, 0.05)    \n",
194 |     "    perci = bootstrap_ci_percentile(obs, statistic, 100, 0.05)\n",
195 |     "    \n",
196 |     "    if i % 100 == 0:\n",
197 |     "        print(nci, pivci, perci)\n",
198 |     "    \n",
199 |     "    data.get('lower').append(nci.lower)    \n",
200 |     "    data.get('upper').append(nci.upper)\n",
201 |     "    data.get('type').append('normal')\n",
202 |     "    \n",
203 |     "    data.get('lower').append(pivci.lower)    \n",
204 |     "    data.get('upper').append(pivci.upper)\n",
205 |     "    data.get('type').append('pivot')\n",
206 |     "    \n",
207 |     "    data.get('lower').append(perci.lower)    \n",
208 |     "    data.get('upper').append(perci.upper)\n",
209 |     "    data.get('type').append('percentile')\n",
210 |     "    \n",
211 |     "df = pd.DataFrame(data)\n",
212 |     "df['contains_true'] = df.apply(lambda r: r.lower <= theta <= r.upper, axis=1)\n",
213 |     "\n",
214 |     "#df.to_csv('../data/ch08q03.csv', index=False)\n",
215 |     "\n",
216 |     "df.head()"
217 |    ]
218 |   },
219 |   {
220 |    "cell_type": "code",
221 |    "execution_count": 19,
222 |    "metadata": {},
223 |    "outputs": [
224 |     {
225 |      "data": {
226 |       "text/plain": [
227 |        "type\n",
228 |        "normal        0.947\n",
229 |        "percentile    0.957\n",
230 |        "pivot         0.814\n",
231 |        "Name: contains_true, dtype: float64"
232 |       ]
233 |      },
234 |      "execution_count": 19,
235 |      "metadata": {},
236 |      "output_type": "execute_result"
237 |     }
238 |    ],
239 |    "source": [
240 |     "df.groupby('type').contains_true.mean()"
241 |    ]
242 |   },
243 |   {
244 |    "cell_type": "code",
245 |    "execution_count": null,
246 |    "metadata": {
247 |     "collapsed": true
248 |    },
249 |    "outputs": [],
250 |    "source": []
251 |   }
252 |  ],
253 |  "metadata": {
254 |   "kernelspec": {
255 |    "display_name": "Python 3",
256 |    "language": "python",
257 |    "name": "python3"
258 |   },
259 |   "language_info": {
260 |    "codemirror_mode": {
261 |     "name": "ipython",
262 |     "version": 3
263 |    },
264 |    "file_extension": ".py",
265 |    "mimetype": "text/x-python",
266 |    "name": "python",
267 |    "nbconvert_exporter": "python",
268 |    "pygments_lexer": "ipython3",
269 |    "version": "3.5.2"
270 |   }
271 |  },
272 |  "nbformat": 4,
273 |  "nbformat_minor": 2
274 | }
275 | 


--------------------------------------------------------------------------------
/solutions/ch10q11.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "import sys\n",
 12 |     "sys.path.append('..')\n",
 13 |     "\n",
 14 |     "from scipy.stats import norm\n",
 15 |     "import pandas as pd\n",
 16 |     "import numpy as np\n",
 17 |     "import seaborn as sns\n",
 18 |     "import matplotlib.pyplot as plt\n",
 19 |     "\n",
 20 |     "from chapters.chapter10 import bonferroni, benjamini_hochberg\n",
 21 |     "\n",
 22 |     "%load_ext autoreload\n",
 23 |     "%autoreload 2\n",
 24 |     "\n",
 25 |     "%matplotlib inline\n",
 26 |     "plt.style.use('ggplot')"
 27 |    ]
 28 |   },
 29 |   {
 30 |    "cell_type": "code",
 31 |    "execution_count": 4,
 32 |    "metadata": {},
 33 |    "outputs": [
 34 |     {
 35 |      "data": {
 36 |       "text/html": [
 37 |        "<div>\n",
 38 |        "<table border=\"1\" class=\"dataframe\">\n",
 39 |        "  <thead>\n",
 40 |        "    <tr style=\"text-align: right;\">\n",
 41 |        "      <th></th>\n",
 42 |        "      <th>drug</th>\n",
 43 |        "      <th>total</th>\n",
 44 |        "      <th>nausea</th>\n",
 45 |        "      <th>p</th>\n",
 46 |        "    </tr>\n",
 47 |        "  </thead>\n",
 48 |        "  <tbody>\n",
 49 |        "    <tr>\n",
 50 |        "      <th>0</th>\n",
 51 |        "      <td>placebo</td>\n",
 52 |        "      <td>80</td>\n",
 53 |        "      <td>45</td>\n",
 54 |        "      <td>0.562500</td>\n",
 55 |        "    </tr>\n",
 56 |        "    <tr>\n",
 57 |        "      <th>1</th>\n",
 58 |        "      <td>chlorpromazine</td>\n",
 59 |        "      <td>75</td>\n",
 60 |        "      <td>26</td>\n",
 61 |        "      <td>0.346667</td>\n",
 62 |        "    </tr>\n",
 63 |        "    <tr>\n",
 64 |        "      <th>2</th>\n",
 65 |        "      <td>dimenhydrinate</td>\n",
 66 |        "      <td>85</td>\n",
 67 |        "      <td>52</td>\n",
 68 |        "      <td>0.611765</td>\n",
 69 |        "    </tr>\n",
 70 |        "    <tr>\n",
 71 |        "      <th>3</th>\n",
 72 |        "      <td>pentobarbital100</td>\n",
 73 |        "      <td>67</td>\n",
 74 |        "      <td>35</td>\n",
 75 |        "      <td>0.522388</td>\n",
 76 |        "    </tr>\n",
 77 |        "    <tr>\n",
 78 |        "      <th>4</th>\n",
 79 |        "      <td>pentobarbital150</td>\n",
 80 |        "      <td>85</td>\n",
 81 |        "      <td>37</td>\n",
 82 |        "      <td>0.435294</td>\n",
 83 |        "    </tr>\n",
 84 |        "  </tbody>\n",
 85 |        "</table>\n",
 86 |        "</div>"
 87 |       ],
 88 |       "text/plain": [
 89 |        "               drug  total  nausea         p\n",
 90 |        "0           placebo     80      45  0.562500\n",
 91 |        "1    chlorpromazine     75      26  0.346667\n",
 92 |        "2    dimenhydrinate     85      52  0.611765\n",
 93 |        "3  pentobarbital100     67      35  0.522388\n",
 94 |        "4  pentobarbital150     85      37  0.435294"
 95 |       ]
 96 |      },
 97 |      "execution_count": 4,
 98 |      "metadata": {},
 99 |      "output_type": "execute_result"
100 |     }
101 |    ],
102 |    "source": [
103 |     "df = pd.read_csv('../data/chap10q11.csv')\n",
104 |     "df['p'] = df.nausea / df.total\n",
105 |     "df.head()"
106 |    ]
107 |   },
108 |   {
109 |    "cell_type": "code",
110 |    "execution_count": 8,
111 |    "metadata": {},
112 |    "outputs": [
113 |     {
114 |      "data": {
115 |       "text/plain": [
116 |        "0.5625"
117 |       ]
118 |      },
119 |      "execution_count": 8,
120 |      "metadata": {},
121 |      "output_type": "execute_result"
122 |     }
123 |    ],
124 |    "source": [
125 |     "placebo = df[df.drug == 'placebo']\n",
126 |     "p_placebo = placebo.p.max()\n",
127 |     "p_placebo"
128 |    ]
129 |   },
130 |   {
131 |    "cell_type": "code",
132 |    "execution_count": 10,
133 |    "metadata": {},
134 |    "outputs": [
135 |     {
136 |      "data": {
137 |       "text/plain": [
138 |        "80"
139 |       ]
140 |      },
141 |      "execution_count": 10,
142 |      "metadata": {},
143 |      "output_type": "execute_result"
144 |     }
145 |    ],
146 |    "source": [
147 |     "n_placebo = placebo.total.max()\n",
148 |     "n_placebo"
149 |    ]
150 |   },
151 |   {
152 |    "cell_type": "code",
153 |    "execution_count": 23,
154 |    "metadata": {},
155 |    "outputs": [
156 |     {
157 |      "data": {
158 |       "text/html": [
159 |        "<div>\n",
160 |        "<table border=\"1\" class=\"dataframe\">\n",
161 |        "  <thead>\n",
162 |        "    <tr style=\"text-align: right;\">\n",
163 |        "      <th></th>\n",
164 |        "      <th>drug</th>\n",
165 |        "      <th>total</th>\n",
166 |        "      <th>nausea</th>\n",
167 |        "      <th>p</th>\n",
168 |        "      <th>diff</th>\n",
169 |        "      <th>se</th>\n",
170 |        "      <th>ci_lower</th>\n",
171 |        "      <th>ci_upper</th>\n",
172 |        "      <th>significant</th>\n",
173 |        "    </tr>\n",
174 |        "  </thead>\n",
175 |        "  <tbody>\n",
176 |        "    <tr>\n",
177 |        "      <th>0</th>\n",
178 |        "      <td>placebo</td>\n",
179 |        "      <td>80</td>\n",
180 |        "      <td>45</td>\n",
181 |        "      <td>0.562500</td>\n",
182 |        "      <td>0.000000</td>\n",
183 |        "      <td>0.078437</td>\n",
184 |        "      <td>-0.129017</td>\n",
185 |        "      <td>0.129017</td>\n",
186 |        "      <td>False</td>\n",
187 |        "    </tr>\n",
188 |        "    <tr>\n",
189 |        "      <th>1</th>\n",
190 |        "      <td>chlorpromazine</td>\n",
191 |        "      <td>75</td>\n",
192 |        "      <td>26</td>\n",
193 |        "      <td>0.346667</td>\n",
194 |        "      <td>-0.215833</td>\n",
195 |        "      <td>0.078077</td>\n",
196 |        "      <td>-0.344259</td>\n",
197 |        "      <td>-0.087408</td>\n",
198 |        "      <td>True</td>\n",
199 |        "    </tr>\n",
200 |        "    <tr>\n",
201 |        "      <th>2</th>\n",
202 |        "      <td>dimenhydrinate</td>\n",
203 |        "      <td>85</td>\n",
204 |        "      <td>52</td>\n",
205 |        "      <td>0.611765</td>\n",
206 |        "      <td>0.049265</td>\n",
207 |        "      <td>0.076618</td>\n",
208 |        "      <td>-0.076761</td>\n",
209 |        "      <td>0.175291</td>\n",
210 |        "      <td>False</td>\n",
211 |        "    </tr>\n",
212 |        "    <tr>\n",
213 |        "      <th>3</th>\n",
214 |        "      <td>pentobarbital100</td>\n",
215 |        "      <td>67</td>\n",
216 |        "      <td>35</td>\n",
217 |        "      <td>0.522388</td>\n",
218 |        "      <td>-0.040112</td>\n",
219 |        "      <td>0.082462</td>\n",
220 |        "      <td>-0.175750</td>\n",
221 |        "      <td>0.095527</td>\n",
222 |        "      <td>False</td>\n",
223 |        "    </tr>\n",
224 |        "    <tr>\n",
225 |        "      <th>4</th>\n",
226 |        "      <td>pentobarbital150</td>\n",
227 |        "      <td>85</td>\n",
228 |        "      <td>37</td>\n",
229 |        "      <td>0.435294</td>\n",
230 |        "      <td>-0.127206</td>\n",
231 |        "      <td>0.077253</td>\n",
232 |        "      <td>-0.254276</td>\n",
233 |        "      <td>-0.000135</td>\n",
234 |        "      <td>True</td>\n",
235 |        "    </tr>\n",
236 |        "  </tbody>\n",
237 |        "</table>\n",
238 |        "</div>"
239 |       ],
240 |       "text/plain": [
241 |        "               drug  total  nausea         p      diff        se  ci_lower  \\\n",
242 |        "0           placebo     80      45  0.562500  0.000000  0.078437 -0.129017   \n",
243 |        "1    chlorpromazine     75      26  0.346667 -0.215833  0.078077 -0.344259   \n",
244 |        "2    dimenhydrinate     85      52  0.611765  0.049265  0.076618 -0.076761   \n",
245 |        "3  pentobarbital100     67      35  0.522388 -0.040112  0.082462 -0.175750   \n",
246 |        "4  pentobarbital150     85      37  0.435294 -0.127206  0.077253 -0.254276   \n",
247 |        "\n",
248 |        "   ci_upper significant  \n",
249 |        "0  0.129017       False  \n",
250 |        "1 -0.087408        True  \n",
251 |        "2  0.175291       False  \n",
252 |        "3  0.095527       False  \n",
253 |        "4 -0.000135        True  "
254 |       ]
255 |      },
256 |      "execution_count": 23,
257 |      "metadata": {},
258 |      "output_type": "execute_result"
259 |     }
260 |    ],
261 |    "source": [
262 |     "alpha = 0.05\n",
263 |     "z_alpha = norm.ppf(1 - alpha)\n",
264 |     "\n",
265 |     "df['diff'] = df.p - p_placebo\n",
266 |     "df['se'] = np.sqrt((df.p * (1 - df.p) / df.total) + (p_placebo * (1 - p_placebo) / n_placebo))\n",
267 |     "df['ci_lower'] = df['diff'] - df.se * z_alpha\n",
268 |     "df['ci_upper'] = df['diff'] + df.se * z_alpha\n",
269 |     "df['significant'] = (0 < df.ci_lower) | (df.ci_upper < 0)\n",
270 |     "\n",
271 |     "df.head()"
272 |    ]
273 |   },
274 |   {
275 |    "cell_type": "code",
276 |    "execution_count": null,
277 |    "metadata": {
278 |     "collapsed": true
279 |    },
280 |    "outputs": [],
281 |    "source": []
282 |   }
283 |  ],
284 |  "metadata": {
285 |   "kernelspec": {
286 |    "display_name": "Python 3",
287 |    "language": "python",
288 |    "name": "python3"
289 |   },
290 |   "language_info": {
291 |    "codemirror_mode": {
292 |     "name": "ipython",
293 |     "version": 3
294 |    },
295 |    "file_extension": ".py",
296 |    "mimetype": "text/x-python",
297 |    "name": "python",
298 |    "nbconvert_exporter": "python",
299 |    "pygments_lexer": "ipython3",
300 |    "version": "3.5.2"
301 |   }
302 |  },
303 |  "nbformat": 4,
304 |  "nbformat_minor": 2
305 | }
306 | 


--------------------------------------------------------------------------------
/solutions/ch09q03.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "import sys\n",
 12 |     "sys.path.append('..')\n",
 13 |     "\n",
 14 |     "import pandas as pd\n",
 15 |     "import numpy as np\n",
 16 |     "from scipy.stats import norm\n",
 17 |     "\n",
 18 |     "from chapters.chapter7 import CI\n",
 19 |     "from chapters.chapter8 import bootstrap_ci_percentile\n",
 20 |     "from chapters.chapter9 import parametric_bootstrap_variance"
 21 |    ]
 22 |   },
 23 |   {
 24 |    "cell_type": "markdown",
 25 |    "metadata": {},
 26 |    "source": [
 27 |     "## Estimators"
 28 |    ]
 29 |   },
 30 |   {
 31 |    "cell_type": "code",
 32 |    "execution_count": 2,
 33 |    "metadata": {},
 34 |    "outputs": [
 35 |     {
 36 |      "data": {
 37 |       "text/html": [
 38 |        "<div>\n",
 39 |        "<table border=\"1\" class=\"dataframe\">\n",
 40 |        "  <thead>\n",
 41 |        "    <tr style=\"text-align: right;\">\n",
 42 |        "      <th></th>\n",
 43 |        "      <th>value</th>\n",
 44 |        "    </tr>\n",
 45 |        "  </thead>\n",
 46 |        "  <tbody>\n",
 47 |        "    <tr>\n",
 48 |        "      <th>0</th>\n",
 49 |        "      <td>3.23</td>\n",
 50 |        "    </tr>\n",
 51 |        "    <tr>\n",
 52 |        "      <th>1</th>\n",
 53 |        "      <td>-2.50</td>\n",
 54 |        "    </tr>\n",
 55 |        "    <tr>\n",
 56 |        "      <th>2</th>\n",
 57 |        "      <td>1.88</td>\n",
 58 |        "    </tr>\n",
 59 |        "    <tr>\n",
 60 |        "      <th>3</th>\n",
 61 |        "      <td>-0.68</td>\n",
 62 |        "    </tr>\n",
 63 |        "    <tr>\n",
 64 |        "      <th>4</th>\n",
 65 |        "      <td>4.43</td>\n",
 66 |        "    </tr>\n",
 67 |        "  </tbody>\n",
 68 |        "</table>\n",
 69 |        "</div>"
 70 |       ],
 71 |       "text/plain": [
 72 |        "   value\n",
 73 |        "0   3.23\n",
 74 |        "1  -2.50\n",
 75 |        "2   1.88\n",
 76 |        "3  -0.68\n",
 77 |        "4   4.43"
 78 |       ]
 79 |      },
 80 |      "execution_count": 2,
 81 |      "metadata": {},
 82 |      "output_type": "execute_result"
 83 |     }
 84 |    ],
 85 |    "source": [
 86 |     "df = pd.read_csv('../data/ch09q03.csv')\n",
 87 |     "n = len(df)\n",
 88 |     "df.head()"
 89 |    ]
 90 |   },
 91 |   {
 92 |    "cell_type": "code",
 93 |    "execution_count": 3,
 94 |    "metadata": {},
 95 |    "outputs": [
 96 |     {
 97 |      "data": {
 98 |       "text/plain": [
 99 |        "value    1.1908\n",
100 |        "dtype: float64"
101 |       ]
102 |      },
103 |      "execution_count": 3,
104 |      "metadata": {},
105 |      "output_type": "execute_result"
106 |     }
107 |    ],
108 |    "source": [
109 |     "mu_hat = df.mean()\n",
110 |     "mu_hat"
111 |    ]
112 |   },
113 |   {
114 |    "cell_type": "code",
115 |    "execution_count": 4,
116 |    "metadata": {},
117 |    "outputs": [
118 |     {
119 |      "data": {
120 |       "text/plain": [
121 |        "value    3.303503\n",
122 |        "dtype: float64"
123 |       ]
124 |      },
125 |      "execution_count": 4,
126 |      "metadata": {},
127 |      "output_type": "execute_result"
128 |     }
129 |    ],
130 |    "source": [
131 |     "v_hat = np.var(df)\n",
132 |     "v_hat"
133 |    ]
134 |   },
135 |   {
136 |    "cell_type": "code",
137 |    "execution_count": 5,
138 |    "metadata": {},
139 |    "outputs": [
140 |     {
141 |      "data": {
142 |       "text/plain": [
143 |        "value    1.817554\n",
144 |        "dtype: float64"
145 |       ]
146 |      },
147 |      "execution_count": 5,
148 |      "metadata": {},
149 |      "output_type": "execute_result"
150 |     }
151 |    ],
152 |    "source": [
153 |     "sigma_hat = np.sqrt(v_hat)\n",
154 |     "sigma_hat"
155 |    ]
156 |   },
157 |   {
158 |    "cell_type": "code",
159 |    "execution_count": 6,
160 |    "metadata": {},
161 |    "outputs": [
162 |     {
163 |      "data": {
164 |       "text/plain": [
165 |        "1.6448536269514722"
166 |       ]
167 |      },
168 |      "execution_count": 6,
169 |      "metadata": {},
170 |      "output_type": "execute_result"
171 |     }
172 |    ],
173 |    "source": [
174 |     "alpha = 0.05\n",
175 |     "z95 = norm.ppf(1 - alpha)\n",
176 |     "z95"
177 |    ]
178 |   },
179 |   {
180 |    "cell_type": "code",
181 |    "execution_count": 7,
182 |    "metadata": {},
183 |    "outputs": [
184 |     {
185 |      "data": {
186 |       "text/plain": [
187 |        "value    4.180411\n",
188 |        "dtype: float64"
189 |       ]
190 |      },
191 |      "execution_count": 7,
192 |      "metadata": {},
193 |      "output_type": "execute_result"
194 |     }
195 |    ],
196 |    "source": [
197 |     "tau_hat = z95 * sigma_hat + mu_hat\n",
198 |     "tau_hat"
199 |    ]
200 |   },
201 |   {
202 |    "cell_type": "markdown",
203 |    "metadata": {},
204 |    "source": [
205 |     "## Delta method confidence interval"
206 |    ]
207 |   },
208 |   {
209 |    "cell_type": "code",
210 |    "execution_count": 10,
211 |    "metadata": {},
212 |    "outputs": [
213 |     {
214 |      "data": {
215 |       "text/plain": [
216 |        "value    0.310896\n",
217 |        "dtype: float64"
218 |       ]
219 |      },
220 |      "execution_count": 10,
221 |      "metadata": {},
222 |      "output_type": "execute_result"
223 |     }
224 |    ],
225 |    "source": [
226 |     "se_delta = (v_hat + (v_hat * z95**2) / 2) / n\n",
227 |     "se_delta"
228 |    ]
229 |   },
230 |   {
231 |    "cell_type": "code",
232 |    "execution_count": 11,
233 |    "metadata": {},
234 |    "outputs": [
235 |     {
236 |      "data": {
237 |       "text/plain": [
238 |        "CI(lower=value    3.669033\n",
239 |        "dtype: float64, upper=value    4.691788\n",
240 |        "dtype: float64)"
241 |       ]
242 |      },
243 |      "execution_count": 11,
244 |      "metadata": {},
245 |      "output_type": "execute_result"
246 |     }
247 |    ],
248 |    "source": [
249 |     "alpha = 0.05\n",
250 |     "z_alpha = norm.ppf(1 - alpha)\n",
251 |     "\n",
252 |     "ci_delta = CI(tau_hat - z_alpha * se_delta, tau_hat + z_alpha * se_delta)\n",
253 |     "ci_delta"
254 |    ]
255 |   },
256 |   {
257 |    "cell_type": "markdown",
258 |    "metadata": {},
259 |    "source": [
260 |     "## Bootstrapped confidence interval"
261 |    ]
262 |   },
263 |   {
264 |    "cell_type": "markdown",
265 |    "metadata": {},
266 |    "source": [
267 |     "Since we are trying to estimate the 95th percentile, it could make sense to use the percentile function as our statistic.  We will create a non-parametric bootstrapped confidence interval this way."
268 |    ]
269 |   },
270 |   {
271 |    "cell_type": "code",
272 |    "execution_count": 12,
273 |    "metadata": {},
274 |    "outputs": [
275 |     {
276 |      "data": {
277 |       "text/plain": [
278 |        "4.3439999999999985"
279 |       ]
280 |      },
281 |      "execution_count": 12,
282 |      "metadata": {},
283 |      "output_type": "execute_result"
284 |     }
285 |    ],
286 |    "source": [
287 |     "statistic = lambda xs: np.percentile(xs, 95)\n",
288 |     "statistic(df)"
289 |    ]
290 |   },
291 |   {
292 |    "cell_type": "markdown",
293 |    "metadata": {},
294 |    "source": [
295 |     "In the parametric case under consideration, we can write down the 95th percentile as a function of the mean and standard deviation."
296 |    ]
297 |   },
298 |   {
299 |    "cell_type": "code",
300 |    "execution_count": 13,
301 |    "metadata": {},
302 |    "outputs": [
303 |     {
304 |      "data": {
305 |       "text/plain": [
306 |        "value    4.180411\n",
307 |        "dtype: float64"
308 |       ]
309 |      },
310 |      "execution_count": 13,
311 |      "metadata": {},
312 |      "output_type": "execute_result"
313 |     }
314 |    ],
315 |    "source": [
316 |     "pstatistic = lambda xs: np.mean(xs) + z95 * np.std(xs)\n",
317 |     "pstatistic(df)"
318 |    ]
319 |   },
320 |   {
321 |    "cell_type": "code",
322 |    "execution_count": 14,
323 |    "metadata": {},
324 |    "outputs": [
325 |     {
326 |      "data": {
327 |       "text/plain": [
328 |        "1.0031753544847091"
329 |       ]
330 |      },
331 |      "execution_count": 14,
332 |      "metadata": {},
333 |      "output_type": "execute_result"
334 |     }
335 |    ],
336 |    "source": [
337 |     "v_pboot = parametric_bootstrap_variance(dist=norm(mu_hat, v_hat), n=n, statistic=pstatistic, iters=10000, random_state=484488)\n",
338 |     "se_pboot = np.sqrt(v_pboot)\n",
339 |     "se_pboot"
340 |    ]
341 |   },
342 |   {
343 |    "cell_type": "code",
344 |    "execution_count": 15,
345 |    "metadata": {},
346 |    "outputs": [
347 |     {
348 |      "data": {
349 |       "text/plain": [
350 |        "CI(lower=value    2.530334\n",
351 |        "dtype: float64, upper=value    5.830487\n",
352 |        "dtype: float64)"
353 |       ]
354 |      },
355 |      "execution_count": 15,
356 |      "metadata": {},
357 |      "output_type": "execute_result"
358 |     }
359 |    ],
360 |    "source": [
361 |     "ci_pboot = CI(tau_hat - z_alpha * se_pboot, tau_hat + z_alpha * se_pboot)\n",
362 |     "ci_pboot"
363 |    ]
364 |   },
365 |   {
366 |    "cell_type": "code",
367 |    "execution_count": 16,
368 |    "metadata": {},
369 |    "outputs": [
370 |     {
371 |      "data": {
372 |       "text/plain": [
373 |        "CI(lower=2.3300000000000001, upper=5.4299999999999997)"
374 |       ]
375 |      },
376 |      "execution_count": 16,
377 |      "metadata": {},
378 |      "output_type": "execute_result"
379 |     }
380 |    ],
381 |    "source": [
382 |     "ci_boot = bootstrap_ci_percentile(df, statistic, 10000, a=alpha, random_state=46111110)\n",
383 |     "ci_boot"
384 |    ]
385 |   },
386 |   {
387 |    "cell_type": "markdown",
388 |    "metadata": {},
389 |    "source": [
390 |     "## Comparison of confidence intervals\n",
391 |     "\n",
392 |     "In this case, the delta method yields a tighter confidence interval."
393 |    ]
394 |   },
395 |   {
396 |    "cell_type": "code",
397 |    "execution_count": null,
398 |    "metadata": {
399 |     "collapsed": true
400 |    },
401 |    "outputs": [],
402 |    "source": []
403 |   }
404 |  ],
405 |  "metadata": {
406 |   "kernelspec": {
407 |    "display_name": "Python 3",
408 |    "language": "python",
409 |    "name": "python3"
410 |   },
411 |   "language_info": {
412 |    "codemirror_mode": {
413 |     "name": "ipython",
414 |     "version": 3
415 |    },
416 |    "file_extension": ".py",
417 |    "mimetype": "text/x-python",
418 |    "name": "python",
419 |    "nbconvert_exporter": "python",
420 |    "pygments_lexer": "ipython3",
421 |    "version": "3.5.2"
422 |   }
423 |  },
424 |  "nbformat": 4,
425 |  "nbformat_minor": 2
426 | }
427 | 


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/solutions/ch10q07.ipynb:
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  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 15,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "import pandas as pd"
 12 |    ]
 13 |   },
 14 |   {
 15 |    "cell_type": "code",
 16 |    "execution_count": 16,
 17 |    "metadata": {
 18 |     "collapsed": true
 19 |    },
 20 |    "outputs": [],
 21 |    "source": [
 22 |     "data = pd.read_csv('../data/snodgrass.csv')"
 23 |    ]
 24 |   },
 25 |   {
 26 |    "cell_type": "code",
 27 |    "execution_count": 17,
 28 |    "metadata": {
 29 |     "scrolled": true
 30 |    },
 31 |    "outputs": [
 32 |     {
 33 |      "data": {
 34 |       "text/html": [
 35 |        "<div>\n",
 36 |        "<table border=\"1\" class=\"dataframe\">\n",
 37 |        "  <thead>\n",
 38 |        "    <tr style=\"text-align: right;\">\n",
 39 |        "      <th></th>\n",
 40 |        "      <th>author</th>\n",
 41 |        "      <th>total</th>\n",
 42 |        "    </tr>\n",
 43 |        "  </thead>\n",
 44 |        "  <tbody>\n",
 45 |        "    <tr>\n",
 46 |        "      <th>0</th>\n",
 47 |        "      <td>twain</td>\n",
 48 |        "      <td>0.225</td>\n",
 49 |        "    </tr>\n",
 50 |        "    <tr>\n",
 51 |        "      <th>1</th>\n",
 52 |        "      <td>twain</td>\n",
 53 |        "      <td>0.262</td>\n",
 54 |        "    </tr>\n",
 55 |        "    <tr>\n",
 56 |        "      <th>2</th>\n",
 57 |        "      <td>twain</td>\n",
 58 |        "      <td>0.217</td>\n",
 59 |        "    </tr>\n",
 60 |        "    <tr>\n",
 61 |        "      <th>3</th>\n",
 62 |        "      <td>twain</td>\n",
 63 |        "      <td>0.240</td>\n",
 64 |        "    </tr>\n",
 65 |        "    <tr>\n",
 66 |        "      <th>4</th>\n",
 67 |        "      <td>twain</td>\n",
 68 |        "      <td>0.230</td>\n",
 69 |        "    </tr>\n",
 70 |        "    <tr>\n",
 71 |        "      <th>5</th>\n",
 72 |        "      <td>twain</td>\n",
 73 |        "      <td>0.229</td>\n",
 74 |        "    </tr>\n",
 75 |        "    <tr>\n",
 76 |        "      <th>6</th>\n",
 77 |        "      <td>twain</td>\n",
 78 |        "      <td>0.235</td>\n",
 79 |        "    </tr>\n",
 80 |        "    <tr>\n",
 81 |        "      <th>7</th>\n",
 82 |        "      <td>twain</td>\n",
 83 |        "      <td>0.217</td>\n",
 84 |        "    </tr>\n",
 85 |        "    <tr>\n",
 86 |        "      <th>8</th>\n",
 87 |        "      <td>snodgrass</td>\n",
 88 |        "      <td>0.209</td>\n",
 89 |        "    </tr>\n",
 90 |        "    <tr>\n",
 91 |        "      <th>9</th>\n",
 92 |        "      <td>snodgrass</td>\n",
 93 |        "      <td>0.205</td>\n",
 94 |        "    </tr>\n",
 95 |        "    <tr>\n",
 96 |        "      <th>10</th>\n",
 97 |        "      <td>snodgrass</td>\n",
 98 |        "      <td>0.196</td>\n",
 99 |        "    </tr>\n",
100 |        "    <tr>\n",
101 |        "      <th>11</th>\n",
102 |        "      <td>snodgrass</td>\n",
103 |        "      <td>0.210</td>\n",
104 |        "    </tr>\n",
105 |        "    <tr>\n",
106 |        "      <th>12</th>\n",
107 |        "      <td>snodgrass</td>\n",
108 |        "      <td>0.202</td>\n",
109 |        "    </tr>\n",
110 |        "    <tr>\n",
111 |        "      <th>13</th>\n",
112 |        "      <td>snodgrass</td>\n",
113 |        "      <td>0.207</td>\n",
114 |        "    </tr>\n",
115 |        "    <tr>\n",
116 |        "      <th>14</th>\n",
117 |        "      <td>snodgrass</td>\n",
118 |        "      <td>0.224</td>\n",
119 |        "    </tr>\n",
120 |        "    <tr>\n",
121 |        "      <th>15</th>\n",
122 |        "      <td>snodgrass</td>\n",
123 |        "      <td>0.223</td>\n",
124 |        "    </tr>\n",
125 |        "    <tr>\n",
126 |        "      <th>16</th>\n",
127 |        "      <td>snodgrass</td>\n",
128 |        "      <td>0.220</td>\n",
129 |        "    </tr>\n",
130 |        "    <tr>\n",
131 |        "      <th>17</th>\n",
132 |        "      <td>snodgrass</td>\n",
133 |        "      <td>0.201</td>\n",
134 |        "    </tr>\n",
135 |        "  </tbody>\n",
136 |        "</table>\n",
137 |        "</div>"
138 |       ],
139 |       "text/plain": [
140 |        "       author  total\n",
141 |        "0       twain  0.225\n",
142 |        "1       twain  0.262\n",
143 |        "2       twain  0.217\n",
144 |        "3       twain  0.240\n",
145 |        "4       twain  0.230\n",
146 |        "5       twain  0.229\n",
147 |        "6       twain  0.235\n",
148 |        "7       twain  0.217\n",
149 |        "8   snodgrass  0.209\n",
150 |        "9   snodgrass  0.205\n",
151 |        "10  snodgrass  0.196\n",
152 |        "11  snodgrass  0.210\n",
153 |        "12  snodgrass  0.202\n",
154 |        "13  snodgrass  0.207\n",
155 |        "14  snodgrass  0.224\n",
156 |        "15  snodgrass  0.223\n",
157 |        "16  snodgrass  0.220\n",
158 |        "17  snodgrass  0.201"
159 |       ]
160 |      },
161 |      "execution_count": 17,
162 |      "metadata": {},
163 |      "output_type": "execute_result"
164 |     }
165 |    ],
166 |    "source": [
167 |     "data"
168 |    ]
169 |   },
170 |   {
171 |    "cell_type": "code",
172 |    "execution_count": 18,
173 |    "metadata": {},
174 |    "outputs": [
175 |     {
176 |      "data": {
177 |       "text/html": [
178 |        "<div>\n",
179 |        "<table border=\"1\" class=\"dataframe\">\n",
180 |        "  <thead>\n",
181 |        "    <tr>\n",
182 |        "      <th></th>\n",
183 |        "      <th colspan=\"2\" halign=\"left\">total</th>\n",
184 |        "    </tr>\n",
185 |        "    <tr>\n",
186 |        "      <th></th>\n",
187 |        "      <th>mean</th>\n",
188 |        "      <th>count</th>\n",
189 |        "    </tr>\n",
190 |        "    <tr>\n",
191 |        "      <th>author</th>\n",
192 |        "      <th></th>\n",
193 |        "      <th></th>\n",
194 |        "    </tr>\n",
195 |        "  </thead>\n",
196 |        "  <tbody>\n",
197 |        "    <tr>\n",
198 |        "      <th>snodgrass</th>\n",
199 |        "      <td>0.209700</td>\n",
200 |        "      <td>10</td>\n",
201 |        "    </tr>\n",
202 |        "    <tr>\n",
203 |        "      <th>twain</th>\n",
204 |        "      <td>0.231875</td>\n",
205 |        "      <td>8</td>\n",
206 |        "    </tr>\n",
207 |        "  </tbody>\n",
208 |        "</table>\n",
209 |        "</div>"
210 |       ],
211 |       "text/plain": [
212 |        "              total      \n",
213 |        "               mean count\n",
214 |        "author                   \n",
215 |        "snodgrass  0.209700    10\n",
216 |        "twain      0.231875     8"
217 |       ]
218 |      },
219 |      "execution_count": 18,
220 |      "metadata": {},
221 |      "output_type": "execute_result"
222 |     }
223 |    ],
224 |    "source": [
225 |     "data.groupby('author').aggregate(['mean', 'count'])"
226 |    ]
227 |   },
228 |   {
229 |    "cell_type": "markdown",
230 |    "metadata": {},
231 |    "source": [
232 |     "$$t_{obs}$$ is \n",
233 |     "\n",
234 |     "$$|.2097 - .231875| = .022175$$"
235 |    ]
236 |   },
237 |   {
238 |    "cell_type": "code",
239 |    "execution_count": 24,
240 |    "metadata": {
241 |     "collapsed": true
242 |    },
243 |    "outputs": [],
244 |    "source": [
245 |     "t_obs = .022175"
246 |    ]
247 |   },
248 |   {
249 |    "cell_type": "markdown",
250 |    "metadata": {},
251 |    "source": [
252 |     "## Permutation test"
253 |    ]
254 |   },
255 |   {
256 |    "cell_type": "markdown",
257 |    "metadata": {},
258 |    "source": [
259 |     "The full set of observations in $$X_1,\\ldots,X_{10}, Y_1,\\ldots,Y_{8}$$\n",
260 |     "\n",
261 |     "For all 18! permutations of the data, compute\n",
262 |     "\n",
263 |     "$$|(\\bar{X}) - (\\bar{Y})|$$\n",
264 |     "\n",
265 |     "where $$(\\bar{X})$$ is the mean of the first 10 observations, and $$(\\bar{Y})$$ is the mean of the last 8."
266 |    ]
267 |   },
268 |   {
269 |    "cell_type": "code",
270 |    "execution_count": 19,
271 |    "metadata": {
272 |     "collapsed": true
273 |    },
274 |    "outputs": [],
275 |    "source": [
276 |     "from itertools import permutations"
277 |    ]
278 |   },
279 |   {
280 |    "cell_type": "code",
281 |    "execution_count": 22,
282 |    "metadata": {},
283 |    "outputs": [],
284 |    "source": [
285 |     "obs = list(data['total'])"
286 |    ]
287 |   },
288 |   {
289 |    "cell_type": "code",
290 |    "execution_count": 42,
291 |    "metadata": {
292 |     "collapsed": true
293 |    },
294 |    "outputs": [],
295 |    "source": [
296 |     "import numpy as np"
297 |    ]
298 |   },
299 |   {
300 |    "cell_type": "code",
301 |    "execution_count": 48,
302 |    "metadata": {},
303 |    "outputs": [
304 |     {
305 |      "name": "stdout",
306 |      "output_type": "stream",
307 |      "text": [
308 |       "-1.5\n",
309 |       "0.0\n",
310 |       "-1.5\n",
311 |       "1.5\n",
312 |       "0.0\n",
313 |       "1.5\n"
314 |      ]
315 |     }
316 |    ],
317 |    "source": [
318 |     "perms = (p for p in permutations([1,2,3]))\n",
319 |     "for p in perms:\n",
320 |     "    print(np.mean(p[:2]) - np.mean(p[2:]))"
321 |    ]
322 |   },
323 |   {
324 |    "cell_type": "code",
325 |    "execution_count": 103,
326 |    "metadata": {
327 |     "collapsed": true
328 |    },
329 |    "outputs": [],
330 |    "source": [
331 |     "# there are too many permutations to count all of them, so we set some limit N\n",
332 |     "# on the total number of observed permutations\n",
333 |     "\n",
334 |     "\n",
335 |     "def permutation_test(obs, m, c, N):\n",
336 |     "    i = 0 # counter for T>c\n",
337 |     "    \n",
338 |     "    # adjust m so there's at least one observation in each sample\n",
339 |     "    m = min(m, len(obs)-1)\n",
340 |     "\n",
341 |     "    # evaluate permutations\n",
342 |     "    for j in range(N):\n",
343 |     "        p = np.random.permutation(obs)\n",
344 |     "        # calculate stat\n",
345 |     "        T = np.mean(p[:m]) - np.mean(p[m:])\n",
346 |     "        # count if > c\n",
347 |     "        if T > c:\n",
348 |     "            i += 1\n",
349 |     "            \n",
350 |     "    # i/N approximates the p-value as N -> N!\n",
351 |     "    return i/N\n"
352 |    ]
353 |   },
354 |   {
355 |    "cell_type": "code",
356 |    "execution_count": 104,
357 |    "metadata": {},
358 |    "outputs": [
359 |     {
360 |      "data": {
361 |       "text/plain": [
362 |        "0.00023"
363 |       ]
364 |      },
365 |      "execution_count": 104,
366 |      "metadata": {},
367 |      "output_type": "execute_result"
368 |     }
369 |    ],
370 |    "source": [
371 |     "permutation_test(obs, 10, t_obs, N=100000)"
372 |    ]
373 |   },
374 |   {
375 |    "cell_type": "markdown",
376 |    "metadata": {},
377 |    "source": [
378 |     "## Wald test"
379 |    ]
380 |   },
381 |   {
382 |    "cell_type": "markdown",
383 |    "metadata": {},
384 |    "source": [
385 |     "The Wald test of two means can be constructed as (see example 10.7)\n",
386 |     "\n",
387 |     "$$ W = \\frac{\\bar{X}-\\bar{Y}}{\\sqrt{\\frac{s_x^2}{m}+\\frac{s_y^2}{n}}} $$"
388 |    ]
389 |   },
390 |   {
391 |    "cell_type": "code",
392 |    "execution_count": 107,
393 |    "metadata": {
394 |     "collapsed": true
395 |    },
396 |    "outputs": [],
397 |    "source": [
398 |     "X = data[data['author']=='snodgrass']['total']\n",
399 |     "Y = data[data['author']=='twain']['total']\n",
400 |     "\n",
401 |     "x_bar = np.mean(X)\n",
402 |     "m = len(X)\n",
403 |     "s_x = np.std(X)\n",
404 |     "\n",
405 |     "y_bar = np.mean(Y)\n",
406 |     "n = len(Y)\n",
407 |     "s_y = np.std(Y)\n"
408 |    ]
409 |   },
410 |   {
411 |    "cell_type": "code",
412 |    "execution_count": 116,
413 |    "metadata": {},
414 |    "outputs": [],
415 |    "source": [
416 |     "W = (x_bar - y_bar)/np.sqrt(s_x**2/m + s_y**2/n)"
417 |    ]
418 |   },
419 |   {
420 |    "cell_type": "markdown",
421 |    "metadata": {},
422 |    "source": [
423 |     "Finally we just need to test that $$W > z_{\\alpha/2}$$\n"
424 |    ]
425 |   },
426 |   {
427 |    "cell_type": "code",
428 |    "execution_count": 119,
429 |    "metadata": {},
430 |    "outputs": [
431 |     {
432 |      "data": {
433 |       "text/plain": [
434 |        "True"
435 |       ]
436 |      },
437 |      "execution_count": 119,
438 |      "metadata": {},
439 |      "output_type": "execute_result"
440 |     }
441 |    ],
442 |    "source": [
443 |     "np.abs(W) > 1.96"
444 |    ]
445 |   },
446 |   {
447 |    "cell_type": "markdown",
448 |    "metadata": {},
449 |    "source": [
450 |     "We can get the p-value:"
451 |    ]
452 |   },
453 |   {
454 |    "cell_type": "code",
455 |    "execution_count": 120,
456 |    "metadata": {
457 |     "collapsed": true
458 |    },
459 |    "outputs": [],
460 |    "source": [
461 |     "from scipy.stats import norm"
462 |    ]
463 |   },
464 |   {
465 |    "cell_type": "code",
466 |    "execution_count": 123,
467 |    "metadata": {},
468 |    "outputs": [
469 |     {
470 |      "data": {
471 |       "text/plain": [
472 |        "3.9963324780729e-05"
473 |       ]
474 |      },
475 |      "execution_count": 123,
476 |      "metadata": {},
477 |      "output_type": "execute_result"
478 |     }
479 |    ],
480 |    "source": [
481 |     "norm.cdf(W)"
482 |    ]
483 |   },
484 |   {
485 |    "cell_type": "markdown",
486 |    "metadata": {},
487 |    "source": [
488 |     "To get the CI we need $$\\hat{\\theta}$$, which here is $$\\bar{X}-\\bar{Y}$$, and se_hat, which is $$\\sqrt{\\frac{s_x^2}{m}+\\frac{s_y^2}{n}}$$."
489 |    ]
490 |   },
491 |   {
492 |    "cell_type": "code",
493 |    "execution_count": 124,
494 |    "metadata": {
495 |     "collapsed": true
496 |    },
497 |    "outputs": [],
498 |    "source": [
499 |     "theta_hat = x_bar-y_bar\n",
500 |     "se_hat = np.sqrt(s_x**2/m + s_y**2/n)"
501 |    ]
502 |   },
503 |   {
504 |    "cell_type": "code",
505 |    "execution_count": 125,
506 |    "metadata": {},
507 |    "outputs": [
508 |     {
509 |      "data": {
510 |       "text/plain": [
511 |        "(-0.022175, -0.010931838189370394, -0.033418161810629607)"
512 |       ]
513 |      },
514 |      "execution_count": 125,
515 |      "metadata": {},
516 |      "output_type": "execute_result"
517 |     }
518 |    ],
519 |    "source": [
520 |     "(theta_hat, theta_hat+2*se_hat, theta_hat-2*se_hat)"
521 |    ]
522 |   },
523 |   {
524 |    "cell_type": "markdown",
525 |    "metadata": {},
526 |    "source": [
527 |     "## Conclusions\n",
528 |     "\n",
529 |     "Our p-value from both tests is very small, which is strong evidence for rejecting the null that the means of the two samples are the same.\n",
530 |     "\n",
531 |     "Additionally, the confidence intervals do not overlap, which again is evidence against $$H_0$$"
532 |    ]
533 |   }
534 |  ],
535 |  "metadata": {
536 |   "kernelspec": {
537 |    "display_name": "Python 3",
538 |    "language": "python",
539 |    "name": "python3"
540 |   },
541 |   "language_info": {
542 |    "codemirror_mode": {
543 |     "name": "ipython",
544 |     "version": 3
545 |    },
546 |    "file_extension": ".py",
547 |    "mimetype": "text/x-python",
548 |    "name": "python",
549 |    "nbconvert_exporter": "python",
550 |    "pygments_lexer": "ipython3",
551 |    "version": "3.5.1"
552 |   }
553 |  },
554 |  "nbformat": 4,
555 |  "nbformat_minor": 2
556 | }
557 | 


--------------------------------------------------------------------------------
/solutions/ch08q07.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "import sys\n",
 12 |     "sys.path.append('..')\n",
 13 |     "\n",
 14 |     "import pandas as pd\n",
 15 |     "import numpy as np\n",
 16 |     "import seaborn as sns\n",
 17 |     "import re\n",
 18 |     "import matplotlib as mpl\n",
 19 |     "import matplotlib.pyplot as plt\n",
 20 |     "plt.style.use('ggplot')\n",
 21 |     "%matplotlib inline\n",
 22 |     "%load_ext autoreload\n",
 23 |     "%autoreload 2\n",
 24 |     "from scipy.stats import uniform\n",
 25 |     "\n",
 26 |     "from chapters.chapter8 import *"
 27 |    ]
 28 |   },
 29 |   {
 30 |    "cell_type": "code",
 31 |    "execution_count": 2,
 32 |    "metadata": {},
 33 |    "outputs": [
 34 |     {
 35 |      "data": {
 36 |       "text/plain": [
 37 |        "0.96152258315923522"
 38 |       ]
 39 |      },
 40 |      "execution_count": 2,
 41 |      "metadata": {},
 42 |      "output_type": "execute_result"
 43 |     }
 44 |    ],
 45 |    "source": [
 46 |     "n = 50\n",
 47 |     "theta = 1\n",
 48 |     "obs = uniform.rvs(0, theta, size=n)\n",
 49 |     "statistic = np.max\n",
 50 |     "statistic(obs)"
 51 |    ]
 52 |   },
 53 |   {
 54 |    "cell_type": "code",
 55 |    "execution_count": 3,
 56 |    "metadata": {},
 57 |    "outputs": [
 58 |     {
 59 |      "data": {
 60 |       "text/html": [
 61 |        "<div>\n",
 62 |        "<table border=\"1\" class=\"dataframe\">\n",
 63 |        "  <thead>\n",
 64 |        "    <tr style=\"text-align: right;\">\n",
 65 |        "      <th></th>\n",
 66 |        "      <th>value</th>\n",
 67 |        "      <th>estimator</th>\n",
 68 |        "    </tr>\n",
 69 |        "  </thead>\n",
 70 |        "  <tbody>\n",
 71 |        "    <tr>\n",
 72 |        "      <th>0</th>\n",
 73 |        "      <td>0.996009</td>\n",
 74 |        "      <td>max</td>\n",
 75 |        "    </tr>\n",
 76 |        "    <tr>\n",
 77 |        "      <th>1</th>\n",
 78 |        "      <td>0.974337</td>\n",
 79 |        "      <td>max</td>\n",
 80 |        "    </tr>\n",
 81 |        "    <tr>\n",
 82 |        "      <th>2</th>\n",
 83 |        "      <td>0.993295</td>\n",
 84 |        "      <td>max</td>\n",
 85 |        "    </tr>\n",
 86 |        "    <tr>\n",
 87 |        "      <th>3</th>\n",
 88 |        "      <td>0.987775</td>\n",
 89 |        "      <td>max</td>\n",
 90 |        "    </tr>\n",
 91 |        "    <tr>\n",
 92 |        "      <th>4</th>\n",
 93 |        "      <td>0.996820</td>\n",
 94 |        "      <td>max</td>\n",
 95 |        "    </tr>\n",
 96 |        "  </tbody>\n",
 97 |        "</table>\n",
 98 |        "</div>"
 99 |       ],
100 |       "text/plain": [
101 |        "      value estimator\n",
102 |        "0  0.996009       max\n",
103 |        "1  0.974337       max\n",
104 |        "2  0.993295       max\n",
105 |        "3  0.987775       max\n",
106 |        "4  0.996820       max"
107 |       ]
108 |      },
109 |      "execution_count": 3,
110 |      "metadata": {},
111 |      "output_type": "execute_result"
112 |     }
113 |    ],
114 |    "source": [
115 |     "iters = 10000\n",
116 |     "df_true = pd.DataFrame({'value': [statistic(uniform.rvs(0, theta, size=n)) for _ in range(iters)]})\n",
117 |     "df_true['estimator'] = 'max'\n",
118 |     "df_true.head()"
119 |    ]
120 |   },
121 |   {
122 |    "cell_type": "code",
123 |    "execution_count": 4,
124 |    "metadata": {},
125 |    "outputs": [
126 |     {
127 |      "data": {
128 |       "text/html": [
129 |        "<div>\n",
130 |        "<table border=\"1\" class=\"dataframe\">\n",
131 |        "  <thead>\n",
132 |        "    <tr style=\"text-align: right;\">\n",
133 |        "      <th></th>\n",
134 |        "      <th>value</th>\n",
135 |        "      <th>estimator</th>\n",
136 |        "    </tr>\n",
137 |        "  </thead>\n",
138 |        "  <tbody>\n",
139 |        "    <tr>\n",
140 |        "      <th>0</th>\n",
141 |        "      <td>0.961523</td>\n",
142 |        "      <td>max bootstrap</td>\n",
143 |        "    </tr>\n",
144 |        "    <tr>\n",
145 |        "      <th>1</th>\n",
146 |        "      <td>0.961523</td>\n",
147 |        "      <td>max bootstrap</td>\n",
148 |        "    </tr>\n",
149 |        "    <tr>\n",
150 |        "      <th>2</th>\n",
151 |        "      <td>0.876382</td>\n",
152 |        "      <td>max bootstrap</td>\n",
153 |        "    </tr>\n",
154 |        "    <tr>\n",
155 |        "      <th>3</th>\n",
156 |        "      <td>0.961523</td>\n",
157 |        "      <td>max bootstrap</td>\n",
158 |        "    </tr>\n",
159 |        "    <tr>\n",
160 |        "      <th>4</th>\n",
161 |        "      <td>0.876382</td>\n",
162 |        "      <td>max bootstrap</td>\n",
163 |        "    </tr>\n",
164 |        "  </tbody>\n",
165 |        "</table>\n",
166 |        "</div>"
167 |       ],
168 |       "text/plain": [
169 |        "      value      estimator\n",
170 |        "0  0.961523  max bootstrap\n",
171 |        "1  0.961523  max bootstrap\n",
172 |        "2  0.876382  max bootstrap\n",
173 |        "3  0.961523  max bootstrap\n",
174 |        "4  0.876382  max bootstrap"
175 |       ]
176 |      },
177 |      "execution_count": 4,
178 |      "metadata": {},
179 |      "output_type": "execute_result"
180 |     }
181 |    ],
182 |    "source": [
183 |     "df_boot = pd.DataFrame({'value': list(bootstrap(pd.Series(obs), statistic, iters))})\n",
184 |     "df_boot['estimator'] = 'max bootstrap'\n",
185 |     "df_boot.head()"
186 |    ]
187 |   },
188 |   {
189 |    "cell_type": "code",
190 |    "execution_count": 5,
191 |    "metadata": {},
192 |    "outputs": [
193 |     {
194 |      "data": {
195 |       "text/html": [
196 |        "<div>\n",
197 |        "<table border=\"1\" class=\"dataframe\">\n",
198 |        "  <thead>\n",
199 |        "    <tr style=\"text-align: right;\">\n",
200 |        "      <th></th>\n",
201 |        "      <th>value</th>\n",
202 |        "      <th>estimator</th>\n",
203 |        "    </tr>\n",
204 |        "  </thead>\n",
205 |        "  <tbody>\n",
206 |        "    <tr>\n",
207 |        "      <th>0</th>\n",
208 |        "      <td>0.996009</td>\n",
209 |        "      <td>max</td>\n",
210 |        "    </tr>\n",
211 |        "    <tr>\n",
212 |        "      <th>1</th>\n",
213 |        "      <td>0.974337</td>\n",
214 |        "      <td>max</td>\n",
215 |        "    </tr>\n",
216 |        "    <tr>\n",
217 |        "      <th>2</th>\n",
218 |        "      <td>0.993295</td>\n",
219 |        "      <td>max</td>\n",
220 |        "    </tr>\n",
221 |        "    <tr>\n",
222 |        "      <th>3</th>\n",
223 |        "      <td>0.987775</td>\n",
224 |        "      <td>max</td>\n",
225 |        "    </tr>\n",
226 |        "    <tr>\n",
227 |        "      <th>4</th>\n",
228 |        "      <td>0.996820</td>\n",
229 |        "      <td>max</td>\n",
230 |        "    </tr>\n",
231 |        "  </tbody>\n",
232 |        "</table>\n",
233 |        "</div>"
234 |       ],
235 |       "text/plain": [
236 |        "      value estimator\n",
237 |        "0  0.996009       max\n",
238 |        "1  0.974337       max\n",
239 |        "2  0.993295       max\n",
240 |        "3  0.987775       max\n",
241 |        "4  0.996820       max"
242 |       ]
243 |      },
244 |      "execution_count": 5,
245 |      "metadata": {},
246 |      "output_type": "execute_result"
247 |     }
248 |    ],
249 |    "source": [
250 |     "df = pd.concat((df_true, df_boot))\n",
251 |     "df.head()"
252 |    ]
253 |   },
254 |   {
255 |    "cell_type": "code",
256 |    "execution_count": 6,
257 |    "metadata": {},
258 |    "outputs": [
259 |     {
260 |      "data": {
261 |       "text/html": [
262 |        "<div>\n",
263 |        "<table border=\"1\" class=\"dataframe\">\n",
264 |        "  <thead>\n",
265 |        "    <tr style=\"text-align: right;\">\n",
266 |        "      <th></th>\n",
267 |        "      <th>value</th>\n",
268 |        "    </tr>\n",
269 |        "    <tr>\n",
270 |        "      <th>estimator</th>\n",
271 |        "      <th></th>\n",
272 |        "    </tr>\n",
273 |        "  </thead>\n",
274 |        "  <tbody>\n",
275 |        "    <tr>\n",
276 |        "      <th>max</th>\n",
277 |        "      <td>10000</td>\n",
278 |        "    </tr>\n",
279 |        "    <tr>\n",
280 |        "      <th>max bootstrap</th>\n",
281 |        "      <td>10000</td>\n",
282 |        "    </tr>\n",
283 |        "  </tbody>\n",
284 |        "</table>\n",
285 |        "</div>"
286 |       ],
287 |       "text/plain": [
288 |        "               value\n",
289 |        "estimator           \n",
290 |        "max            10000\n",
291 |        "max bootstrap  10000"
292 |       ]
293 |      },
294 |      "execution_count": 6,
295 |      "metadata": {},
296 |      "output_type": "execute_result"
297 |     }
298 |    ],
299 |    "source": [
300 |     "df.groupby('estimator').count()"
301 |    ]
302 |   },
303 |   {
304 |    "cell_type": "code",
305 |    "execution_count": 7,
306 |    "metadata": {},
307 |    "outputs": [
308 |     {
309 |      "data": {
310 |       "image/png": 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kT0kDsHfdweNId1+QX/MLgH2A7dVCFVmYznFKXbj7f0mto89WTN4H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\niEgBBaeIiEgBBaeIiEgBBaeIiEiB/w8isMMBnRHKcgAAAABJRU5ErkJggg==\n",
311 |       "text/plain": [
312 |        "<matplotlib.figure.Figure at 0x7f60480a9c50>"
313 |       ]
314 |      },
315 |      "metadata": {},
316 |      "output_type": "display_data"
317 |     }
318 |    ],
319 |    "source": [
320 |     "g = sns.FacetGrid(df, hue='estimator', size=5)\n",
321 |     "g.map(sns.distplot, 'value', kde=False).add_legend()\n",
322 |     "g.set(xlabel='Value of the Estimator', ylabel='Frequency', title='Diststribution of the Estimators')\n",
323 |     "g.savefig('../images/ch08q07_histogram_true_vs_bootstrap.svg')\n",
324 |     "g.savefig('../images/ch08q07_histogram_true_vs_bootstrap_bbox.svg', bbox_inches='tight')\n",
325 |     "g.savefig('../images/ch08q07_histogram_true_vs_bootstrap.png', dpi=600)"
326 |    ]
327 |   },
328 |   {
329 |    "cell_type": "code",
330 |    "execution_count": null,
331 |    "metadata": {
332 |     "collapsed": true
333 |    },
334 |    "outputs": [],
335 |    "source": []
336 |   }
337 |  ],
338 |  "metadata": {
339 |   "kernelspec": {
340 |    "display_name": "Python 3",
341 |    "language": "python",
342 |    "name": "python3"
343 |   },
344 |   "language_info": {
345 |    "codemirror_mode": {
346 |     "name": "ipython",
347 |     "version": 3
348 |    },
349 |    "file_extension": ".py",
350 |    "mimetype": "text/x-python",
351 |    "name": "python",
352 |    "nbconvert_exporter": "python",
353 |    "pygments_lexer": "ipython3",
354 |    "version": "3.5.2"
355 |   }
356 |  },
357 |  "nbformat": 4,
358 |  "nbformat_minor": 2
359 | }
360 | 


--------------------------------------------------------------------------------
/data/fijiquakes.csv:
--------------------------------------------------------------------------------
   1 | obs	lat	long	depth	mag	stations
   2 | 1	-20.42	181.62	562	4.8	41
   3 | 2	-20.62	181.03	650	4.2	15
   4 | 3	-26.00	184.10	42	5.4	43
   5 | 4	-17.97	181.66	626	4.1	19
   6 | 5	-20.42	181.96	649	4.0	11
   7 | 6	-19.68	184.31	195	4.0	12
   8 | 7	-11.70	166.10	82	4.8	43
   9 | 8	-28.11	181.93	194	4.4	15
  10 | 9	-28.74	181.74	211	4.7	35
  11 | 10	-17.47	179.59	622	4.3	19
  12 | 11	-21.44	180.69	583	4.4	13
  13 | 12	-12.26	167.00	249	4.6	16
  14 | 13	-18.54	182.11	554	4.4	19
  15 | 14	-21.00	181.66	600	4.4	10
  16 | 15	-20.70	169.92	139	6.1	94
  17 | 16	-15.94	184.95	306	4.3	11
  18 | 17	-13.64	165.96	50	6.0	83
  19 | 18	-17.83	181.50	590	4.5	21
  20 | 19	-23.50	179.78	570	4.4	13
  21 | 20	-22.63	180.31	598	4.4	18
  22 | 21	-20.84	181.16	576	4.5	17
  23 | 22	-10.98	166.32	211	4.2	12
  24 | 23	-23.30	180.16	512	4.4	18
  25 | 24	-30.20	182.00	125	4.7	22
  26 | 25	-19.66	180.28	431	5.4	57
  27 | 26	-17.94	181.49	537	4.0	15
  28 | 27	-14.72	167.51	155	4.6	18
  29 | 28	-16.46	180.79	498	5.2	79
  30 | 29	-20.97	181.47	582	4.5	25
  31 | 30	-19.84	182.37	328	4.4	17
  32 | 31	-22.58	179.24	553	4.6	21
  33 | 32	-16.32	166.74	50	4.7	30
  34 | 33	-15.55	185.05	292	4.8	42
  35 | 34	-23.55	180.80	349	4.0	10
  36 | 35	-16.30	186.00	48	4.5	10
  37 | 36	-25.82	179.33	600	4.3	13
  38 | 37	-18.73	169.23	206	4.5	17
  39 | 38	-17.64	181.28	574	4.6	17
  40 | 39	-17.66	181.40	585	4.1	17
  41 | 40	-18.82	169.33	230	4.4	11
  42 | 41	-37.37	176.78	263	4.7	34
  43 | 42	-15.31	186.10	96	4.6	32
  44 | 43	-24.97	179.82	511	4.4	23
  45 | 44	-15.49	186.04	94	4.3	26
  46 | 45	-19.23	169.41	246	4.6	27
  47 | 46	-30.10	182.30	56	4.9	34
  48 | 47	-26.40	181.70	329	4.5	24
  49 | 48	-11.77	166.32	70	4.4	18
  50 | 49	-24.12	180.08	493	4.3	21
  51 | 50	-18.97	185.25	129	5.1	73
  52 | 51	-18.75	182.35	554	4.2	13
  53 | 52	-19.26	184.42	223	4.0	15
  54 | 53	-22.75	173.20	46	4.6	26
  55 | 54	-21.37	180.67	593	4.3	13
  56 | 55	-20.10	182.16	489	4.2	16
  57 | 56	-19.85	182.13	562	4.4	31
  58 | 57	-22.70	181.00	445	4.5	17
  59 | 58	-22.06	180.60	584	4.0	11
  60 | 59	-17.80	181.35	535	4.4	23
  61 | 60	-24.20	179.20	530	4.3	12
  62 | 61	-20.69	181.55	582	4.7	35
  63 | 62	-21.16	182.40	260	4.1	12
  64 | 63	-13.82	172.38	613	5.0	61
  65 | 64	-11.49	166.22	84	4.6	32
  66 | 65	-20.68	181.41	593	4.9	40
  67 | 66	-17.10	184.93	286	4.7	25
  68 | 67	-20.14	181.60	587	4.1	13
  69 | 68	-21.96	179.62	627	5.0	45
  70 | 69	-20.42	181.86	530	4.5	27
  71 | 70	-15.46	187.81	40	5.5	91
  72 | 71	-15.31	185.80	152	4.0	11
  73 | 72	-19.86	184.35	201	4.5	30
  74 | 73	-11.55	166.20	96	4.3	14
  75 | 74	-23.74	179.99	506	5.2	75
  76 | 75	-17.70	181.23	546	4.4	35
  77 | 76	-23.54	180.04	564	4.3	15
  78 | 77	-19.21	184.70	197	4.1	11
  79 | 78	-12.11	167.06	265	4.5	23
  80 | 79	-21.81	181.71	323	4.2	15
  81 | 80	-28.98	181.11	304	5.3	60
  82 | 81	-34.02	180.21	75	5.2	65
  83 | 82	-23.84	180.99	367	4.5	27
  84 | 83	-19.57	182.38	579	4.6	38
  85 | 84	-20.12	183.40	284	4.3	15
  86 | 85	-17.70	181.70	450	4.0	11
  87 | 86	-19.66	184.31	170	4.3	15
  88 | 87	-21.50	170.50	117	4.7	32
  89 | 88	-23.64	179.96	538	4.5	26
  90 | 89	-15.43	186.30	123	4.2	16
  91 | 90	-15.41	186.44	69	4.3	42
  92 | 91	-15.48	167.53	128	5.1	61
  93 | 92	-13.36	167.06	236	4.7	22
  94 | 93	-20.64	182.02	497	5.2	64
  95 | 94	-19.72	169.71	271	4.2	14
  96 | 95	-15.44	185.26	224	4.2	21
  97 | 96	-19.73	182.40	375	4.0	18
  98 | 97	-27.24	181.11	365	4.5	21
  99 | 98	-18.16	183.41	306	5.2	54
 100 | 99	-13.66	166.54	50	5.1	45
 101 | 100	-24.57	179.92	484	4.7	33
 102 | 101	-16.98	185.61	108	4.1	12
 103 | 102	-26.20	178.41	583	4.6	25
 104 | 103	-21.88	180.39	608	4.7	30
 105 | 104	-33.00	181.60	72	4.7	22
 106 | 105	-21.33	180.69	636	4.6	29
 107 | 106	-19.44	183.50	293	4.2	15
 108 | 107	-34.89	180.60	42	4.4	25
 109 | 108	-20.24	169.49	100	4.6	22
 110 | 109	-22.55	185.90	42	5.7	76
 111 | 110	-36.95	177.81	146	5.0	35
 112 | 111	-15.75	185.23	280	4.5	28
 113 | 112	-16.85	182.31	388	4.2	14
 114 | 113	-19.06	182.45	477	4.0	16
 115 | 114	-26.11	178.30	617	4.8	39
 116 | 115	-26.20	178.35	606	4.4	21
 117 | 116	-26.13	178.31	609	4.2	25
 118 | 117	-13.66	172.23	46	5.3	67
 119 | 118	-13.47	172.29	64	4.7	14
 120 | 119	-14.60	167.40	178	4.8	52
 121 | 120	-18.96	169.48	248	4.2	13
 122 | 121	-14.65	166.97	82	4.8	28
 123 | 122	-19.90	178.90	81	4.3	11
 124 | 123	-22.05	180.40	606	4.7	27
 125 | 124	-19.22	182.43	571	4.5	23
 126 | 125	-31.24	180.60	328	4.4	18
 127 | 126	-17.93	167.89	49	5.1	43
 128 | 127	-19.30	183.84	517	4.2	21
 129 | 128	-26.53	178.57	600	5.0	69
 130 | 129	-27.72	181.70	94	4.8	59
 131 | 130	-19.19	183.51	307	4.3	19
 132 | 131	-17.43	185.43	189	4.5	22
 133 | 132	-17.05	181.22	527	4.2	24
 134 | 133	-19.52	168.98	63	4.5	21
 135 | 134	-23.71	180.30	510	4.6	30
 136 | 135	-21.30	180.82	624	4.3	14
 137 | 136	-16.24	168.02	53	4.7	12
 138 | 137	-16.14	187.32	42	5.1	68
 139 | 138	-23.95	182.80	199	4.6	14
 140 | 139	-25.20	182.60	149	4.9	31
 141 | 140	-18.84	184.16	210	4.2	17
 142 | 141	-12.66	169.46	658	4.6	43
 143 | 142	-20.65	181.40	582	4.0	14
 144 | 143	-13.23	167.10	220	5.0	46
 145 | 144	-29.91	181.43	205	4.4	34
 146 | 145	-14.31	173.50	614	4.2	23
 147 | 146	-20.10	184.40	186	4.2	10
 148 | 147	-17.80	185.17	97	4.4	22
 149 | 148	-21.27	173.49	48	4.9	42
 150 | 149	-23.58	180.17	462	5.3	63
 151 | 150	-17.90	181.50	573	4.0	19
 152 | 151	-23.34	184.50	56	5.7	106
 153 | 152	-15.56	167.62	127	6.4	122
 154 | 153	-23.83	182.56	229	4.3	24
 155 | 154	-11.80	165.80	112	4.2	20
 156 | 155	-15.54	167.68	140	4.7	16
 157 | 156	-20.65	181.32	597	4.7	39
 158 | 157	-11.75	166.07	69	4.2	14
 159 | 158	-24.81	180.00	452	4.3	19
 160 | 159	-20.90	169.84	93	4.9	31
 161 | 160	-11.34	166.24	103	4.6	30
 162 | 161	-17.98	180.50	626	4.1	19
 163 | 162	-24.34	179.52	504	4.8	34
 164 | 163	-13.86	167.16	202	4.6	30
 165 | 164	-35.56	180.20	42	4.6	32
 166 | 165	-35.48	179.90	59	4.8	35
 167 | 166	-34.20	179.43	40	5.0	37
 168 | 167	-26.00	182.12	205	5.6	98
 169 | 168	-19.89	183.84	244	5.3	73
 170 | 169	-23.43	180.00	553	4.7	41
 171 | 170	-18.89	169.42	239	4.5	27
 172 | 171	-17.82	181.83	640	4.3	24
 173 | 172	-25.68	180.34	434	4.6	41
 174 | 173	-20.20	180.90	627	4.1	11
 175 | 174	-15.20	184.68	99	4.1	14
 176 | 175	-15.03	182.29	399	4.1	10
 177 | 176	-32.22	180.20	216	5.7	90
 178 | 177	-22.64	180.64	544	5.0	50
 179 | 178	-17.42	185.16	206	4.5	22
 180 | 179	-17.84	181.48	542	4.1	20
 181 | 180	-15.02	184.24	339	4.6	27
 182 | 181	-18.04	181.75	640	4.5	47
 183 | 182	-24.60	183.50	67	4.3	25
 184 | 183	-19.88	184.30	161	4.4	17
 185 | 184	-20.30	183.00	375	4.2	15
 186 | 185	-20.45	181.85	534	4.1	14
 187 | 186	-17.67	187.09	45	4.9	62
 188 | 187	-22.30	181.90	309	4.3	11
 189 | 188	-19.85	181.85	576	4.9	54
 190 | 189	-24.27	179.88	523	4.6	24
 191 | 190	-15.85	185.13	290	4.6	29
 192 | 191	-20.02	184.09	234	5.3	71
 193 | 192	-18.56	169.31	223	4.7	35
 194 | 193	-17.87	182.00	569	4.6	12
 195 | 194	-24.08	179.50	605	4.1	21
 196 | 195	-32.20	179.61	422	4.6	41
 197 | 196	-20.36	181.19	637	4.2	23
 198 | 197	-23.85	182.53	204	4.6	27
 199 | 198	-24.00	182.75	175	4.5	14
 200 | 199	-20.41	181.74	538	4.3	31
 201 | 200	-17.72	180.30	595	5.2	74
 202 | 201	-19.67	182.18	360	4.3	23
 203 | 202	-17.70	182.20	445	4.0	12
 204 | 203	-16.23	183.59	367	4.7	35
 205 | 204	-26.72	183.35	190	4.5	36
 206 | 205	-12.95	169.09	629	4.5	19
 207 | 206	-21.97	182.32	261	4.3	13
 208 | 207	-21.96	180.54	603	5.2	66
 209 | 208	-20.32	181.69	508	4.5	14
 210 | 209	-30.28	180.62	350	4.7	32
 211 | 210	-20.20	182.30	533	4.2	11
 212 | 211	-30.66	180.13	411	4.7	42
 213 | 212	-16.17	184.10	338	4.3	13
 214 | 213	-28.25	181.71	226	4.1	19
 215 | 214	-20.47	185.68	93	5.4	85
 216 | 215	-23.55	180.27	535	4.3	22
 217 | 216	-20.94	181.58	573	4.3	21
 218 | 217	-26.67	182.40	186	4.2	17
 219 | 218	-18.13	181.52	618	4.6	41
 220 | 219	-20.21	183.83	242	4.4	29
 221 | 220	-18.31	182.39	342	4.2	14
 222 | 221	-16.52	185.70	90	4.7	30
 223 | 222	-22.36	171.65	130	4.6	39
 224 | 223	-22.43	184.48	65	4.9	48
 225 | 224	-20.37	182.10	397	4.2	22
 226 | 225	-23.77	180.16	505	4.5	26
 227 | 226	-13.65	166.66	71	4.9	52
 228 | 227	-21.55	182.90	207	4.2	18
 229 | 228	-16.24	185.75	154	4.5	22
 230 | 229	-23.73	182.53	232	5.0	55
 231 | 230	-22.34	171.52	106	5.0	43
 232 | 231	-19.40	180.94	664	4.7	34
 233 | 232	-24.64	180.81	397	4.3	24
 234 | 233	-16.00	182.82	431	4.4	16
 235 | 234	-19.62	185.35	57	4.9	31
 236 | 235	-23.84	180.13	525	4.5	15
 237 | 236	-23.54	179.93	574	4.0	12
 238 | 237	-28.23	182.68	74	4.4	20
 239 | 238	-21.68	180.63	617	5.0	63
 240 | 239	-13.44	166.53	44	4.7	27
 241 | 240	-24.96	180.22	470	4.8	41
 242 | 241	-20.08	182.74	298	4.5	33
 243 | 242	-24.36	182.84	148	4.1	16
 244 | 243	-14.70	166.00	48	5.3	16
 245 | 244	-18.20	183.68	107	4.8	52
 246 | 245	-16.65	185.51	218	5.0	52
 247 | 246	-18.11	181.67	597	4.6	28
 248 | 247	-17.95	181.65	619	4.3	26
 249 | 248	-15.50	186.90	46	4.7	18
 250 | 249	-23.36	180.01	553	5.3	61
 251 | 250	-19.15	169.50	150	4.2	12
 252 | 251	-10.97	166.26	180	4.7	26
 253 | 252	-14.85	167.24	97	4.5	26
 254 | 253	-17.80	181.38	587	5.1	47
 255 | 254	-22.50	170.40	106	4.9	38
 256 | 255	-29.10	182.10	179	4.4	19
 257 | 256	-20.32	180.88	680	4.2	22
 258 | 257	-16.09	184.89	304	4.6	34
 259 | 258	-19.18	169.33	254	4.7	35
 260 | 259	-23.81	179.36	521	4.2	23
 261 | 260	-23.79	179.89	526	4.9	43
 262 | 261	-19.02	184.23	270	5.1	72
 263 | 262	-20.90	181.51	548	4.7	32
 264 | 263	-19.06	169.01	158	4.4	10
 265 | 264	-17.88	181.47	562	4.4	27
 266 | 265	-19.41	183.05	300	4.2	16
 267 | 266	-26.17	184.20	65	4.9	37
 268 | 267	-14.95	167.24	130	4.6	16
 269 | 268	-18.73	168.80	82	4.4	14
 270 | 269	-20.21	182.37	482	4.6	37
 271 | 270	-21.29	180.85	607	4.5	23
 272 | 271	-19.76	181.41	105	4.4	15
 273 | 272	-22.09	180.38	590	4.9	35
 274 | 273	-23.80	179.90	498	4.1	12
 275 | 274	-20.16	181.99	504	4.2	11
 276 | 275	-22.13	180.38	577	5.7	104
 277 | 276	-17.44	181.40	529	4.6	25
 278 | 277	-23.33	180.18	528	5.0	59
 279 | 278	-24.78	179.22	492	4.3	16
 280 | 279	-22.00	180.52	561	4.5	19
 281 | 280	-19.13	182.51	579	5.2	56
 282 | 281	-30.72	180.10	413	4.4	22
 283 | 282	-22.32	180.54	565	4.2	12
 284 | 283	-16.45	177.77	138	4.6	17
 285 | 284	-17.70	185.00	383	4.0	10
 286 | 285	-17.95	184.68	260	4.4	21
 287 | 286	-24.40	179.85	522	4.7	29
 288 | 287	-19.30	180.60	671	4.2	16
 289 | 288	-21.13	185.32	123	4.7	36
 290 | 289	-18.07	181.57	572	4.5	26
 291 | 290	-20.60	182.28	529	5.0	50
 292 | 291	-18.48	181.49	641	5.0	49
 293 | 292	-13.34	166.20	67	4.8	18
 294 | 293	-20.92	181.50	546	4.6	31
 295 | 294	-25.31	179.69	507	4.6	35
 296 | 295	-15.24	186.21	158	5.0	57
 297 | 296	-16.40	185.86	148	5.0	47
 298 | 297	-24.57	178.40	562	5.6	80
 299 | 298	-17.94	181.51	601	4.0	16
 300 | 299	-30.64	181.20	175	4.0	16
 301 | 300	-18.64	169.32	260	4.6	23
 302 | 301	-13.09	169.28	654	4.4	22
 303 | 302	-19.68	184.14	242	4.8	40
 304 | 303	-16.44	185.74	126	4.7	30
 305 | 304	-21.09	181.38	555	4.6	15
 306 | 305	-14.99	171.39	637	4.3	21
 307 | 306	-23.30	179.70	500	4.7	29
 308 | 307	-17.68	181.36	515	4.1	19
 309 | 308	-22.00	180.53	583	4.9	20
 310 | 309	-21.38	181.39	501	4.6	36
 311 | 310	-32.62	181.50	55	4.8	26
 312 | 311	-13.05	169.58	644	4.9	68
 313 | 312	-12.93	169.63	641	5.1	57
 314 | 313	-18.60	181.91	442	5.4	82
 315 | 314	-21.34	181.41	464	4.5	21
 316 | 315	-21.48	183.78	200	4.9	54
 317 | 316	-17.40	181.02	479	4.4	14
 318 | 317	-17.32	181.03	497	4.1	13
 319 | 318	-18.77	169.24	218	5.3	53
 320 | 319	-26.16	179.50	492	4.5	25
 321 | 320	-12.59	167.10	325	4.9	26
 322 | 321	-14.82	167.32	123	4.8	28
 323 | 322	-21.79	183.48	210	5.2	69
 324 | 323	-19.83	182.04	575	4.4	23
 325 | 324	-29.50	182.31	129	4.4	14
 326 | 325	-12.49	166.36	74	4.9	55
 327 | 326	-26.10	182.30	49	4.4	11
 328 | 327	-21.04	181.20	483	4.2	10
 329 | 328	-10.78	165.77	93	4.6	20
 330 | 329	-20.76	185.77	118	4.6	15
 331 | 330	-11.41	166.24	83	5.3	55
 332 | 331	-19.10	183.87	61	5.3	42
 333 | 332	-23.91	180.00	534	4.5	11
 334 | 333	-27.33	182.60	42	4.4	11
 335 | 334	-12.25	166.60	219	5.0	28
 336 | 335	-23.49	179.07	544	5.1	58
 337 | 336	-27.18	182.18	56	4.5	14
 338 | 337	-25.80	182.10	68	4.5	26
 339 | 338	-27.19	182.18	69	5.4	68
 340 | 339	-27.27	182.38	45	4.5	16
 341 | 340	-27.10	182.18	43	4.7	17
 342 | 341	-27.22	182.28	65	4.2	14
 343 | 342	-27.38	181.70	80	4.8	13
 344 | 343	-27.27	182.50	51	4.5	13
 345 | 344	-27.54	182.50	68	4.3	12
 346 | 345	-27.20	182.39	69	4.3	14
 347 | 346	-27.71	182.47	103	4.3	11
 348 | 347	-27.60	182.40	61	4.6	11
 349 | 348	-27.38	182.39	69	4.5	12
 350 | 349	-21.54	185.48	51	5.0	29
 351 | 350	-27.21	182.43	55	4.6	10
 352 | 351	-28.96	182.61	54	4.6	15
 353 | 352	-12.01	166.29	59	4.9	27
 354 | 353	-17.46	181.32	573	4.1	17
 355 | 354	-30.17	182.02	56	5.5	68
 356 | 355	-27.27	182.36	65	4.7	21
 357 | 356	-17.79	181.32	587	5.0	49
 358 | 357	-22.19	171.40	150	5.1	49
 359 | 358	-17.10	182.68	403	5.5	82
 360 | 359	-27.18	182.53	60	4.6	21
 361 | 360	-11.64	166.47	130	4.7	19
 362 | 361	-17.98	181.58	590	4.2	14
 363 | 362	-16.90	185.72	135	4.0	22
 364 | 363	-21.98	179.60	583	5.4	67
 365 | 364	-32.14	179.90	406	4.3	19
 366 | 365	-18.80	169.21	221	4.4	16
 367 | 366	-26.78	183.61	40	4.6	22
 368 | 367	-20.43	182.37	502	5.1	48
 369 | 368	-18.30	183.20	103	4.5	14
 370 | 369	-15.83	182.51	423	4.2	21
 371 | 370	-23.44	182.93	158	4.1	20
 372 | 371	-23.73	179.99	527	5.1	49
 373 | 372	-19.89	184.08	219	5.4	105
 374 | 373	-17.59	181.09	536	5.1	61
 375 | 374	-19.77	181.40	630	5.1	54
 376 | 375	-20.31	184.06	249	4.4	21
 377 | 376	-15.33	186.75	48	5.7	123
 378 | 377	-18.20	181.60	553	4.4	14
 379 | 378	-15.36	186.66	112	5.1	57
 380 | 379	-15.29	186.42	153	4.6	31
 381 | 380	-15.36	186.71	130	5.5	95
 382 | 381	-16.24	167.95	188	5.1	68
 383 | 382	-13.47	167.14	226	4.4	26
 384 | 383	-25.50	182.82	124	5.0	25
 385 | 384	-14.32	167.33	204	5.0	49
 386 | 385	-20.04	182.01	605	5.1	49
 387 | 386	-28.83	181.66	221	5.1	63
 388 | 387	-17.82	181.49	573	4.2	14
 389 | 388	-27.23	180.98	401	4.5	39
 390 | 389	-10.72	165.99	195	4.0	14
 391 | 390	-27.00	183.88	56	4.9	36
 392 | 391	-20.36	186.16	102	4.3	21
 393 | 392	-27.17	183.68	44	4.8	27
 394 | 393	-20.94	181.26	556	4.4	21
 395 | 394	-17.46	181.90	417	4.2	14
 396 | 395	-21.04	181.20	591	4.9	45
 397 | 396	-23.70	179.60	646	4.2	21
 398 | 397	-17.72	181.42	565	5.3	89
 399 | 398	-15.87	188.13	52	5.0	30
 400 | 399	-17.84	181.30	535	5.7	112
 401 | 400	-13.45	170.30	641	5.3	93
 402 | 401	-30.80	182.16	41	4.7	24
 403 | 402	-11.63	166.14	109	4.6	36
 404 | 403	-30.40	181.40	40	4.3	17
 405 | 404	-26.18	178.59	548	5.4	65
 406 | 405	-15.70	184.50	118	4.4	30
 407 | 406	-17.95	181.50	593	4.3	16
 408 | 407	-20.51	182.30	492	4.3	23
 409 | 408	-15.36	167.51	123	4.7	28
 410 | 409	-23.61	180.23	475	4.4	26
 411 | 410	-33.20	181.60	153	4.2	21
 412 | 411	-17.68	186.80	112	4.5	35
 413 | 412	-22.24	184.56	99	4.8	57
 414 | 413	-20.07	169.14	66	4.8	37
 415 | 414	-25.04	180.10	481	4.3	15
 416 | 415	-21.50	185.20	139	4.4	15
 417 | 416	-14.28	167.26	211	5.1	51
 418 | 417	-14.43	167.26	151	4.4	17
 419 | 418	-32.70	181.70	211	4.4	40
 420 | 419	-34.10	181.80	246	4.3	23
 421 | 420	-19.70	186.20	47	4.8	19
 422 | 421	-24.19	180.38	484	4.3	27
 423 | 422	-26.60	182.77	119	4.5	29
 424 | 423	-17.04	186.80	70	4.1	22
 425 | 424	-22.10	179.71	579	5.1	58
 426 | 425	-32.60	180.90	57	4.7	44
 427 | 426	-33.00	182.40	176	4.6	28
 428 | 427	-20.58	181.24	602	4.7	44
 429 | 428	-20.61	182.60	488	4.6	12
 430 | 429	-19.47	169.15	149	4.4	15
 431 | 430	-17.47	180.96	546	4.2	23
 432 | 431	-18.40	183.40	343	4.1	10
 433 | 432	-23.33	180.26	530	4.7	22
 434 | 433	-18.55	182.23	563	4.0	17
 435 | 434	-26.16	178.47	537	4.8	33
 436 | 435	-21.80	183.20	325	4.4	19
 437 | 436	-27.63	182.93	80	4.3	14
 438 | 437	-18.89	169.48	259	4.4	21
 439 | 438	-20.30	182.30	476	4.5	10
 440 | 439	-20.56	182.04	499	4.5	29
 441 | 440	-16.10	185.32	257	4.7	30
 442 | 441	-12.66	166.37	165	4.3	18
 443 | 442	-21.05	184.68	136	4.7	29
 444 | 443	-17.97	168.52	146	4.8	33
 445 | 444	-19.83	182.54	524	4.6	14
 446 | 445	-22.55	183.81	82	5.1	68
 447 | 446	-22.28	183.52	90	4.7	19
 448 | 447	-15.72	185.64	138	4.3	21
 449 | 448	-20.85	181.59	499	5.1	91
 450 | 449	-21.11	181.50	538	5.5	104
 451 | 450	-25.31	180.15	467	4.5	25
 452 | 451	-26.46	182.50	184	4.3	11
 453 | 452	-24.09	179.68	538	4.3	21
 454 | 453	-16.96	167.70	45	4.7	23
 455 | 454	-23.19	182.80	237	4.3	18
 456 | 455	-20.81	184.70	162	4.3	20
 457 | 456	-15.03	167.32	136	4.6	20
 458 | 457	-18.06	181.59	604	4.5	23
 459 | 458	-19.00	185.60	107	4.5	15
 460 | 459	-23.53	179.99	538	5.4	87
 461 | 460	-18.18	180.63	639	4.6	39
 462 | 461	-15.66	186.80	45	4.4	11
 463 | 462	-18.00	180.62	636	5.0	100
 464 | 463	-18.08	180.70	628	5.2	72
 465 | 464	-18.05	180.86	632	4.4	15
 466 | 465	-29.90	181.16	215	5.1	51
 467 | 466	-20.90	181.90	556	4.4	17
 468 | 467	-15.61	167.50	135	4.4	21
 469 | 468	-16.03	185.43	297	4.8	25
 470 | 469	-17.68	181.11	568	4.4	22
 471 | 470	-31.94	180.57	168	4.7	39
 472 | 471	-19.14	184.36	269	4.7	31
 473 | 472	-18.00	185.48	143	4.4	29
 474 | 473	-16.95	185.94	95	4.3	12
 475 | 474	-10.79	166.06	142	5.0	40
 476 | 475	-20.83	185.90	104	4.5	19
 477 | 476	-32.90	181.60	169	4.6	27
 478 | 477	-37.93	177.47	65	5.4	65
 479 | 478	-29.09	183.20	54	4.6	23
 480 | 479	-23.56	180.23	474	4.5	13
 481 | 480	-19.60	185.20	125	4.4	13
 482 | 481	-21.39	180.68	617	4.5	18
 483 | 482	-14.85	184.87	294	4.1	10
 484 | 483	-22.70	183.30	180	4.0	13
 485 | 484	-32.42	181.21	47	4.9	39
 486 | 485	-17.90	181.30	593	4.1	13
 487 | 486	-23.58	183.40	94	5.2	79
 488 | 487	-34.40	180.50	201	4.4	41
 489 | 488	-17.61	181.20	537	4.1	11
 490 | 489	-21.07	181.13	594	4.9	43
 491 | 490	-13.84	170.62	638	4.6	20
 492 | 491	-30.24	181.63	80	4.5	17
 493 | 492	-18.49	169.04	211	4.8	30
 494 | 493	-23.45	180.23	520	4.2	19
 495 | 494	-16.04	183.54	384	4.2	23
 496 | 495	-17.14	185.31	223	4.1	15
 497 | 496	-22.54	172.91	54	5.5	71
 498 | 497	-15.90	185.30	57	4.4	19
 499 | 498	-30.04	181.20	49	4.8	20
 500 | 499	-24.03	180.22	508	4.2	23
 501 | 500	-18.89	184.46	242	4.8	36
 502 | 501	-16.51	187.10	62	4.9	46
 503 | 502	-20.10	186.30	63	4.6	19
 504 | 503	-21.06	183.81	203	4.5	34
 505 | 504	-13.07	166.87	132	4.4	24
 506 | 505	-23.46	180.09	543	4.6	28
 507 | 506	-19.41	182.30	589	4.2	19
 508 | 507	-11.81	165.98	51	4.7	28
 509 | 508	-11.76	165.96	45	4.4	51
 510 | 509	-12.08	165.76	63	4.5	51
 511 | 510	-25.59	180.02	485	4.9	48
 512 | 511	-26.54	183.63	66	4.7	34
 513 | 512	-20.90	184.28	58	5.5	92
 514 | 513	-16.99	187.00	70	4.7	30
 515 | 514	-23.46	180.17	541	4.6	32
 516 | 515	-17.81	181.82	598	4.1	14
 517 | 516	-15.17	187.20	50	4.7	28
 518 | 517	-11.67	166.02	102	4.6	21
 519 | 518	-20.75	184.52	144	4.3	25
 520 | 519	-19.50	186.90	58	4.4	20
 521 | 520	-26.18	179.79	460	4.7	44
 522 | 521	-20.66	185.77	69	4.3	25
 523 | 522	-19.22	182.54	570	4.1	22
 524 | 523	-24.68	183.33	70	4.7	30
 525 | 524	-15.43	167.38	137	4.5	16
 526 | 525	-32.45	181.15	41	5.5	81
 527 | 526	-21.31	180.84	586	4.5	17
 528 | 527	-15.44	167.18	140	4.6	44
 529 | 528	-13.26	167.01	213	5.1	70
 530 | 529	-15.26	183.13	393	4.4	28
 531 | 530	-33.57	180.80	51	4.7	35
 532 | 531	-15.77	167.01	64	5.5	73
 533 | 532	-15.79	166.83	45	4.6	39
 534 | 533	-21.00	183.20	296	4.0	16
 535 | 534	-16.28	166.94	50	4.6	24
 536 | 535	-23.28	184.60	44	4.8	34
 537 | 536	-16.10	167.25	68	4.7	36
 538 | 537	-17.70	181.31	549	4.7	33
 539 | 538	-15.96	166.69	150	4.2	20
 540 | 539	-15.95	167.34	47	5.4	87
 541 | 540	-17.56	181.59	543	4.6	34
 542 | 541	-15.90	167.42	40	5.5	86
 543 | 542	-15.29	166.90	100	4.2	15
 544 | 543	-15.86	166.85	85	4.5	22
 545 | 544	-16.20	166.80	98	4.5	21
 546 | 545	-15.71	166.91	58	4.8	20
 547 | 546	-16.45	167.54	125	4.6	18
 548 | 547	-11.54	166.18	89	5.4	80
 549 | 548	-19.61	181.91	590	4.6	34
 550 | 549	-15.61	187.15	49	5.0	30
 551 | 550	-21.16	181.41	543	4.3	17
 552 | 551	-20.65	182.22	506	4.3	24
 553 | 552	-20.33	168.71	40	4.8	38
 554 | 553	-15.08	166.62	42	4.7	23
 555 | 554	-23.28	184.61	76	4.7	36
 556 | 555	-23.44	184.60	63	4.8	27
 557 | 556	-23.12	184.42	104	4.2	17
 558 | 557	-23.65	184.46	93	4.2	16
 559 | 558	-22.91	183.95	64	5.9	118
 560 | 559	-22.06	180.47	587	4.6	28
 561 | 560	-13.56	166.49	83	4.5	25
 562 | 561	-17.99	181.57	579	4.9	49
 563 | 562	-23.92	184.47	40	4.7	17
 564 | 563	-30.69	182.10	62	4.9	25
 565 | 564	-21.92	182.80	273	5.3	78
 566 | 565	-25.04	180.97	393	4.2	21
 567 | 566	-19.92	183.91	264	4.2	23
 568 | 567	-27.75	182.26	174	4.5	18
 569 | 568	-17.71	181.18	574	5.2	67
 570 | 569	-19.60	183.84	309	4.5	23
 571 | 570	-34.68	179.82	75	5.6	79
 572 | 571	-14.46	167.26	195	5.2	87
 573 | 572	-18.85	187.55	44	4.8	35
 574 | 573	-17.02	182.41	420	4.5	29
 575 | 574	-20.41	186.51	63	5.0	28
 576 | 575	-18.18	182.04	609	4.4	26
 577 | 576	-16.49	187.80	40	4.5	18
 578 | 577	-17.74	181.31	575	4.6	42
 579 | 578	-20.49	181.69	559	4.5	24
 580 | 579	-18.51	182.64	405	5.2	74
 581 | 580	-27.28	183.40	70	5.1	54
 582 | 581	-15.90	167.16	41	4.8	42
 583 | 582	-20.57	181.33	605	4.3	18
 584 | 583	-11.25	166.36	130	5.1	55
 585 | 584	-20.04	181.87	577	4.7	19
 586 | 585	-20.89	181.25	599	4.6	20
 587 | 586	-16.62	186.74	82	4.8	51
 588 | 587	-20.09	168.75	50	4.6	23
 589 | 588	-24.96	179.87	480	4.4	25
 590 | 589	-20.95	181.42	559	4.6	27
 591 | 590	-23.31	179.27	566	5.1	49
 592 | 591	-20.95	181.06	611	4.3	20
 593 | 592	-21.58	181.90	409	4.4	19
 594 | 593	-13.62	167.15	209	4.7	30
 595 | 594	-12.72	166.28	70	4.8	47
 596 | 595	-21.79	185.00	74	4.1	15
 597 | 596	-20.48	169.76	134	4.6	33
 598 | 597	-12.84	166.78	150	4.9	35
 599 | 598	-17.02	182.93	406	4.0	17
 600 | 599	-23.89	182.39	243	4.7	32
 601 | 600	-23.07	184.03	89	4.7	32
 602 | 601	-27.98	181.96	53	5.2	89
 603 | 602	-28.10	182.25	68	4.6	18
 604 | 603	-21.24	180.81	605	4.6	34
 605 | 604	-21.24	180.86	615	4.9	23
 606 | 605	-19.89	174.46	546	5.7	99
 607 | 606	-32.82	179.80	176	4.7	26
 608 | 607	-22.00	185.50	52	4.4	18
 609 | 608	-21.57	185.62	66	4.9	38
 610 | 609	-24.50	180.92	377	4.8	43
 611 | 610	-33.03	180.20	186	4.6	27
 612 | 611	-30.09	182.40	51	4.4	18
 613 | 612	-22.75	170.99	67	4.8	35
 614 | 613	-17.99	168.98	234	4.7	28
 615 | 614	-19.60	181.87	597	4.2	18
 616 | 615	-15.65	186.26	64	5.1	54
 617 | 616	-17.78	181.53	511	4.8	56
 618 | 617	-22.04	184.91	47	4.9	47
 619 | 618	-20.06	168.69	49	5.1	49
 620 | 619	-18.07	181.54	546	4.3	28
 621 | 620	-12.85	165.67	75	4.4	30
 622 | 621	-33.29	181.30	60	4.7	33
 623 | 622	-34.63	179.10	278	4.7	24
 624 | 623	-24.18	179.02	550	5.3	86
 625 | 624	-23.78	180.31	518	5.1	71
 626 | 625	-22.37	171.50	116	4.9	38
 627 | 626	-23.97	179.91	518	4.5	23
 628 | 627	-34.12	181.75	75	4.7	41
 629 | 628	-25.25	179.86	491	4.2	23
 630 | 629	-22.87	172.65	56	5.1	50
 631 | 630	-18.48	182.37	376	4.8	57
 632 | 631	-21.46	181.02	584	4.2	18
 633 | 632	-28.56	183.47	48	4.8	56
 634 | 633	-28.56	183.59	53	4.4	20
 635 | 634	-21.30	180.92	617	4.5	26
 636 | 635	-20.08	183.22	294	4.3	18
 637 | 636	-18.82	182.21	417	5.6	129
 638 | 637	-19.51	183.97	280	4.0	16
 639 | 638	-12.05	167.39	332	5.0	36
 640 | 639	-17.40	186.54	85	4.2	28
 641 | 640	-23.93	180.18	525	4.6	31
 642 | 641	-21.23	181.09	613	4.6	18
 643 | 642	-16.23	167.91	182	4.5	28
 644 | 643	-28.15	183.40	57	5.0	32
 645 | 644	-20.81	185.01	79	4.7	42
 646 | 645	-20.72	181.41	595	4.6	36
 647 | 646	-23.29	184.00	164	4.8	50
 648 | 647	-38.46	176.03	148	4.6	44
 649 | 648	-15.48	186.73	82	4.4	17
 650 | 649	-37.03	177.52	153	5.6	87
 651 | 650	-20.48	181.38	556	4.2	13
 652 | 651	-18.12	181.88	649	5.4	88
 653 | 652	-18.17	181.98	651	4.8	43
 654 | 653	-11.40	166.07	93	5.6	94
 655 | 654	-23.10	180.12	533	4.4	27
 656 | 655	-14.28	170.34	642	4.7	29
 657 | 656	-22.87	171.72	47	4.6	27
 658 | 657	-17.59	180.98	548	5.1	79
 659 | 658	-27.60	182.10	154	4.6	22
 660 | 659	-17.94	180.60	627	4.5	29
 661 | 660	-17.88	180.58	622	4.2	23
 662 | 661	-30.01	180.80	286	4.8	43
 663 | 662	-19.19	182.30	390	4.9	48
 664 | 663	-18.14	180.87	624	5.5	105
 665 | 664	-23.46	180.11	539	5.0	41
 666 | 665	-18.44	181.04	624	4.2	21
 667 | 666	-18.21	180.87	631	5.2	69
 668 | 667	-18.26	180.98	631	4.8	36
 669 | 668	-15.85	184.83	299	4.4	30
 670 | 669	-23.82	180.09	498	4.8	40
 671 | 670	-18.60	184.28	255	4.4	31
 672 | 671	-17.80	181.32	539	4.1	12
 673 | 672	-10.78	166.10	195	4.9	45
 674 | 673	-18.12	181.71	594	4.6	24
 675 | 674	-19.34	182.62	573	4.5	32
 676 | 675	-15.34	167.10	128	5.3	18
 677 | 676	-24.97	182.85	137	4.8	40
 678 | 677	-15.97	186.08	143	4.6	41
 679 | 678	-23.47	180.24	511	4.8	37
 680 | 679	-23.11	179.15	564	4.7	17
 681 | 680	-20.54	181.66	559	4.9	50
 682 | 681	-18.92	169.37	248	5.3	60
 683 | 682	-20.16	184.27	210	4.4	27
 684 | 683	-25.48	180.94	390	4.6	33
 685 | 684	-18.19	181.74	616	4.3	17
 686 | 685	-15.35	186.40	98	4.4	17
 687 | 686	-18.69	169.10	218	4.2	27
 688 | 687	-18.89	181.24	655	4.1	14
 689 | 688	-17.61	183.32	356	4.2	15
 690 | 689	-20.93	181.54	564	5.0	64
 691 | 690	-17.60	181.50	548	4.1	10
 692 | 691	-17.96	181.40	655	4.3	20
 693 | 692	-18.80	182.41	385	5.2	67
 694 | 693	-20.61	182.44	518	4.2	10
 695 | 694	-20.74	181.53	598	4.5	36
 696 | 695	-25.23	179.86	476	4.4	29
 697 | 696	-23.90	179.90	579	4.4	16
 698 | 697	-18.07	181.58	603	5.0	65
 699 | 698	-15.43	185.19	249	4.0	11
 700 | 699	-14.30	167.32	208	4.8	25
 701 | 700	-18.04	181.57	587	5.0	51
 702 | 701	-13.90	167.18	221	4.2	21
 703 | 702	-17.64	177.01	545	5.2	91
 704 | 703	-17.98	181.51	586	5.2	68
 705 | 704	-25.00	180.00	488	4.5	10
 706 | 705	-19.45	184.48	246	4.3	15
 707 | 706	-16.11	187.48	61	4.5	19
 708 | 707	-23.73	179.98	524	4.6	11
 709 | 708	-17.74	186.78	104	5.1	71
 710 | 709	-21.56	183.23	271	4.4	36
 711 | 710	-20.97	181.72	487	4.3	16
 712 | 711	-15.45	186.73	83	4.7	37
 713 | 712	-15.93	167.91	183	5.6	109
 714 | 713	-21.47	185.86	55	4.9	46
 715 | 714	-21.44	170.45	166	5.1	22
 716 | 715	-22.16	180.49	586	4.6	13
 717 | 716	-13.36	172.76	618	4.4	18
 718 | 717	-21.22	181.51	524	4.8	49
 719 | 718	-26.10	182.50	133	4.2	17
 720 | 719	-18.35	185.27	201	4.7	57
 721 | 720	-17.20	182.90	383	4.1	11
 722 | 721	-22.42	171.40	86	4.7	33
 723 | 722	-17.91	181.48	555	4.0	17
 724 | 723	-26.53	178.30	605	4.9	43
 725 | 724	-26.50	178.29	609	5.0	50
 726 | 725	-16.31	168.08	204	4.5	16
 727 | 726	-18.76	169.71	287	4.4	23
 728 | 727	-17.10	182.80	390	4.0	14
 729 | 728	-19.28	182.78	348	4.5	30
 730 | 729	-23.50	180.00	550	4.7	23
 731 | 730	-21.26	181.69	487	4.4	20
 732 | 731	-17.97	181.48	578	4.7	43
 733 | 732	-26.02	181.20	361	4.7	32
 734 | 733	-30.30	180.80	275	4.0	14
 735 | 734	-24.89	179.67	498	4.2	14
 736 | 735	-14.57	167.24	162	4.5	18
 737 | 736	-15.40	186.87	78	4.7	44
 738 | 737	-22.06	183.95	134	4.5	17
 739 | 738	-25.14	178.42	554	4.1	15
 740 | 739	-20.30	181.40	608	4.6	13
 741 | 740	-25.28	181.17	367	4.3	25
 742 | 741	-20.63	181.61	599	4.6	30
 743 | 742	-19.02	186.83	45	5.2	65
 744 | 743	-22.10	185.30	50	4.6	22
 745 | 744	-38.59	175.70	162	4.7	36
 746 | 745	-19.30	183.00	302	5.0	65
 747 | 746	-31.03	181.59	57	5.2	49
 748 | 747	-30.51	181.30	203	4.4	20
 749 | 748	-22.55	183.34	66	4.6	18
 750 | 749	-22.14	180.64	591	4.5	18
 751 | 750	-25.60	180.30	440	4.0	12
 752 | 751	-18.04	181.84	611	4.2	20
 753 | 752	-21.29	185.77	57	5.3	69
 754 | 753	-21.08	180.85	627	5.9	119
 755 | 754	-20.64	169.66	89	4.9	42
 756 | 755	-24.41	180.03	500	4.5	34
 757 | 756	-12.16	167.03	264	4.4	14
 758 | 757	-17.10	185.90	127	5.4	75
 759 | 758	-21.13	185.60	85	5.3	86
 760 | 759	-12.34	167.43	50	5.1	47
 761 | 760	-16.43	186.73	75	4.1	20
 762 | 761	-20.70	184.30	182	4.3	17
 763 | 762	-21.18	180.92	619	4.5	18
 764 | 763	-17.78	185.33	223	4.1	10
 765 | 764	-21.57	183.86	156	5.1	70
 766 | 765	-13.70	166.75	46	5.3	71
 767 | 766	-12.27	167.41	50	4.5	29
 768 | 767	-19.10	184.52	230	4.1	16
 769 | 768	-19.85	184.51	184	4.4	26
 770 | 769	-11.37	166.55	188	4.7	24
 771 | 770	-20.70	186.30	80	4.0	10
 772 | 771	-20.24	185.10	86	5.1	61
 773 | 772	-16.40	182.73	391	4.0	16
 774 | 773	-19.60	184.53	199	4.3	21
 775 | 774	-21.63	180.77	592	4.3	21
 776 | 775	-21.60	180.50	595	4.0	22
 777 | 776	-21.77	181.00	618	4.1	10
 778 | 777	-21.80	183.60	213	4.4	17
 779 | 778	-21.05	180.90	616	4.3	10
 780 | 779	-10.80	165.80	175	4.2	12
 781 | 780	-17.90	181.50	589	4.0	12
 782 | 781	-22.26	171.44	83	4.5	25
 783 | 782	-22.33	171.46	119	4.7	32
 784 | 783	-24.04	184.85	70	5.0	48
 785 | 784	-20.40	186.10	74	4.3	22
 786 | 785	-15.00	184.62	40	5.1	54
 787 | 786	-27.87	183.40	87	4.7	34
 788 | 787	-14.12	166.64	63	5.3	69
 789 | 788	-23.61	180.27	537	5.0	63
 790 | 789	-21.56	185.50	47	4.5	29
 791 | 790	-21.19	181.58	490	5.0	77
 792 | 791	-18.07	181.65	593	4.1	16
 793 | 792	-26.00	178.43	644	4.9	27
 794 | 793	-20.21	181.90	576	4.1	16
 795 | 794	-28.00	182.00	199	4.0	16
 796 | 795	-20.74	180.70	589	4.4	27
 797 | 796	-31.80	180.60	178	4.5	19
 798 | 797	-18.91	169.46	248	4.4	33
 799 | 798	-20.45	182.10	500	4.5	37
 800 | 799	-22.90	183.80	71	4.3	19
 801 | 800	-18.11	181.63	568	4.3	36
 802 | 801	-23.80	184.70	42	5.0	36
 803 | 802	-23.42	180.21	510	4.5	37
 804 | 803	-23.20	184.80	97	4.5	13
 805 | 804	-12.93	169.52	663	4.4	30
 806 | 805	-21.14	181.06	625	4.5	35
 807 | 806	-19.13	184.97	210	4.1	22
 808 | 807	-21.08	181.30	557	4.9	78
 809 | 808	-20.07	181.75	582	4.7	27
 810 | 809	-20.90	182.02	402	4.3	18
 811 | 810	-25.04	179.84	474	4.6	32
 812 | 811	-21.85	180.89	577	4.6	43
 813 | 812	-19.34	186.59	56	5.2	49
 814 | 813	-15.83	167.10	43	4.5	19
 815 | 814	-23.73	183.00	118	4.3	11
 816 | 815	-18.10	181.72	544	4.6	52
 817 | 816	-22.12	180.49	532	4.0	14
 818 | 817	-15.39	185.10	237	4.5	39
 819 | 818	-16.21	186.52	111	4.8	30
 820 | 819	-21.75	180.67	595	4.6	30
 821 | 820	-22.10	180.40	603	4.1	11
 822 | 821	-24.97	179.54	505	4.9	50
 823 | 822	-19.36	186.36	100	4.7	40
 824 | 823	-22.14	179.62	587	4.1	23
 825 | 824	-21.48	182.44	364	4.3	20
 826 | 825	-18.54	168.93	100	4.4	17
 827 | 826	-21.62	182.40	350	4.0	12
 828 | 827	-13.40	166.90	228	4.8	15
 829 | 828	-15.50	185.30	93	4.4	25
 830 | 829	-15.67	185.23	66	4.4	34
 831 | 830	-21.78	183.11	225	4.6	21
 832 | 831	-30.63	180.90	334	4.2	28
 833 | 832	-15.70	185.10	70	4.1	15
 834 | 833	-19.20	184.37	220	4.2	18
 835 | 834	-19.70	182.44	397	4.0	12
 836 | 835	-19.40	182.29	326	4.1	15
 837 | 836	-15.85	185.90	121	4.1	17
 838 | 837	-17.38	168.63	209	4.7	29
 839 | 838	-24.33	179.97	510	4.8	44
 840 | 839	-20.89	185.26	54	5.1	44
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1000 | 999	-17.40	187.80	40	4.5	14
1001 | 1000	-21.59	170.56	165	6.0	119
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 232 | L 48.578125 21.734375 
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 240 | Q 15.4375 19.96875 14.203125 18.09375 
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 280 |        <use x="166.845703" xlink:href="#ArialMT-74"/>
 281 |        <use x="194.628906" xlink:href="#ArialMT-73"/>
 282 |        <use x="244.628906" xlink:href="#ArialMT-74"/>
 283 |        <use x="272.412109" xlink:href="#ArialMT-72"/>
 284 |        <use x="305.712891" xlink:href="#ArialMT-61"/>
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 342 | Q 9.46875 46.734375 15.15625 49.875 
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 354 | Q 39.5 12.40625 40.4375 19 
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 359 |        <use xlink:href="#ArialMT-70"/>
 360 |        <use x="55.615234" xlink:href="#ArialMT-61"/>
 361 |        <use x="111.230469" xlink:href="#ArialMT-72"/>
 362 |        <use x="144.53125" xlink:href="#ArialMT-61"/>
 363 |        <use x="200.146484" xlink:href="#ArialMT-6d"/>
 364 |        <use x="283.447266" xlink:href="#ArialMT-65"/>
 365 |        <use x="339.0625" xlink:href="#ArialMT-74"/>
 366 |        <use x="366.845703" xlink:href="#ArialMT-72"/>
 367 |        <use x="400.146484" xlink:href="#ArialMT-69"/>
 368 |        <use x="422.363281" xlink:href="#ArialMT-63"/>
 369 |        <use x="472.363281" xlink:href="#ArialMT-20"/>
 370 |        <use x="500.146484" xlink:href="#ArialMT-62"/>
 371 |        <use x="555.761719" xlink:href="#ArialMT-6f"/>
 372 |        <use x="611.376953" xlink:href="#ArialMT-6f"/>
 373 |        <use x="666.992188" xlink:href="#ArialMT-74"/>
 374 |        <use x="694.775391" xlink:href="#ArialMT-73"/>
 375 |        <use x="744.775391" xlink:href="#ArialMT-74"/>
 376 |        <use x="772.558594" xlink:href="#ArialMT-72"/>
 377 |        <use x="805.859375" xlink:href="#ArialMT-61"/>
 378 |        <use x="861.474609" xlink:href="#ArialMT-70"/>
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 380 |      </g>
 381 |     </g>
 382 |     <g id="xtick_4">
 383 |      <g id="line2d_4"/>
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 414 | L 15.1875 71.578125 
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 417 | " id="ArialMT-6c"/>
 418 |       </defs>
 419 |       <g style="fill:#555555;" transform="translate(336.108594 644.157812)scale(0.1 -0.1)">
 420 |        <use xlink:href="#ArialMT-64"/>
 421 |        <use x="55.615234" xlink:href="#ArialMT-65"/>
 422 |        <use x="111.230469" xlink:href="#ArialMT-6c"/>
 423 |        <use x="133.447266" xlink:href="#ArialMT-74"/>
 424 |        <use x="161.230469" xlink:href="#ArialMT-61"/>
 425 |       </g>
 426 |      </g>
 427 |     </g>
 428 |     <g id="text_5">
 429 |      <!-- Estimator -->
 430 |      <defs>
 431 |       <path d="M 7.90625 0 
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 433 | L 59.671875 71.578125 
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 443 | z
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 445 |      </defs>
 446 |      <g style="fill:#555555;" transform="translate(196.062187 658.734688)scale(0.12 -0.12)">
 447 |       <use xlink:href="#ArialMT-45"/>
 448 |       <use x="66.699219" xlink:href="#ArialMT-73"/>
 449 |       <use x="116.699219" xlink:href="#ArialMT-74"/>
 450 |       <use x="144.482422" xlink:href="#ArialMT-69"/>
 451 |       <use x="166.699219" xlink:href="#ArialMT-6d"/>
 452 |       <use x="250" xlink:href="#ArialMT-61"/>
 453 |       <use x="305.615234" xlink:href="#ArialMT-74"/>
 454 |       <use x="333.398438" xlink:href="#ArialMT-6f"/>
 455 |       <use x="389.013672" xlink:href="#ArialMT-72"/>
 456 |      </g>
 457 |     </g>
 458 |    </g>
 459 |    <g id="matplotlib.axis_2">
 460 |     <g id="ytick_1">
 461 |      <g id="line2d_5">
 462 |       <path clip-path="url(#pc951bdcb39)" d="M 54 577.965041 
 463 | L 388.8 577.965041 
 464 | " style="fill:none;stroke:#ffffff;stroke-linecap:round;"/>
 465 |      </g>
 466 |      <g id="line2d_6"/>
 467 |      <g id="text_6">
 468 |       <!-- −200 -->
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 518 | Q 41.796875 52.984375 37.671875 58.78125 
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 524 |       <g style="fill:#555555;" transform="translate(24.476562 581.543947)scale(0.1 -0.1)">
 525 |        <use xlink:href="#ArialMT-2212"/>
 526 |        <use x="58.398438" xlink:href="#ArialMT-32"/>
 527 |        <use x="114.013672" xlink:href="#ArialMT-30"/>
 528 |        <use x="169.628906" xlink:href="#ArialMT-30"/>
 529 |       </g>
 530 |      </g>
 531 |     </g>
 532 |     <g id="ytick_2">
 533 |      <g id="line2d_7">
 534 |       <path clip-path="url(#pc951bdcb39)" d="M 54 516.246618 
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 536 | " style="fill:none;stroke:#ffffff;stroke-linecap:round;"/>
 537 |      </g>
 538 |      <g id="line2d_8"/>
 539 |      <g id="text_7">
 540 |       <!-- 0 -->
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 542 |        <use xlink:href="#ArialMT-30"/>
 543 |       </g>
 544 |      </g>
 545 |     </g>
 546 |     <g id="ytick_3">
 547 |      <g id="line2d_9">
 548 |       <path clip-path="url(#pc951bdcb39)" d="M 54 454.528195 
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 551 |      </g>
 552 |      <g id="line2d_10"/>
 553 |      <g id="text_8">
 554 |       <!-- 200 -->
 555 |       <g style="fill:#555555;" transform="translate(30.317187 458.107101)scale(0.1 -0.1)">
 556 |        <use xlink:href="#ArialMT-32"/>
 557 |        <use x="55.615234" xlink:href="#ArialMT-30"/>
 558 |        <use x="111.230469" xlink:href="#ArialMT-30"/>
 559 |       </g>
 560 |      </g>
 561 |     </g>
 562 |     <g id="ytick_4">
 563 |      <g id="line2d_11">
 564 |       <path clip-path="url(#pc951bdcb39)" d="M 54 392.809772 
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 567 |      </g>
 568 |      <g id="line2d_12"/>
 569 |      <g id="text_9">
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 592 |        <use x="55.615234" xlink:href="#ArialMT-30"/>
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 596 |     </g>
 597 |     <g id="ytick_5">
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 599 |       <path clip-path="url(#pc951bdcb39)" d="M 54 331.091349 
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 603 |      <g id="line2d_14"/>
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 640 |        <use xlink:href="#ArialMT-36"/>
 641 |        <use x="55.615234" xlink:href="#ArialMT-30"/>
 642 |        <use x="111.230469" xlink:href="#ArialMT-30"/>
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 645 |     </g>
 646 |     <g id="ytick_6">
 647 |      <g id="line2d_15">
 648 |       <path clip-path="url(#pc951bdcb39)" d="M 54 269.372926 
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