├── README.md ├── admissions.csv └── college_admissions_prediction.ipynb /README.md: -------------------------------------------------------------------------------- 1 | # Project: College Admissions Prediction 2 | 3 | ## Project Goal 4 | Predict a candidate's chances of being admitted into a college based on GPA and GRE score. 5 | ## Dataset Information: 6 | admissions.csv contains data on the candidates' GPA and GRE Score and whether they were admitted. 7 | ## Tech Stack 8 | Python
9 | Google Colaboratory
10 | NumPy
11 | Pandas
12 | Matplotlib
13 | Scikit-learn
14 | 15 | ## Featured ML Algorithms 16 | Linear Regression
17 | Logistic Regression
18 | -------------------------------------------------------------------------------- /admissions.csv: -------------------------------------------------------------------------------- 1 | admit,gpa,gre 2 | 0,3.1772772600730947,594.1029915771487 3 | 0,3.4126553589367825,631.5286067220945 4 | 0,2.7280971435972337,553.7143989347039 5 | 0,3.0935590768541186,551.0899851159896 6 | 0,3.1419228288909364,537.1848938066419 7 | 0,3.599107765322437,442.7635672275836 8 | 0,3.238971962763903,667.4721888917547 9 | 0,3.4201768220815576,561.7139053278995 10 | 0,3.562482406012416,590.3403713673283 11 | 0,3.910494575439653,463.4701830286301 12 | 0,3.2643412097203486,636.4531655238836 13 | 0,3.3086233708202384,604.4055577685214 14 | 0,3.0189219146088115,567.7148296553638 15 | 0,3.1518344059816688,503.30729838232423 16 | 0,3.2981327505758458,628.1782052279433 17 | 0,2.652201106090184,644.3002614821658 18 | 0,3.11560326159216,533.4798096290625 19 | 0,3.1052418325806608,562.9397148907857 20 | 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| { 30 | "cell_type": "markdown", 31 | "metadata": { 32 | "id": "b43b6DNdUPru" 33 | }, 34 | "source": [ 35 | "# Predicting College Admission Chances for Candidates" 36 | ] 37 | }, 38 | { 39 | "cell_type": "code", 40 | "metadata": { 41 | "id": "AZ5l6H6gSrel" 42 | }, 43 | "source": [ 44 | "import pandas as pd\n", 45 | "import numpy as np\n", 46 | "import matplotlib.pyplot as plt" 47 | ], 48 | "execution_count": 59, 49 | "outputs": [] 50 | }, 51 | { 52 | "cell_type": "markdown", 53 | "metadata": { 54 | "id": "GdHIJhT6aSdr" 55 | }, 56 | "source": [ 57 | "## College Admissions Dataset" 58 | ] 59 | }, 60 | { 61 | "cell_type": "code", 62 | "metadata": { 63 | "colab": { 64 | "base_uri": "https://localhost:8080/", 65 | "height": 419 66 | }, 67 | "id": "lMAc5d0WaOG5", 68 | "outputId": "66fa6e1a-d9bd-4c34-8f20-53adc5350fcd" 69 | }, 70 | "source": [ 71 | "admissions = pd.read_csv(\"admissions.csv\")\n", 72 | "admissions" 73 | ], 74 | "execution_count": 60, 75 | "outputs": [ 76 | { 77 | "output_type": "execute_result", 78 | "data": { 79 | "text/html": [ 80 | "
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644 rows × 3 columns

\n", 173 | "
" 174 | ], 175 | "text/plain": [ 176 | " admit gpa gre\n", 177 | "0 0 3.177277 594.102992\n", 178 | "1 0 3.412655 631.528607\n", 179 | "2 0 2.728097 553.714399\n", 180 | "3 0 3.093559 551.089985\n", 181 | "4 0 3.141923 537.184894\n", 182 | ".. ... ... ...\n", 183 | "639 1 3.381359 720.718438\n", 184 | "640 1 3.083956 556.918021\n", 185 | "641 1 3.114419 734.297679\n", 186 | "642 1 3.549012 604.697503\n", 187 | "643 1 3.532753 588.986175\n", 188 | "\n", 189 | "[644 rows x 3 columns]" 190 | ] 191 | }, 192 | "metadata": { 193 | "tags": [] 194 | }, 195 | "execution_count": 60 196 | } 197 | ] 198 | }, 199 | { 200 | "cell_type": "code", 201 | "metadata": { 202 | "colab": { 203 | "base_uri": "https://localhost:8080/", 204 | "height": 265 205 | }, 206 | "id": "ytZo7jztTGMw", 207 | "outputId": "7a3fe7be-0b2c-46e0-de2c-89c55875859f" 208 | }, 209 | "source": [ 210 | "plt.scatter(admissions['gpa'], admissions['admit'])\n", 211 | "plt.show()" 212 | ], 213 | "execution_count": 61, 214 | "outputs": [ 215 | { 216 | "output_type": "display_data", 217 | "data": { 218 | "image/png": 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\n", 219 | "text/plain": [ 220 | "
" 221 | ] 222 | }, 223 | "metadata": { 224 | "tags": [], 225 | "needs_background": "light" 226 | } 227 | } 228 | ] 229 | }, 230 | { 231 | "cell_type": "markdown", 232 | "metadata": { 233 | "id": "FtdLm9dvUfoa" 234 | }, 235 | "source": [ 236 | "## Exploring the Logistic Function" 237 | ] 238 | }, 239 | { 240 | "cell_type": "code", 241 | "metadata": { 242 | "colab": { 243 | "base_uri": "https://localhost:8080/", 244 | "height": 265 245 | }, 246 | "id": "MvceOIR7Tl9v", 247 | "outputId": "419effb4-48db-4f7b-a5a5-2a5c46fa795d" 248 | }, 249 | "source": [ 250 | "# Logistic Function\n", 251 | "def logistic(x):\n", 252 | " # np.exp(x) raises x to the exponential power, ie e^x. e ~= 2.71828\n", 253 | " return np.exp(x) / (1 + np.exp(x)) \n", 254 | " \n", 255 | "# Generate 50 real values, evenly spaced, between -6 and 6.\n", 256 | "x = np.linspace(-6,6,50, dtype=float)\n", 257 | "\n", 258 | "# Transform each number in t using the logistic function.\n", 259 | "y = logistic(x)\n", 260 | "\n", 261 | "# Plot the resulting data.\n", 262 | "plt.plot(x, y)\n", 263 | "plt.ylabel(\"Probability\")\n", 264 | "plt.show()" 265 | ], 266 | "execution_count": 62, 267 | "outputs": [ 268 | { 269 | "output_type": "display_data", 270 | "data": { 271 | "image/png": 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\n", 272 | "text/plain": [ 273 | "
" 274 | ] 275 | }, 276 | "metadata": { 277 | "tags": [], 278 | "needs_background": "light" 279 | } 280 | } 281 | ] 282 | }, 283 | { 284 | "cell_type": "markdown", 285 | "metadata": { 286 | "id": "inj-lXuhUqHx" 287 | }, 288 | "source": [ 289 | "## Linear Regression vs. Logistic Regression" 290 | ] 291 | }, 292 | { 293 | "cell_type": "markdown", 294 | "metadata": { 295 | "id": "Ta70oULrU09M" 296 | }, 297 | "source": [ 298 | "### Linear Regression" 299 | ] 300 | }, 301 | { 302 | "cell_type": "code", 303 | "metadata": { 304 | "colab": { 305 | "base_uri": "https://localhost:8080/" 306 | }, 307 | "id": "lKicAKsYTvV7", 308 | "outputId": "166f3bb8-46a6-411a-ca0f-ad16ef73ce83" 309 | }, 310 | "source": [ 311 | "from sklearn.linear_model import LinearRegression\n", 312 | "linear_model = LinearRegression()\n", 313 | "linear_model.fit(admissions[[\"gpa\"]], admissions[\"admit\"])" 314 | ], 315 | "execution_count": 63, 316 | "outputs": [ 317 | { 318 | "output_type": "execute_result", 319 | "data": { 320 | "text/plain": [ 321 | "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)" 322 | ] 323 | }, 324 | "metadata": { 325 | "tags": [] 326 | }, 327 | "execution_count": 63 328 | } 329 | ] 330 | }, 331 | { 332 | "cell_type": "markdown", 333 | "metadata": { 334 | "id": "cb0xGeGTU49z" 335 | }, 336 | "source": [ 337 | "### Logistic Regression" 338 | ] 339 | }, 340 | { 341 | "cell_type": "code", 342 | "metadata": { 343 | "colab": { 344 | "base_uri": "https://localhost:8080/" 345 | }, 346 | "id": "JYzbu9uTVD9K", 347 | "outputId": "db25c771-ec99-4311-bcdf-1691bfad6676" 348 | }, 349 | "source": [ 350 | "from sklearn.linear_model import LogisticRegression\n", 351 | "logistic_model = LogisticRegression()\n", 352 | "logistic_model.fit(admissions[[\"gpa\"]], admissions[\"admit\"])" 353 | ], 354 | "execution_count": 64, 355 | "outputs": [ 356 | { 357 | "output_type": "execute_result", 358 | "data": { 359 | "text/plain": [ 360 | "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n", 361 | " intercept_scaling=1, l1_ratio=None, max_iter=100,\n", 362 | " multi_class='auto', n_jobs=None, penalty='l2',\n", 363 | " random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n", 364 | " warm_start=False)" 365 | ] 366 | }, 367 | "metadata": { 368 | "tags": [] 369 | }, 370 | "execution_count": 64 371 | } 372 | ] 373 | }, 374 | { 375 | "cell_type": "markdown", 376 | "metadata": { 377 | "id": "0fC2y-lJWFaK" 378 | }, 379 | "source": [ 380 | "## Use Logistic Regression and Predict Probabilities" 381 | ] 382 | }, 383 | { 384 | "cell_type": "markdown", 385 | "metadata": { 386 | "id": "EKAZmXwUWMMC" 387 | }, 388 | "source": [ 389 | "Used the LogisticRegression method `predict_proba` to return the predicted probabilities for the data in the gpa column. Then the returned probabilities were assigned to `pred_probs_gpa`.\n", 390 | "Here is a scatter plot of predicted probability vs. gpa." 391 | ] 392 | }, 393 | { 394 | "cell_type": "code", 395 | "metadata": { 396 | "colab": { 397 | "base_uri": "https://localhost:8080/", 398 | "height": 296 399 | }, 400 | "id": "gH8wpdSKVJLq", 401 | "outputId": "530a982d-dc55-4c98-c604-1ce439627da2" 402 | }, 403 | "source": [ 404 | "pred_probs_gpa = logistic_model.predict_proba(admissions[[\"gpa\"]])\n", 405 | "plt.scatter(admissions[\"gpa\"], pred_probs_gpa[:,1])\n", 406 | "plt.xlabel('gpa')\n", 407 | "plt.ylabel('Admission Probability')" 408 | ], 409 | "execution_count": 65, 410 | "outputs": [ 411 | { 412 | "output_type": "execute_result", 413 | "data": { 414 | "text/plain": [ 415 | "Text(0, 0.5, 'Admission Probability')" 416 | ] 417 | }, 418 | "metadata": { 419 | "tags": [] 420 | }, 421 | "execution_count": 65 422 | }, 423 | { 424 | "output_type": "display_data", 425 | "data": { 426 | "image/png": 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\n", 427 | "text/plain": [ 428 | "
" 429 | ] 430 | }, 431 | "metadata": { 432 | "tags": [], 433 | "needs_background": "light" 434 | } 435 | } 436 | ] 437 | }, 438 | { 439 | "cell_type": "markdown", 440 | "metadata": { 441 | "id": "DNzZfMUmXp6H" 442 | }, 443 | "source": [ 444 | "Here, the scatter plot suggests a linear relationship between the gpa values and the probability of being admitted. This is because logistic regression is an adapted version of linear regression for classification problems. Both logistic and linear regression are used to capture linear relationships between the independent variables and the dependent variable. \n", 445 | "\n", 446 | "Next is predicting whether the students based on the gpa is admitted." 447 | ] 448 | }, 449 | { 450 | "cell_type": "code", 451 | "metadata": { 452 | "colab": { 453 | "base_uri": "https://localhost:8080/", 454 | "height": 296 455 | }, 456 | "id": "jIxQMarZXSTC", 457 | "outputId": "376d882c-af9a-421d-83e5-b540c492d66e" 458 | }, 459 | "source": [ 460 | "fitted_labels_gpa = logistic_model.predict(admissions[[\"gpa\"]])\n", 461 | "plt.scatter(admissions[\"gpa\"], fitted_labels_gpa)\n", 462 | "plt.xlabel('gpa')\n", 463 | "plt.ylabel('Predicted Admission Result')" 464 | ], 465 | "execution_count": 66, 466 | "outputs": [ 467 | { 468 | "output_type": "execute_result", 469 | "data": { 470 | "text/plain": [ 471 | "Text(0, 0.5, 'Predicted Admission Result')" 472 | ] 473 | }, 474 | "metadata": { 475 | "tags": [] 476 | }, 477 | "execution_count": 66 478 | }, 479 | { 480 | "output_type": "display_data", 481 | "data": { 482 | "image/png": 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\n", 483 | "text/plain": [ 484 | "
" 485 | ] 486 | }, 487 | "metadata": { 488 | "tags": [], 489 | "needs_background": "light" 490 | } 491 | } 492 | ] 493 | }, 494 | { 495 | "cell_type": "markdown", 496 | "metadata": { 497 | "id": "7fiRjDu7Yi8T" 498 | }, 499 | "source": [ 500 | "Based on the above scatterplot, looks like any student with a gpa >= 3.5 has a chance of being admitted." 501 | ] 502 | }, 503 | { 504 | "cell_type": "markdown", 505 | "metadata": { 506 | "id": "8ibvONAtcPyA" 507 | }, 508 | "source": [ 509 | "## For fun, repeat the process again, this time with GRE score" 510 | ] 511 | }, 512 | { 513 | "cell_type": "code", 514 | "metadata": { 515 | "id": "ndjyD1E-aylu" 516 | }, 517 | "source": [ 518 | "logistic_model2 = LogisticRegression()\n", 519 | "logistic_model2.fit(admissions[[\"gre\"]], admissions[\"admit\"])\n", 520 | "pred_probs_gre = logistic_model2.predict_proba(admissions[[\"gre\"]])\n", 521 | "fitted_labels_gre = logistic_model2.predict(admissions[[\"gre\"]])" 522 | ], 523 | "execution_count": 67, 524 | "outputs": [] 525 | }, 526 | { 527 | "cell_type": "code", 528 | "metadata": { 529 | "colab": { 530 | "base_uri": "https://localhost:8080/", 531 | "height": 296 532 | }, 533 | "id": "ku4fgE0AcyZD", 534 | "outputId": "bd7afc09-e541-463c-c418-dcbf8acd7e1e" 535 | }, 536 | "source": [ 537 | "plt.scatter(admissions[\"gre\"], pred_probs_gre[:,1])\n", 538 | "plt.xlabel('gre')\n", 539 | "plt.ylabel('Admission Probability')" 540 | ], 541 | "execution_count": 68, 542 | "outputs": [ 543 | { 544 | "output_type": "execute_result", 545 | "data": { 546 | "text/plain": [ 547 | "Text(0, 0.5, 'Admission Probability')" 548 | ] 549 | }, 550 | "metadata": { 551 | "tags": [] 552 | }, 553 | "execution_count": 68 554 | }, 555 | { 556 | "output_type": "display_data", 557 | "data": { 558 | "image/png": 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\n", 559 | "text/plain": [ 560 | "
" 561 | ] 562 | }, 563 | "metadata": { 564 | "tags": [], 565 | "needs_background": "light" 566 | } 567 | } 568 | ] 569 | }, 570 | { 571 | "cell_type": "code", 572 | "metadata": { 573 | "colab": { 574 | "base_uri": "https://localhost:8080/", 575 | "height": 296 576 | }, 577 | "id": "K2iuGk39c-jt", 578 | "outputId": "a4917795-aade-48c3-fcff-8ec158b070d6" 579 | }, 580 | "source": [ 581 | "plt.scatter(admissions[\"gre\"], fitted_labels_gre)\n", 582 | "plt.xlabel('gre')\n", 583 | "plt.ylabel('Predicted Admission Result')" 584 | ], 585 | "execution_count": 69, 586 | "outputs": [ 587 | { 588 | "output_type": "execute_result", 589 | "data": { 590 | "text/plain": [ 591 | "Text(0, 0.5, 'Predicted Admission Result')" 592 | ] 593 | }, 594 | "metadata": { 595 | "tags": [] 596 | }, 597 | "execution_count": 69 598 | }, 599 | { 600 | "output_type": "display_data", 601 | "data": { 602 | "image/png": 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\n", 603 | "text/plain": [ 604 | "
" 605 | ] 606 | }, 607 | "metadata": { 608 | "tags": [], 609 | "needs_background": "light" 610 | } 611 | } 612 | ] 613 | }, 614 | { 615 | "cell_type": "markdown", 616 | "metadata": { 617 | "id": "FXZVpcJFd6eo" 618 | }, 619 | "source": [ 620 | "Based on the above scatterplot, looks like any student with a GRE >= 660 has a chance of being admitted." 621 | ] 622 | }, 623 | { 624 | "cell_type": "markdown", 625 | "metadata": { 626 | "id": "jNwln7VMeSvI" 627 | }, 628 | "source": [ 629 | "## Let's use both GPA and GRE" 630 | ] 631 | }, 632 | { 633 | "cell_type": "code", 634 | "metadata": { 635 | "id": "4wUoJJQvdCHS" 636 | }, 637 | "source": [ 638 | "logistic_model3 = LogisticRegression()\n", 639 | "logistic_model3.fit(admissions[[\"gpa\",\"gre\"]], admissions[\"admit\"])\n", 640 | "pred_probs_gre_gpa = logistic_model3.predict_proba(admissions[[\"gpa\",\"gre\"]])\n", 641 | "fitted_labels_gre_gpa = logistic_model3.predict(admissions[[\"gpa\",\"gre\"]])" 642 | ], 643 | "execution_count": 70, 644 | "outputs": [] 645 | }, 646 | { 647 | "cell_type": "markdown", 648 | "metadata": { 649 | "id": "9MHUoodxgNDd" 650 | }, 651 | "source": [ 652 | "# Comparing Logistic Models' Accuracy" 653 | ] 654 | }, 655 | { 656 | "cell_type": "code", 657 | "metadata": { 658 | "colab": { 659 | "base_uri": "https://localhost:8080/" 660 | }, 661 | "id": "FNUZ6wZne05w", 662 | "outputId": "6b2f2d36-3412-44c4-e3dd-6bc2f937ebdd" 663 | }, 664 | "source": [ 665 | "sum(fitted_labels_gpa == admissions['admit'])/admissions.shape[0]" 666 | ], 667 | "execution_count": 71, 668 | "outputs": [ 669 | { 670 | "output_type": "execute_result", 671 | "data": { 672 | "text/plain": [ 673 | "0.6847826086956522" 674 | ] 675 | }, 676 | "metadata": { 677 | "tags": [] 678 | }, 679 | "execution_count": 71 680 | } 681 | ] 682 | }, 683 | { 684 | "cell_type": "code", 685 | "metadata": { 686 | "colab": { 687 | "base_uri": "https://localhost:8080/" 688 | }, 689 | "id": "FLMOkvYUfKMo", 690 | "outputId": "ebf9aef7-0398-477e-dc06-a61c8d3e3b2a" 691 | }, 692 | "source": [ 693 | "sum(fitted_labels_gre == admissions['admit'])/admissions.shape[0]" 694 | ], 695 | "execution_count": 72, 696 | "outputs": [ 697 | { 698 | "output_type": "execute_result", 699 | "data": { 700 | "text/plain": [ 701 | "0.7267080745341615" 702 | ] 703 | }, 704 | "metadata": { 705 | "tags": [] 706 | }, 707 | "execution_count": 72 708 | } 709 | ] 710 | }, 711 | { 712 | "cell_type": "code", 713 | "metadata": { 714 | "colab": { 715 | "base_uri": "https://localhost:8080/" 716 | }, 717 | "id": "7q3Ql7thgd-L", 718 | "outputId": "4c70c5e8-63b8-4164-c105-5b41a051974e" 719 | }, 720 | "source": [ 721 | "sum(fitted_labels_gre_gpa == admissions['admit'])/admissions.shape[0]" 722 | ], 723 | "execution_count": 73, 724 | "outputs": [ 725 | { 726 | "output_type": "execute_result", 727 | "data": { 728 | "text/plain": [ 729 | "0.7872670807453416" 730 | ] 731 | }, 732 | "metadata": { 733 | "tags": [] 734 | }, 735 | "execution_count": 73 736 | } 737 | ] 738 | }, 739 | { 740 | "cell_type": "markdown", 741 | "metadata": { 742 | "id": "CGM05kiAg2V0" 743 | }, 744 | "source": [ 745 | "GPA and GRE together can predict admission chances of a candidate better than either solely GPA or solely GRE." 746 | ] 747 | }, 748 | { 749 | "cell_type": "markdown", 750 | "metadata": { 751 | "id": "4pXq2KN4R-jg" 752 | }, 753 | "source": [ 754 | "## Evaluating Specificity and Sensitivity of these Models" 755 | ] 756 | }, 757 | { 758 | "cell_type": "markdown", 759 | "metadata": { 760 | "id": "f__sKfekScpw" 761 | }, 762 | "source": [ 763 | "\r\n", 764 | "* **True Positive (TP)**: model correctly predicted that a candidate would be admitted.\r\n", 765 | "* **True Negative (TN)**: model correctly predicted that a candidate would not be admitted.\r\n", 766 | "* **False Positive (FP)** model incorrectly predicted that a candidate would be admitted even though the student got rejected.\r\n", 767 | "* **False Negative (FN)**: model incorrectly predicted that a candidate would not be admitted even though the student got admitted." 768 | ] 769 | }, 770 | { 771 | "cell_type": "markdown", 772 | "metadata": { 773 | "id": "Q9viFzi0C9MQ" 774 | }, 775 | "source": [ 776 | "**Calculating Sensitivity or True Positive Rate (TPR)**\r\n", 777 | "\r\n", 778 | "\\begin{equation*}\r\n", 779 | "TPR = \\frac{TP}{TP+FN}\r\n", 780 | "\\end{equation*}\r\n", 781 | "\r\n", 782 | "**Calculating Specificity or True Negative Rate (TNR)**\r\n", 783 | "\r\n", 784 | "\\begin{equation*}\r\n", 785 | "TNR = \\frac{TN}{TN+FP}\r\n", 786 | "\\end{equation*}\r\n" 787 | ] 788 | }, 789 | { 790 | "cell_type": "code", 791 | "metadata": { 792 | "id": "QsYHzS-4sRhk" 793 | }, 794 | "source": [ 795 | "def build_logReg(df, cols, target):\r\n", 796 | " model = LogisticRegression()\r\n", 797 | " model.fit(df[cols], df[target])\r\n", 798 | " return model.predict(df[cols])" 799 | ], 800 | "execution_count": 74, 801 | "outputs": [] 802 | }, 803 | { 804 | "cell_type": "code", 805 | "metadata": { 806 | "colab": { 807 | "base_uri": "https://localhost:8080/", 808 | "height": 419 809 | }, 810 | "id": "SU4TlX6wjxzX", 811 | "outputId": "926b9ae0-6a72-4b5f-a2d1-b3749be441c3" 812 | }, 813 | "source": [ 814 | "admissions['predicted_by_gpa'] = build_logReg(admissions, ['gpa'], 'admit')\r\n", 815 | "admissions['predicted_by_gre'] = build_logReg(admissions, ['gre'], 'admit')\r\n", 816 | "admissions['predicted_by_gre_gpa'] = build_logReg(admissions, ['gpa','gre'], 'admit')\r\n", 817 | "admissions" 818 | ], 819 | "execution_count": 75, 820 | "outputs": [ 821 | { 822 | "output_type": "execute_result", 823 | "data": { 824 | "text/html": [ 825 | "
\n", 826 | "\n", 839 | "\n", 840 | " \n", 841 | " \n", 842 | " \n", 843 | " \n", 844 | " \n", 845 | " \n", 846 | " \n", 847 | " \n", 848 | " \n", 849 | " \n", 850 | " \n", 851 | " \n", 852 | " \n", 853 | " \n", 854 | " \n", 855 | " \n", 856 | " \n", 857 | " \n", 858 | " \n", 859 | " \n", 860 | " \n", 861 | " \n", 862 | " \n", 863 | " \n", 864 | " \n", 865 | " \n", 866 | " \n", 867 | " \n", 868 | " \n", 869 | " \n", 870 | " \n", 871 | " \n", 872 | " \n", 873 | " \n", 874 | " \n", 875 | " \n", 876 | " \n", 877 | " \n", 878 | " \n", 879 | " \n", 880 | " \n", 881 | " \n", 882 | " \n", 883 | " \n", 884 | " \n", 885 | " \n", 886 | " \n", 887 | " \n", 888 | " \n", 889 | " \n", 890 | " \n", 891 | " \n", 892 | " \n", 893 | " \n", 894 | " \n", 895 | " \n", 896 | " \n", 897 | " \n", 898 | " \n", 899 | " \n", 900 | " \n", 901 | " \n", 902 | " \n", 903 | " \n", 904 | " \n", 905 | " \n", 906 | " \n", 907 | " \n", 908 | " \n", 909 | " \n", 910 | " \n", 911 | " \n", 912 | " \n", 913 | " \n", 914 | " \n", 915 | " \n", 916 | " \n", 917 | " \n", 918 | " \n", 919 | " \n", 920 | " \n", 921 | " \n", 922 | " \n", 923 | " \n", 924 | " \n", 925 | " \n", 926 | " \n", 927 | " \n", 928 | " \n", 929 | " \n", 930 | " \n", 931 | " \n", 932 | " \n", 933 | " \n", 934 | " \n", 935 | " \n", 936 | " \n", 937 | " \n", 938 | " \n", 939 | " \n", 940 | " \n", 941 | " \n", 942 | " \n", 943 | " \n", 944 | " \n", 945 | " \n", 946 | " \n", 947 | " \n", 948 | " \n", 949 | " \n", 950 | " \n", 951 | " \n", 952 | "
admitgpagrepredicted_by_gpapredicted_by_grepredicted_by_gre_gpa
003.177277594.102992000
103.412655631.528607001
202.728097553.714399000
303.093559551.089985000
403.141923537.184894000
.....................
63913.381359720.718438011
64013.083956556.918021000
64113.114419734.297679011
64213.549012604.697503101
64313.532753588.986175100
\n", 953 | "

644 rows × 6 columns

\n", 954 | "
" 955 | ], 956 | "text/plain": [ 957 | " admit gpa ... predicted_by_gre predicted_by_gre_gpa\n", 958 | "0 0 3.177277 ... 0 0\n", 959 | "1 0 3.412655 ... 0 1\n", 960 | "2 0 2.728097 ... 0 0\n", 961 | "3 0 3.093559 ... 0 0\n", 962 | "4 0 3.141923 ... 0 0\n", 963 | ".. ... ... ... ... ...\n", 964 | "639 1 3.381359 ... 1 1\n", 965 | "640 1 3.083956 ... 0 0\n", 966 | "641 1 3.114419 ... 1 1\n", 967 | "642 1 3.549012 ... 0 1\n", 968 | "643 1 3.532753 ... 0 0\n", 969 | "\n", 970 | "[644 rows x 6 columns]" 971 | ] 972 | }, 973 | "metadata": { 974 | "tags": [] 975 | }, 976 | "execution_count": 75 977 | } 978 | ] 979 | }, 980 | { 981 | "cell_type": "code", 982 | "metadata": { 983 | "colab": { 984 | "base_uri": "https://localhost:8080/" 985 | }, 986 | "id": "VV1gwooTRYaP", 987 | "outputId": "3fe549e6-8db2-4e01-cc09-441f47e70c17" 988 | }, 989 | "source": [ 990 | "def TPTN(df, prediction, actual):\r\n", 991 | " true_positive_filter = (df[prediction] == 1) & (df[actual] == 1)\r\n", 992 | " true_positives = len(df[true_positive_filter])\r\n", 993 | " true_negative_filter = (df[prediction] == 0) & (df[actual] == 0)\r\n", 994 | " true_negatives = len(df[true_negative_filter])\r\n", 995 | " false_positive_filter = (df[prediction] == 1) & (df[actual] == 0)\r\n", 996 | " false_positives = len(df[false_positive_filter])\r\n", 997 | " false_negative_filter = (df[prediction] == 0) & (df[actual] == 1)\r\n", 998 | " false_negatives = len(df[false_negative_filter])\r\n", 999 | "\r\n", 1000 | " TPR = true_positives/(true_positives+false_negatives)\r\n", 1001 | " TNR = true_negatives/(true_negatives+false_positives)\r\n", 1002 | "\r\n", 1003 | " print(\"Sensitivity = {}, Specificity = {}\".format(TPR,TNR))\r\n", 1004 | "\r\n", 1005 | "TPTN(admissions, \"predicted_by_gpa\", \"admit\")\r\n", 1006 | "TPTN(admissions, \"predicted_by_gre\", \"admit\")\r\n", 1007 | "TPTN(admissions, \"predicted_by_gre_gpa\", \"admit\")" 1008 | ], 1009 | "execution_count": 76, 1010 | "outputs": [ 1011 | { 1012 | "output_type": "stream", 1013 | "text": [ 1014 | "Sensitivity = 0.36475409836065575, Specificity = 0.88\n", 1015 | "Sensitivity = 0.5409836065573771, Specificity = 0.84\n", 1016 | "Sensitivity = 0.6721311475409836, Specificity = 0.8575\n" 1017 | ], 1018 | "name": "stdout" 1019 | } 1020 | ] 1021 | }, 1022 | { 1023 | "cell_type": "markdown", 1024 | "metadata": { 1025 | "id": "aK6HgMcSFRbw" 1026 | }, 1027 | "source": [ 1028 | "For all of these models, their sensitivity values are unacceptably high. This indicates that the metrics of GPA and GRE scores are not enough information to accurately predict whether or not a candidate would earn admission into the university." 1029 | ] 1030 | } 1031 | ] 1032 | } --------------------------------------------------------------------------------