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Salmons Stores operates a national chain of women's apparel stores. Five thousand copies of an expensive four-color sales catalog have been printed, and each catalog
Salmons Stores operates a national chain of women's apparel stores. Five thousand copies of an expensive four-color sales catalog have been printed, and each catalog includes a coupon that provides a $50 discount on purchases of $200 or more. Salmons would like to send the catalogs only to customers who have the highest probability of using the coupon. For each of 1,000 Salmons customers, three variables were tracked from an earlier promotional campaign: last year's total spending at Salmons (Spending), whether they have a Salmons store credit card (Card), and whether they used the promotional coupon they were sent (Coupon). Apply logistic regression to classify observations as a promotion-responder or not by using Spending and Card as input variables and Coupon as the target (or response) variable.
a. Evaluate candidate logistic regression models based on their predictive performance on the validation set. Recommend a final model and express the model as a mathematical equation relating the target variable to the input variables. b. For the model selected in part (a), provide and interpret the lift measure on the top 10% of the test set observations most likely to use the promotional coupon. c. What is the area under the ROC curve on the test set? To achieve a sensitivity of at least 0.80, how much Class 0 error rate must be tolerated?
| Customer | Spending | Card | Coupon | Partition |
| 1 | 2291 | 1 | 0 | t |
| 5 | 2528 | 1 | 0 | t |
| 8 | 7076 | 0 | 0 | t |
| 15 | 6737 | 0 | 0 | t |
| 18 | 3470 | 1 | 0 | t |
| 20 | 6404 | 0 | 1 | t |
| 21 | 2229 | 0 | 0 | t |
| 22 | 2933 | 0 | 0 | t |
| 23 | 2118 | 0 | 0 | t |
| 25 | 4998 | 0 | 1 | t |
| 26 | 1394 | 0 | 0 | t |
| 28 | 2059 | 0 | 1 | t |
| 29 | 1677 | 0 | 0 | t |
| 32 | 2933 | 1 | 0 | t |
| 33 | 5365 | 1 | 1 | t |
| 35 | 6179 | 0 | 0 | t |
| 37 | 1058 | 1 | 0 | t |
| 45 | 3566 | 0 | 0 | t |
| 47 | 1554 | 1 | 0 | t |
| 48 | 4631 | 0 | 0 | t |
| 49 | 4345 | 1 | 1 | t |
| 54 | 3386 | 1 | 1 | t |
| 56 | 2050 | 1 | 1 | t |
| 57 | 2323 | 1 | 1 | t |
| 59 | 3345 | 0 | 1 | t |
| 60 | 3318 | 1 | 1 | t |
| 61 | 4721 | 0 | 1 | t |
| 62 | 1662 | 0 | 1 | t |
| 65 | 2313 | 0 | 1 | t |
| 66 | 6851 | 0 | 0 | t |
| 68 | 3470 | 1 | 1 | t |
| 73 | 1878 | 1 | 0 | t |
| 81 | 5501 | 1 | 1 | t |
| 82 | 5991 | 1 | 1 | t |
| 83 | 2372 | 1 | 0 | t |
| 84 | 3995 | 1 | 0 | t |
| 88 | 2429 | 1 | 0 | t |
| 91 | 1130 | 1 | 0 | t |
| 92 | 1911 | 1 | 1 | t |
| 95 | 1403 | 1 | 0 | t |
| 97 | 2421 | 1 | 0 | t |
| 98 | 6073 | 0 | 0 | t |
| 108 | 4971 | 0 | 0 | t |
| 109 | 2252 | 1 | 0 | t |
| 110 | 1979 | 1 | 0 | t |
| 112 | 1786 | 1 | 0 | t |
| 113 | 5438 | 1 | 1 | t |
| 114 | 1834 | 0 | 0 | t |
| 115 | 2000 | 1 | 0 | t |
| 118 | 2864 | 1 | 0 | t |
| 119 | 2246 | 1 | 0 | t |
| 120 | 8312 | 0 | 1 | t |
| 122 | 1015 | 0 | 0 | t |
| 123 | 2180 | 0 | 0 | t |
| 128 | 3352 | 1 | 0 | t |
| 129 | 1409 | 1 | 0 | t |
| 132 | 4397 | 0 | 0 | t |
| 133 | 4494 | 1 | 0 | t |
| 134 | 3720 | 0 | 0 | t |
| 136 | 17675 | 0 | 1 | t |
| 141 | 2277 | 0 | 0 | t |
| 142 | 1340 | 0 | 0 | t |
| 143 | 3004 | 0 | 0 | t |
| 146 | 2634 | 1 | 0 | t |
| 148 | 7761 | 1 | 1 | t |
| 150 | 5172 | 1 | 1 | t |
| 153 | 2609 | 0 | 0 | t |
| 156 | 2318 | 1 | 0 | t |
| 157 | 3195 | 0 | 0 | t |
| 159 | 1982 | 0 | 0 | t |
| 161 | 1799 | 0 | 0 | t |
| 164 | 1773 | 1 | 0 | t |
| 167 | 1761 | 0 | 0 | t |
| 169 | 1981 | 0 | 0 | t |
| 174 | 2662 | 0 | 0 | t |
| 179 | 8256 | 0 | 1 | t |
| 181 | 4320 | 0 | 0 | t |
| 182 | 7156 | 0 | 0 | t |
| 187 | 4875 | 1 | 1 | t |
| 188 | 2021 | 1 | 0 | t |
| 189 | 1694 | 0 | 0 | t |
| 190 | 1708 | 0 | 0 | t |
| 192 | 3558 | 1 | 0 | t |
| 193 | 1315 | 0 | 0 | t |
| 196 | 1889 | 1 | 0 | t |
| 200 | 3385 | 0 | 0 | t |
| 201 | 2194 | 0 | 0 | t |
| 202 | 5139 | 1 | 0 | t |
| 205 | 3468 | 1 | 0 | t |
| 209 | 2288 | 0 | 0 | t |
| 210 | 4001 | 0 | 0 | t |
| 211 | 2911 | 0 | 0 | t |
| 212 | 1736 | 0 | 0 | t |
| 215 | 1712 | 0 | 0 | t |
| 217 | 1846 | 0 | 0 | t |
| 219 | 1811 | 0 | 0 | t |
| 220 | 4815 | 0 | 0 | t |
| 230 | 1179 | 0 | 0 | t |
| 232 | 2761 | 0 | 0 | t |
| 234 | 2752 | 0 | 0 | t |
| 239 | 3352 | 1 | 0 | t |
| 241 | 3439 | 1 | 0 | t |
| 244 | 3134 | 0 | 0 | t |
| 246 | 3075 | 1 | 0 | t |
| 249 | 2893 | 1 | 0 | t |
| 250 | 2344 | 1 | 0 | t |
| 254 | 1340 | 0 | 0 | t |
| 256 | 1991 | 1 | 0 | t |
| 261 | 3670 | 0 | 0 | t |
| 262 | 3415 | 1 | 0 | t |
| 263 | 12151 | 1 | 1 | t |
| 266 | 4895 | 1 | 0 | t |
| 267 | 2424 | 0 | 0 | t |
| 269 | 1894 | 1 | 0 | t |
| 270 | 1774 | 1 | 0 | t |
| 272 | 2270 | 0 | 0 | t |
| 274 | 4959 | 0 | 0 | t |
| 277 | 3201 | 1 | 0 | t |
| 278 | 4846 | 1 | 0 | t |
| 280 | 2411 | 1 | 0 | t |
| 282 | 3212 | 1 | 0 | t |
| 287 | 2978 | 1 | 0 | t |
| 289 | 1427 | 1 | 0 | t |
| 292 | 2940 | 0 | 0 | t |
| 297 | 2876 | 1 | 0 | t |
| 298 | 3909 | 0 | 0 | t |
| 300 | 3178 | 1 | 0 | t |
| 302 | 1846 | 0 | 0 | t |
| 303 | 3502 | 0 | 0 | t |
| 308 | 2357 | 0 | 0 | t |
| 311 | 3200 | 1 | 0 | t |
| 315 | 2657 | 0 | 0 | t |
| 316 | 4777 | 0 | 0 | t |
| 317 | 1879 | 1 | 0 | t |
| 320 | 1211 | 1 | 0 | t |
| 321 | 1263 | 1 | 0 | t |
| 322 | 1676 | 1 | 0 | t |
| 323 | 1482 | 1 | 0 | t |
| 325 | 3485 | 1 | 0 | t |
| 327 | 4848 | 0 | 0 | t |
| 329 | 1351 | 0 | 0 | t |
| 332 | 2846 | 1 | 0 | t |
| 334 | 1908 | 0 | 0 | t |
| 336 | 2764 | 0 | 0 | t |
| 340 | 5091 | 0 | 0 | t |
| 343 | 1865 | 1 | 0 | t |
| 346 | 1013 | 1 | 0 | t |
| 348 | 2853 | 0 | 0 | t |
| 355 | 5538 | 0 | 0 | t |
| 356 | 3850 | 1 | 0 | t |
| 357 | 2328 | 1 | 0 | t |
| 363 | 1751 | 0 | 0 | t |
| 366 | 1013 | 0 | 0 | t |
| 371 | 10311 | 1 | 1 | t |
| 372 | 3012 | 0 | 0 | t |
| 373 | 2300 | 1 | 0 | t |
| 375 | 2825 | 0 | 0 | t |
| 376 | 5497 | 0 | 0 | t |
| 377 | 1118 | 0 | 0 | t |
| 380 | 2662 | 1 | 0 | t |
| 381 | 4037 | 1 | 0 | t |
| 384 | 1576 | 1 | 0 | t |
| 386 | 4700 | 0 | 0 | t |
| 387 | 2175 | 1 | 0 | t |
| 390 | 3894 | 1 | 0 | t |
| 393 | 2140 | 1 | 0 | t |
| 396 | 2747 | 0 | 0 | t |
| 397 | 2936 | 1 | 0 | t |
| 398 | 3854 | 0 | 0 | t |
| 399 | 2717 | 0 | 0 | t |
| 400 | 1387 | 1 | 0 | t |
| 402 | 3118 | 0 | 0 | t |
| 404 | 4626 | 0 | 0 | t |
| 408 | 3415 | 0 | 0 | t |
| 412 | 3390 | 0 | 0 | t |
| 413 | 7787 | 0 | 1 | t |
| 415 | 4130 | 1 | 0 | t |
| 416 | 3850 | 0 | 0 | t |
| 418 | 2996 | 0 | 0 | t |
| 420 | 3546 | 0 | 0 | t |
| 427 | 1247 | 0 | 0 | t |
| 429 | 5274 | 0 | 0 | t |
| 431 | 4854 | 1 | 0 | t |
| 432 | 2962 | 1 | 0 | t |
| 433 | 2013 | 0 | 0 | t |
| 434 | 5437 | 1 | 1 | t |
| 436 | 3180 | 0 | 0 | t |
| 444 | 1687 | 1 | 0 | t |
| 446 | 1784 | 1 | 0 | t |
| 448 | 3748 | 0 | 0 | t |
| 449 | 3028 | 1 | 0 | t |
| 452 | 4585 | 0 | 0 | t |
| 453 | 2761 | 0 | 0 | t |
| 454 | 2081 | 0 | 0 | t |
| 455 | 4394 | 0 | 0 | t |
| 464 | 5269 | 1 | 1 | t |
| 465 | 8475 | 1 | 1 | t |
| 466 | 3491 | 0 | 0 | t |
| 474 | 3079 | 0 | 0 | t |
| 475 | 1745 | 1 | 0 | t |
| 477 | 2060 | 0 | 0 | t |
| 478 | 4938 | 0 | 0 | t |
| 479 | 2847 | 0 | 0 | t |
| 481 | 1338 | 1 | 0 | t |
| 482 | 1907 | 0 | 0 | t |
| 485 | 3376 | 0 | 0 | t |
| 488 | 2306 | 0 | 0 | t |
| 491 | 1835 | 0 | 0 | t |
| 494 | 1523 | 1 | 0 | t |
| 495 | 3350 | 0 | 0 | t |
| 496 | 6260 | 1 | 1 | t |
| 498 | 994 | 0 | 0 | t |
| 501 | 1893 | 1 | 0 | t |
| 503 | 3865 | 0 | 0 | t |
| 504 | 2781 | 1 | 0 | t |
| 510 | 2867 | 1 | 0 | t |
| 511 | 7262 | 1 | 1 | t |
| 518 | 1874 | 1 | 0 | t |
| 519 | 2261 | 0 | 0 | t |
| 520 | 2291 | 1 | 0 | t |
| 522 | 1725 | 1 | 0 | t |
| 524 | 1983 | 1 | 0 | t |
| 525 | 2264 | 0 | 0 | t |
| 527 | 6614 | 1 | 1 | t |
| 531 | 4879 | 1 | 0 | t |
| 534 | 6443 | 1 | 1 | t |
| 535 | 3419 | 1 | 1 | t |
| 537 | 2282 | 1 | 0 | t |
| 538 | 2735 | 1 | 0 | t |
| 546 | 1306 | 0 | 0 | t |
| 547 | 6762 | 0 | 0 | t |
| 549 | 4099 | 1 | 0 | t |
| 552 | 5520 | 1 | 0 | t |
| 553 | 1615 | 1 | 0 | t |
| 555 | 1640 | 1 | 0 | t |
| 556 | 3359 | 1 | 0 | t |
| 559 | 5031 | 0 | 0 | t |
| 561 | 3619 | 0 | 0 | t |
| 563 | 3477 | 1 | 0 | t |
| 564 | 2430 | 0 | 0 | t |
| 572 | 1653 | 0 | 0 | t |
| 577 | 1954 | 0 | 0 | t |
| 578 | 4032 | 0 | 0 | t |
| 583 | 2983 | 1 | 0 | t |
| 584 | 2098 | 1 | 0 | t |
| 585 | 1360 | 0 | 0 | t |
| 586 | 4895 | 1 | 1 | t |
| 588 | 1860 | 0 | 0 | t |
| 591 | 1359 | 0 | 0 | t |
| 593 | 2194 | 1 | 0 | t |
| 595 | 5309 | 0 | 0 | t |
| 604 | 2624 | 1 | 0 | t |
| 607 | 4059 | 1 | 1 | t |
| 618 | 3860 | 1 | 0 | t |
| 621 | 1478 | 0 | 0 | t |
| 622 | 3969 | 0 | 0 | t |
| 624 | 1540 | 1 | 0 | t |
| 626 | 2054 | 0 | 0 | t |
| 629 | 6101 | 1 | 1 | t |
| 633 | 2125 | 0 | 0 | t |
| 636 | 1708 | 0 | 0 | t |
| 640 | 1677 | 0 | 0 | t |
| 641 | 3846 | 0 | 0 | t |
| 642 | 2045 | 0 | 0 | t |
| 643 | 3896 | 1 | 1 | t |
| 644 | 872 | 0 | 0 | t |
| 645 | 8750 | 1 | 1 | t |
| 646 | 5464 | 1 | 1 | t |
| 647 | 1615 | 0 | 0 | t |
| 649 | 2485 | 0 | 0 | t |
| 652 | 3898 | 1 | 1 | t |
| 656 | 2948 | 0 | 0 | t |
| 659 | 4010 | 0 | 0 | t |
| 663 | 4539 | 1 | 0 | t |
| 669 | 1181 | 0 | 0 | t |
| 672 | 3854 | 0 | 0 | t |
| 675 | 3651 | 0 | 0 | t |
| 676 | 2982 | 1 | 0 | t |
| 677 | 2753 | 1 | 0 | t |
| 678 | 1633 | 0 | 0 | t |
| 679 | 1168 | 1 | 0 | t |
| 681 | 1148 | 1 | 0 | t |
| 686 | 1744 | 0 | 0 | t |
| 688 | 3145 | 0 | 0 | t |
| 692 | 2901 | 0 | 0 | t |
| 705 | 6489 | 0 | 0 | t |
| 712 | 2162 | 0 | 0 | t |
| 715 | 3319 | 1 | 0 | t |
| 719 | 2994 | 1 | 0 | t |
| 720 | 1899 | 1 | 0 | t |
| 723 | 2438 | 1 | 0 | t |
| 728 | 955 | 0 | 0 | t |
| 732 | 5593 | 1 | 1 | t |
| 737 | 2941 | 0 | 0 | t |
| 739 | 5707 | 0 | 0 | t |
| 743 | 2198 | 0 | 0 | t |
| 744 | 2348 | 1 | 0 | t |
| 745 | 4412 | 0 | 0 | t |
| 749 | 3777 | 1 | 0 | t |
| 753 | 1891 | 0 | 0 | t |
| 755 | 1262 | 0 | 0 | t |
| 766 | 4517 | 0 | 0 | t |
| 767 | 2746 | 1 | 0 | t |
| 770 | 5002 | 0 | 0 | t |
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| 777 | 2097 | 0 | 0 | t |
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| 780 | 2103 | 0 | 0 | t |
| 782 | 4301 | 1 | 1 | t |
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| 850 | 3163 | 1 | 0 | t |
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| 885 |
