Question
Unlike small selective colleges that pay close attention to personal statements, teacher recommendations, etc., large, public state university systems primarily rely on a student's grade
Unlike small selective colleges that pay close attention to personal statements, teacher recommendations, etc., large, public state university systems primarily rely on a student's grade point average (GPA) and scores on the SAT or ACT for the college admission decisions. Data were collected for 120 applicants on college admission (Admit equals 1 if admitted, 0 otherwise) along with the student's GPA and SAT scores. A portion of the data is shown in the accompanying table.
a. Estimate the linear probability model and the logistic regression model. (Round coefficient estimates to 4 decimal places.) Variable. Linear Model Logistic Model
Intercept
GPA
SAT
b. Compute the accuracy rates (%) of both models. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)
Linear Model Logistic Model
c-1. Find the preferred model for prediction. multiple choice
- Logistic Model
- Linear Model
c-2. Use the preferred model to predict the probability of admission for a college student with GPA = 3.0 and SAT = 1400. What if GPA = 4.0? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Note: Report the probability between 0 and 1 (not in %).
SAT=1400, GPA=3.0
SAT=1400, GPA=4.0
| Admit | GPA | SAT |
| 1 | 4.23 | 1025 |
| 0 | 4.24 | 1436 |
| 1 | 3.77 | 1116 |
| 1 | 3.09 | 1309 |
| 1 | 3.09 | 1321 |
| 1 | 3.43 | 1490 |
| 1 | 3.1 | 1533 |
| 0 | 4.08 | 1538 |
| 1 | 2.81 | 1118 |
| 0 | 2.74 | 1307 |
| 1 | 4.49 | 1117 |
| 0 | 3.83 | 1596 |
| 1 | 4.47 | 1398 |
| 1 | 3.23 | 1531 |
| 0 | 3.21 | 1258 |
| 1 | 4.17 | 1351 |
| 1 | 2.81 | 1135 |
| 1 | 3.08 | 1109 |
| 1 | 2.93 | 1109 |
| 1 | 2.61 | 1064 |
| 0 | 2.71 | 1253 |
| 0 | 2.67 | 1015 |
| 1 | 3.02 | 1165 |
| 1 | 3.29 | 1348 |
| 1 | 2.95 | 1219 |
| 0 | 3.85 | 1212 |
| 1 | 4.23 | 1157 |
| 1 | 3.66 | 1250 |
| 0 | 4.03 | 1179 |
| 1 | 4.18 | 1408 |
| 1 | 3.74 | 1572 |
| 1 | 2.86 | 1085 |
| 0 | 3.33 | 1598 |
| 0 | 3.33 | 1360 |
| 0 | 3.51 | 1108 |
| 1 | 4.01 | 1209 |
| 1 | 2.53 | 1471 |
| 0 | 3.99 | 1214 |
| 0 | 3.02 | 1392 |
| 0 | 4.42 | 1218 |
| 1 | 4 | 1141 |
| 0 | 2.99 | 1256 |
| 1 | 4.04 | 1084 |
| 1 | 4.43 | 1172 |
| 1 | 3.36 | 1263 |
| 1 | 3.1 | 1564 |
| 1 | 3.52 | 1182 |
| 1 | 3.57 | 1489 |
| 0 | 4.34 | 1447 |
| 1 | 2.54 | 1191 |
| 0 | 3.98 | 1343 |
| 0 | 2.97 | 1544 |
| 1 | 2.8 | 1517 |
| 1 | 4.11 | 1398 |
| 0 | 3.09 | 1504 |
| 1 | 3.01 | 1357 |
| 0 | 4.29 | 1353 |
| 0 | 4.01 | 1341 |
| 1 | 4.28 | 1425 |
| 0 | 3.07 | 1589 |
| 1 | 2.54 | 1086 |
| 1 | 4.18 | 1436 |
| 1 | 3.21 | 1193 |
| 0 | 4.2 | 1355 |
| 1 | 4.23 | 1022 |
| 0 | 3.85 | 1241 |
| 1 | 4.39 | 1021 |
| 1 | 3.23 | 1378 |
| 0 | 3.02 | 1160 |
| 0 | 2.83 | 1381 |
| 1 | 3.8 | 1066 |
| 0 | 2.72 | 1192 |
| 0 | 3.54 | 1515 |
| 1 | 3.68 | 1500 |
| 1 | 4.47 | 1393 |
| 1 | 3.49 | 1559 |
| 1 | 3.22 | 1039 |
| 1 | 3.78 | 1514 |
| 1 | 3.66 | 1480 |
| 1 | 4.07 | 1261 |
| 1 | 3.89 | 1576 |
| 0 | 3.31 | 1340 |
| 0 | 3.56 | 1521 |
| 0 | 3.25 | 1049 |
| 0 | 3.06 | 1240 |
| 0 | 3.72 | 1401 |
| 0 | 2.88 | 1254 |
| 1 | 3.16 | 1115 |
| 1 | 4.19 | 1460 |
| 0 | 4.43 | 1054 |
| 1 | 4.23 | 1160 |
| 0 | 3.43 | 1508 |
| 1 | 4.23 | 1569 |
| 0 | 3.81 | 1384 |
| 1 | 3.61 | 1324 |
| 1 | 2.8 | 1404 |
| 1 | 2.54 | 1284 |
| 0 | 3.5 | 1269 |
| 1 | 3.74 | 1315 |
| 1 | 4.04 | 1495 |
| 0 | 3.37 | 1566 |
| 1 | 2.91 | 1487 |
| 0 | 2.77 | 1309 |
| 0 | 3.53 | 1226 |
| 1 | 4.37 | 1141 |
| 1 | 2.62 | 1025 |
| 1 | 4.38 | 1216 |
| 1 | 3.09 | 1050 |
| 0 | 3.02 | 1453 |
| 0 | 4.38 | 1231 |
| 1 | 2.99 | 1325 |
| 1 | 3.16 | 1312 |
| 0 | 3.13 | 1184 |
| 1 | 3.74 | 1555 |
| 1 | 4.44 | 1120 |
| 1 | 3.62 | 1418 |
| 0 | 3.85 | 1223 |
| 0 | 3.02 | 1055 |
| 0 | 3.23 | 1340 |
| 1 | 4.31 | 1337 |
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Management Accounting Information for Decision-Making and Strategy Execution
Authors: Anthony A. Atkinson, Robert S. Kaplan, Ella Mae Matsumura, S. Mark Young
6th Edition
137024975, 978-0137024971
