OPTIONS NODATE ls=77 ps=55 PAGENO=1; FILENAME r1data URL "http://www.stat.wmich.edu/naranjo/stat6620/usnewsdata.txt"; TITLE '1995 US News Data on Colleges and Universities'; DATA school1; INFILE r1data; INPUT name $ 7-51 state $ 53-54 type 55-56 MSAT 57-60 applctns 95-100 fulltime 120-125 parttime 126-131 Ituition 132-137 pctphd 174-177 sfratio 182-186 expps 190-195 gradrate 196-199; IF state='MI'; RUN; PROC SORT; BY name; RUN; PROC PRINT DATA=school1; var name fulltime parttime Ituition expps gradrate; RUN; PROC REG; TITLE 'Diagnostics for residuals and influential observations'; MODEL gradrate = fulltime applctns Ituition expps; RUN; DATA school2; TITLE2 "Use rescaled X's for more reasonable slopes" ; SET school1; fulltime2=fulltime/1000; applctns2=applctns/1000; Ituition2=Ituition/1000; expps2=expps/1000; RUN; PROC REG; MODEL gradrate = fulltime2 applctns2 Ituition2 expps2 / R INFLUENCE VIF; RUN; PROC REG; TITLE 'Check on VIF'; MODEL fulltime2=applctns2 Ituition2 expps2; RUN; QUIT; 1995 US News Data on Colleges and Universities 1 f p I g u a t r l r u a l t i e d n t t t x r O a i i i p a b m m m o p t s e e e n s e 1 Adrian College 1036 99 11250 8735 54 2 Albion College 1594 32 13868 11487 73 3 Alma College 1306 28 12572 9305 68 4 Andrews University 1586 326 9996 10908 46 5 Aquinas College 1251 767 11208 6584 65 6 Baker College of Flint 2805 1342 5760 2589 . 7 Calvin College 3401 136 10230 7786 81 8 Center for Creative Studies 525 323 11230 13025 47 9 Central Michigan University 13244 1396 2725 6965 70 10 Concordia College 562 18 10430 . 84 11 Eastern Michigan University 13142 6421 2482 5955 49 12 Ferris State University 8996 1901 3412 6467 57 13 Grand Valley State University 8234 2619 2422 5063 57 14 Hillsdale College 1133 42 11090 12639 79 15 Hope College 2505 208 12275 9284 72 16 Kalamazoo College 1218 . 16179 13207 74 17 Lake Superior State University 2432 592 3312 4310 51 18 Lawrence Technological University 2176 2063 6759 4727 45 19 Madonna University 1367 2662 5040 5518 57 20 Marygrove College 602 488 8094 5889 23 21 Michigan State University 26640 4120 4103 10520 71 22 Michigan Technological University 5524 414 3510 7473 65 23 Northern Michigan University 6261 1634 2076 6886 51 24 Northwood University 1650 5180 9450 5568 35 25 Oakland University 6441 3982 3123 6637 53 26 Olivet College 766 58 10500 6395 51 27 Saginaw Valley State University 3598 2147 2674 5391 40 28 Siena Heights College 686 287 9240 9431 47 29 Spring Arbor College 1501 353 8600 10938 49 30 University of Detroit Mercy 2149 2217 11130 10891 51 31 University of Michigan at Ann Arbor 22045 1339 5040 14847 87 32 University of Michigan at Dearborn 3493 3116 3440 6768 63 33 University of Michigan at Flint 3105 2944 2916 5955 64 34 Wayne State University 9778 10455 3271 10538 41 35 Western Michigan University 15739 4278 2785 5983 55 36 William Tyndale College 235 307 5519 8336 16 Diagnostics for residuals and influential observations 2 The REG Procedure Model: MODEL1 Dependent Variable: gradrate Number of Observations Read 36 Number of Observations Used 33 Number of Observations with Missing Values 3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 2270.88259 567.72065 3.43 0.0211 Error 28 4633.84468 165.49445 Corrected Total 32 6904.72727 Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 38.91331 8.43957 4.61 <.0001 fulltime 1 0.00031101 0.00159 0.20 0.8462 applctns 1 0.00151 0.00210 0.72 0.4787 Ituition 1 0.00186 0.00092382 2.01 0.0537 expps 1 -0.00021131 0.00118 -0.18 0.8596 Diagnostics for residuals and influential observations 3 Use rescaled X's for more reasonable slopes Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 2270.88259 567.72065 3.43 0.0211 Error 28 4633.84468 165.49445 Corrected Total 32 6904.72727 Parameter Standard Variance Variable DF Estimate Error t Value Pr > |t| Inflation Intercept 1 38.91331 8.43957 4.61 <.0001 0 fulltime2 1 0.31101 1.58870 0.20 0.8462 19.97700 applctns2 1 1.50989 2.10310 0.72 0.4787 18.25823 Ituition2 1 1.86093 0.92382 2.01 0.0537 2.87986 expps2 1 -0.21131 1.18347 -0.18 0.8596 2.12484 Diagnostics for residuals and influential observations 4 The REG Procedure Model: MODEL1 Dependent Variable: gradrate Output Statistics Dependent Predicted Std Error Std Error Student Obs Variable Value Mean Predict Residual Residual Residual 1 54.0000 60.4814 3.7161 -6.4814 12.316 -0.526 2 73.0000 65.6565 4.4389 7.3435 12.074 0.608 3 68.0000 62.6620 3.9973 5.3380 12.228 0.437 4 46.0000 57.4097 3.5196 -11.4097 12.374 -0.922 5 65.0000 59.7031 4.7896 5.2969 11.940 0.444 6 . 52.6060 6.1397 . . . 7 81.0000 60.0569 3.6584 20.9431 12.333 1.698 8 47.0000 58.1301 5.2079 -11.1301 11.763 -0.946 9 70.0000 57.6599 4.7336 12.3401 11.962 1.032 10 84.0000 . . . . . 11 49.0000 56.4669 5.5328 -7.4669 11.614 -0.643 12 57.0000 59.7865 7.2597 -2.7865 10.620 -0.262 13 57.0000 52.7101 3.8339 4.2899 12.280 0.349 14 79.0000 58.6219 4.7748 20.3781 11.946 1.706 15 72.0000 63.1585 3.9690 8.8415 12.237 0.723 16 74.0000 68.4576 5.7880 5.5424 11.489 0.482 17 51.0000 47.0453 4.5316 3.9547 12.040 0.328 18 45.0000 52.4784 4.0984 -7.4784 12.194 -0.613 19 57.0000 48.2159 3.6127 8.7841 12.347 0.711 20 23.0000 . . . . . 21 71.0000 79.9614 8.6241 -8.9614 9.546 -0.939 22 65.0000 49.5370 3.6199 15.4630 12.345 1.253 23 51.0000 50.0920 4.4752 0.9080 12.061 0.0753 24 35.0000 57.4861 4.6977 -22.4861 11.976 -1.878 25 53.0000 49.9174 3.5400 3.0826 12.368 0.249 26 51.0000 58.2762 4.4984 -7.2762 12.052 -0.604 27 40.0000 46.2082 3.9633 -6.2082 12.239 -0.507 28 47.0000 55.0295 3.0246 -8.0295 12.504 -0.642 29 49.0000 53.6346 4.3195 -4.6346 12.118 -0.382 30 51.0000 59.3922 3.7885 -8.3922 12.294 -0.683 31 87.0000 80.9289 10.3536 6.0711 7.635 0.795 32 63.0000 47.6829 3.7585 15.3171 12.303 1.245 33 64.0000 45.5118 4.0294 18.4882 12.217 1.513 34 41.0000 52.1850 7.0201 -11.1850 10.780 -1.038 35 55.0000 61.5680 5.6645 -6.5680 11.550 -0.569 36 16.0000 47.8880 4.4892 -31.8880 12.056 -2.645 Diagnostics for residuals and influential observations 5 The REG Procedure Model: MODEL1 Dependent Variable: gradrate Output Statistics Cook's Hat Diag Cov Obs -2-1 0 1 2 D RStudent H Ratio DFFITS 1 | *| | 0.005 -0.5193 0.0834 1.2452 -0.1567 2 | |* | 0.010 0.6012 0.1191 1.2739 0.2210 3 | | | 0.004 0.4301 0.0965 1.2830 0.1406 4 | *| | 0.014 -0.9196 0.0749 1.1112 -0.2616 5 | | | 0.006 0.4372 0.1386 1.3442 0.1754 6 . . 0.2278 . . 7 | |*** | 0.051 1.7606 0.0809 0.7579 0.5222 8 | *| | 0.035 -0.9444 0.1639 1.2194 -0.4181 9 | |** | 0.033 1.0328 0.1354 1.1429 0.4087 10 . . . . . 11 | *| | 0.019 -0.6361 0.1850 1.3662 -0.3030 12 | | | 0.006 -0.2580 0.3185 1.7383 -0.1763 13 | | | 0.002 0.3438 0.0888 1.2879 0.1073 14 | |*** | 0.093 1.7697 0.1378 0.8036 0.7074 15 | |* | 0.011 0.7162 0.0952 1.2065 0.2323 16 | | | 0.012 0.4757 0.2024 1.4424 0.2397 17 | | | 0.003 0.3232 0.1241 1.3432 0.1216 18 | *| | 0.008 -0.6063 0.1015 1.2476 -0.2038 19 | |* | 0.009 0.7050 0.0789 1.1886 0.2063 20 . . . . . 21 | *| | 0.144 -0.9367 0.4494 1.8565 -0.8463 22 | |** | 0.027 1.2660 0.0792 0.9763 0.3712 23 | | | 0.000 0.0739 0.1210 1.3632 0.0274 24 | ***| | 0.108 -1.9721 0.1333 0.7062 -0.7736 25 | | | 0.001 0.2450 0.0757 1.2834 0.0701 26 | *| | 0.010 -0.5967 0.1223 1.2799 -0.2227 27 | *| | 0.005 -0.5004 0.0949 1.2654 -0.1621 28 | *| | 0.005 -0.6353 0.0553 1.1788 -0.1537 29 | | | 0.004 -0.3766 0.1127 1.3169 -0.1342 30 | *| | 0.009 -0.6760 0.0867 1.2076 -0.2083 31 | |* | 0.233 0.7898 0.6477 3.0374 1.0709 32 | |** | 0.029 1.2578 0.0854 0.9864 0.3843 33 | |*** | 0.050 1.5508 0.0981 0.8680 0.5115 34 | **| | 0.091 -1.0390 0.2978 1.4040 -0.6766 35 | *| | 0.016 -0.5617 0.1939 1.4039 -0.2754 36 | *****| | 0.194 -2.9989 0.1218 0.3244 -1.1167 Diagnostics for residuals and influential observations 6 The REG Procedure Model: MODEL1 Dependent Variable: gradrate Output Statistics ---------------------------DFBETAS-------------------------- Obs Intercept fulltime2 applctns2 Ituition2 expps2 1 -0.0402 0.0581 -0.0650 -0.0713 0.0579 2 -0.0678 -0.0193 0.0286 0.1085 0.0072 3 -0.0037 -0.0050 0.0157 0.0948 -0.0490 4 0.0644 0.0173 0.0214 0.0516 -0.1576 5 0.0472 0.0168 0.0030 0.1356 -0.1283 6 . . . . . 7 0.0203 0.1812 -0.1247 0.3935 -0.2703 8 0.1694 0.0265 0.0433 0.1298 -0.3263 9 -0.0247 0.2807 -0.2371 0.0330 -0.0247 10 . . . . . 11 0.0077 -0.2286 0.1959 -0.0592 0.0581 12 -0.1179 0.1461 -0.1593 0.0390 0.0535 13 0.0847 -0.0179 0.0238 -0.0191 -0.0477 14 -0.3003 -0.0102 -0.0984 -0.1779 0.5310 15 -0.0341 0.0452 -0.0220 0.1753 -0.0799 16 -0.1383 0.0517 -0.0447 0.1247 0.0452 17 0.1171 -0.0559 0.0471 -0.0383 -0.0477 18 -0.1471 0.0099 -0.0185 -0.0733 0.1544 19 0.1784 -0.0678 0.0429 -0.0599 -0.0572 20 . . . . . 21 0.3076 -0.3540 0.1323 -0.3088 0.0978 22 0.0998 0.0654 -0.1243 -0.2298 0.1534 23 0.0183 -0.0154 0.0125 -0.0205 0.0051 24 -0.4082 0.0845 -0.1663 -0.4821 0.6343 25 0.0245 0.0213 -0.0283 -0.0309 0.0119 26 -0.0983 0.0282 -0.0481 -0.1438 0.1653 27 -0.1227 0.0279 -0.0046 0.0898 0.0043 28 -0.0158 0.0340 -0.0085 0.0289 -0.0544 29 0.0391 -0.0206 0.0481 0.0557 -0.1036 30 0.0994 -0.0801 0.0953 -0.0424 -0.0856 31 -0.1123 -0.5404 0.6719 -0.2466 0.2874 32 0.2360 -0.1030 0.0323 -0.2749 0.0968 33 0.3075 -0.0250 -0.0691 -0.3168 0.0828 34 0.2736 -0.4116 0.4839 0.2725 -0.4637 35 -0.0046 -0.1686 0.1140 -0.0983 0.1059 36 -0.5074 0.5771 -0.3167 0.8378 -0.5113 Sum of Residuals 0 Sum of Squared Residuals 4633.84468 Predicted Residual SS (PRESS) 6418.35515 Check on VIF 7 The REG Procedure Model: MODEL1 Dependent Variable: fulltime2 Number of Observations Read 36 Number of Observations Used 34 Number of Observations with Missing Values 2 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 1249.67451 416.55817 188.69 <.0001 Error 30 66.22940 2.20765 Corrected Total 33 1315.90390 Root MSE 1.48582 R-Square 0.9497 Dependent Mean 5.22241 Adj R-Sq 0.9446 Coeff Var 28.45075 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 2.67670 0.77426 3.46 0.0017 applctns2 1 1.25049 0.07562 16.54 <.0001 Ituition2 1 -0.22915 0.09670 -2.37 0.0244 expps2 1 -0.00324 0.12647 -0.03 0.9797