The SAS System 1 Obs profit area popn outlets commis 1 1011 16.96 3.881 213 1 2 1318 7.31 3.141 158 1 3 1556 7.81 3.766 203 1 4 1521 7.31 4.587 170 1 5 979 19.84 3.648 142 1 6 1290 12.37 3.456 159 1 7 1596 6.15 3.695 178 1 8 1155 14.21 3.609 182 1 9 1412 7.45 3.801 181 1 10 1194 14.43 3.322 148 1 11 1054 6.12 5.124 227 0 12 1157 11.71 4.158 139 1 13 1001 9.36 3.887 179 0 14 831 19.14 2.230 124 1 15 857 11.75 4.468 205 0 16 188 40.34 0.297 85 1 17 1030 7.16 4.224 211 0 18 1331 9.37 3.427 145 1 19 643 7.62 4.310 205 1 20 992 27.54 2.370 166 1 21 795 15.97 3.903 149 1 22 1340 12.97 3.423 186 1 23 689 17.36 2.390 141 0 24 1726 6.24 4.947 233 1 25 1056 11.20 4.166 176 0 26 989 18.09 4.063 187 1 27 895 13.32 3.105 131 1 28 1028 14.97 4.116 170 0 29 771 21.92 1.510 144 1 30 484 34.91 0.741 126 1 31 917 8.46 5.260 234 0 32 1786 7.52 5.744 210 0 33 1063 14.43 2.703 141 1 34 1001 15.37 3.583 158 0 35 1052 11.20 4.469 167 0 36 1610 7.20 4.951 174 1 37 1486 13.49 3.474 211 1 38 1576 6.56 4.637 172 1 39 1665 9.35 3.900 185 1 40 878 11.12 3.766 166 0 41 849 10.58 3.876 189 0 42 775 17.82 3.753 164 0 43 1012 10.03 4.449 193 0 44 1436 10.01 4.680 157 1 45 798 10.70 4.806 200 0 46 519 24.38 2.367 142 0 47 1701 6.57 5.563 199 0 48 1387 6.64 4.357 166 1 49 1717 9.24 4.670 221 1 50 1032 11.62 3.993 180 0 The SAS System 2 Obs profit area popn outlets commis 51 973 12.85 3.923 193 0 The SAS System 3 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Number of Observations Read 51 Number of Observations Used 51 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 4242550 1060638 22.32 <.0001 Error 46 2186016 47522 Corrected Total 50 6428566 Root MSE 217.99559 R-Square 0.6600 Dependent Mean 1120.03922 Adj R-Sq 0.6304 Coeff Var 19.46321 Parameter Estimates Parameter Variable Label DF Estimate Intercept Intercept 1 700.14983 area Area of district (1000 sq 1 -23.36958 miles) popn 1 103.96061 commis 1 330.15153 outlets Number of outlets in district 1 0.75551 Parameter Estimates Standard Variable Label DF Error t Value Intercept Intercept 1 363.15833 1.93 area Area of district (1000 sq 1 8.21232 -2.85 miles) popn 1 62.45281 1.66 commis 1 67.94095 4.86 outlets Number of outlets in district 1 1.50573 0.50 The SAS System 4 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Parameter Estimates Variable Label DF Pr > |t| Tolerance Intercept Intercept 1 0.0600 . area Area of district (1000 sq 1 0.0066 0.28507 miles) popn 1 0.1028 0.20920 commis 1 <.0001 0.84686 outlets Number of outlets in district 1 0.6182 0.43887 Parameter Estimates Variance Variable Label DF Inflation Intercept Intercept 1 0 area Area of district (1000 sq 1 3.50787 miles) popn 1 4.78017 commis 1 1.18084 outlets Number of outlets in district 1 2.27859 The SAS System 5 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Output Statistics Hat Diag Cov Obs Residual RStudent H Ratio DFFITS 1 -187.3472 -0.9305 0.1495 1.1931 -0.3901 2 12.6201 0.0618 0.1417 1.2999 0.0251 3 163.3317 0.7879 0.1031 1.1621 0.2672 4 56.2269 0.2652 0.0732 1.1949 0.0745 5 -74.1791 -0.3611 0.1288 1.2628 -0.1389 6 69.3670 0.3215 0.0397 1.1490 0.0654 7 190.8071 0.9193 0.0965 1.1256 0.3004 8 -55.9156 -0.2594 0.0418 1.1562 -0.0542 9 23.9012 0.1123 0.0675 1.1953 0.0302 10 43.7496 0.2032 0.0446 1.1630 0.0439 11 -207.3220 -0.9971 0.0904 1.1001 -0.3144 12 -136.9271 -0.6672 0.1243 1.2134 -0.2514 13 -19.7410 -0.0932 0.0770 1.2081 -0.0269 14 -77.5225 -0.3679 0.0834 1.1995 -0.1110 15 -187.9320 -0.8894 0.0648 1.0939 -0.2342 16 5.3331 0.0296 0.3295 1.6645 0.0207 17 -101.3650 -0.4875 0.1052 1.2150 -0.1671 18 53.8502 0.2564 0.0906 1.2185 0.0809 19 -812.1741 -4.6442 0.0687 0.1692 -1.2613 20 233.4962 1.1731 0.1596 1.1424 0.5112 21 -380.4178 -1.8806 0.0914 0.8416 -0.5966 22 116.4208 0.5450 0.0545 1.1423 0.1309 23 39.5539 0.1944 0.1475 1.3038 0.0809 24 151.1988 0.7419 0.1345 1.2135 0.2924 25 51.5205 0.2406 0.0546 1.1731 0.0578 26 -182.2172 -0.8895 0.1210 1.1638 -0.3300 27 -245.7875 -1.1846 0.0862 1.0476 -0.3639 28 121.3549 0.5724 0.0680 1.1550 0.1546 29 -12.8136 -0.0626 0.1386 1.2952 -0.0251 30 97.3021 0.5055 0.2329 1.4144 0.2785 31 -309.0644 -1.5319 0.1184 0.9819 -0.5615 32 505.7834 2.6385 0.1266 0.6225 1.0044 33 -17.6102 -0.0830 0.0732 1.2034 -0.0233 34 168.1798 0.7955 0.0671 1.1157 0.2133 35 22.8200 0.1079 0.0791 1.2105 0.0316 36 101.7926 0.4881 0.0998 1.2076 0.1625 37 250.3834 1.2361 0.1267 1.0816 0.4709 38 86.9907 0.4111 0.0747 1.1838 0.1168 39 307.9892 1.4646 0.0463 0.9273 0.3228 40 -79.2097 -0.3740 0.0736 1.1863 -0.1054 41 -149.6416 -0.7077 0.0694 1.1348 -0.1932 42 -22.7711 -0.1075 0.0764 1.2069 -0.0309 43 -62.0863 -0.2895 0.0517 1.1661 -0.0676 The SAS System 6 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Output Statistics -------------------------DFBETAS------------------------- Obs Intercept area popn commis outlets 1 0.3052 -0.2154 -0.0471 -0.1920 -0.2783 2 0.0197 -0.0218 -0.0170 0.0008 -0.0021 3 0.0296 -0.1325 -0.1687 0.0790 0.1661 4 0.0062 -0.0065 0.0337 0.0364 -0.0375 5 0.0507 -0.0939 -0.1085 -0.0578 0.0686 6 0.0267 -0.0232 -0.0099 0.0265 -0.0174 7 0.1724 -0.2394 -0.1835 0.0562 0.0312 8 0.0196 -0.0106 0.0023 -0.0329 -0.0240 9 0.0129 -0.0204 -0.0155 0.0093 0.0049 10 0.0152 -0.0053 0.0045 0.0168 -0.0221 11 0.0767 0.0049 0.0202 0.1146 -0.1614 12 -0.0368 -0.0286 -0.1539 -0.0829 0.2024 13 -0.0171 0.0154 0.0131 0.0204 0.0008 14 -0.0682 0.0322 0.0339 -0.0080 0.0457 15 0.0687 -0.0575 -0.0131 0.1163 -0.0932 16 -0.0019 0.0108 0.0020 0.0010 -0.0031 17 -0.0465 0.0814 0.1025 0.0935 -0.0842 18 0.0604 -0.0527 -0.0204 0.0116 -0.0412 19 0.2545 0.2576 0.2807 -0.6591 -0.6849 20 -0.3099 0.3584 0.0611 0.1706 0.2216 21 0.1435 -0.3008 -0.4475 -0.2768 0.3383 22 -0.0098 -0.0242 -0.0605 0.0570 0.0781 23 0.0605 -0.0384 -0.0481 -0.0595 -0.0120 24 -0.1603 0.0304 -0.0008 0.1542 0.1990 25 0.0206 -0.0082 0.0009 -0.0431 -0.0151 26 0.2707 -0.2676 -0.2001 -0.1867 -0.0715 27 -0.2438 0.1483 0.0213 -0.0533 0.2459 28 -0.0050 0.0569 0.0654 -0.0886 -0.0515 29 -0.0097 0.0080 0.0190 -0.0002 -0.0081 30 -0.0484 0.1180 -0.0542 0.0253 0.0730 31 0.3118 -0.1869 -0.0996 0.1207 -0.3112 32 -0.4632 0.4750 0.7044 -0.1714 -0.1137 33 -0.0168 0.0135 0.0115 -0.0024 0.0064 34 0.0850 -0.0034 0.0050 -0.1610 -0.0820 35 0.0070 0.0028 0.0134 -0.0176 -0.0183 36 -0.0234 0.0252 0.1086 0.0835 -0.0803 37 -0.1602 -0.0026 -0.2085 0.1681 0.4056 38 0.0136 -0.0174 0.0470 0.0559 -0.0558 39 0.0334 -0.1225 -0.0993 0.1600 0.0925 40 -0.0707 0.0478 0.0317 0.0827 0.0304 41 -0.0796 0.0811 0.1004 0.1419 -0.0476 42 0.0023 -0.0141 -0.0114 0.0175 0.0083 43 -0.0061 0.0034 0.0001 0.0449 -0.0050 The SAS System 7 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Output Statistics Hat Diag Cov Obs Residual RStudent H Ratio DFFITS 44 34.4780 0.1671 0.1234 1.2693 0.0627 45 -302.8312 -1.4543 0.0655 0.9493 -0.3849 46 35.2439 0.1706 0.1210 1.2658 0.0633 47 425.7098 2.1419 0.1039 0.7666 0.7295 48 -66.4977 -0.3136 0.0724 1.1902 -0.0876 49 250.1707 1.2214 0.1077 1.0627 0.4244 50 52.2989 0.2441 0.0535 1.1714 0.0580 51 19.4992 0.0913 0.0603 1.1866 0.0231 Output Statistics -------------------------DFBETAS------------------------- Obs Intercept area popn commis outlets 44 -0.0065 0.0163 0.0469 0.0275 -0.0413 45 0.1213 -0.1360 -0.1478 0.1695 -0.0305 46 0.0122 0.0141 -0.0087 -0.0405 -0.0055 47 -0.1587 0.2044 0.4670 -0.2047 -0.2149 48 -0.0305 0.0319 -0.0166 -0.0344 0.0441 49 -0.2750 0.1147 0.0498 0.2455 0.2714 50 0.0214 -0.0129 -0.0118 -0.0455 -0.0025 51 0.0016 -0.0013 -0.0070 -0.0158 0.0087 Sum of Residuals 0 Sum of Squared Residuals 2186016 Predicted Residual SS (PRESS) 2661030 The SAS System 8 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Number of Observations Read 51 Number of Observations Used 51 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 4110867 1370289 27.79 <.0001 Error 47 2317698 49313 Corrected Total 50 6428566 Root MSE 222.06470 R-Square 0.6395 Dependent Mean 1120.03922 Adj R-Sq 0.6165 Coeff Var 19.82651 Parameter Estimates Parameter Variable Label DF Estimate Intercept Intercept 1 1041.77773 area Area of district (1000 sq 1 -33.19926 miles) commis 1 299.45143 outlets Number of outlets in district 1 1.89312 Parameter Estimates Standard Variable Label DF Error t Value Intercept Intercept 1 305.20134 3.41 area Area of district (1000 sq 1 5.81379 -5.71 miles) commis 1 66.61049 4.50 outlets Number of outlets in district 1 1.36675 1.39 Parameter Estimates Variable Label DF Pr > |t| Tolerance Intercept Intercept 1 0.0013 . area Area of district (1000 sq 1 <.0001 0.59025 miles) The SAS System 9 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Parameter Estimates Variable Label DF Pr > |t| Tolerance commis 1 <.0001 0.91422 outlets Number of outlets in district 1 0.1726 0.55273 Parameter Estimates Variance Variable Label DF Inflation Intercept Intercept 1 0 area Area of district (1000 sq 1 1.69420 miles) commis 1 1.09382 outlets Number of outlets in district 1 1.80920 The SAS System 10 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Output Statistics Hat Diag Cov Obs Residual RStudent H Ratio DFFITS 1 -170.4044 -0.8282 0.1473 1.2047 -0.3443 2 -79.6556 -0.3699 0.0770 1.1669 -0.1069 3 89.7536 0.4136 0.0620 1.1448 0.1064 4 100.6269 0.4630 0.0582 1.1359 0.1151 5 27.6210 0.1263 0.0501 1.1458 0.0290 6 58.4395 0.2658 0.0388 1.1269 0.0534 7 121.9708 0.5625 0.0605 1.1287 0.1428 8 -59.0156 -0.2688 0.0417 1.1302 -0.0561 9 -24.5495 -0.1122 0.0497 1.1456 -0.0257 10 51.6543 0.2355 0.0442 1.1347 0.0506 11 -214.3366 -1.0121 0.0901 1.0967 -0.3184 12 -58.6096 -0.2721 0.0777 1.1741 -0.0790 13 -68.9012 -0.3167 0.0586 1.1477 -0.0790 14 -109.5423 -0.5090 0.0756 1.1528 -0.1456 15 -182.7761 -0.8485 0.0646 1.0950 -0.2230 16 25.1137 0.1364 0.3265 1.6156 0.0950 17 -173.5195 -0.8054 0.0657 1.1029 -0.2135 18 26.3454 0.1227 0.0849 1.1894 0.0374 19 -833.3405 -4.6586 0.0653 0.2485 -1.2312 20 250.8204 1.2373 0.1573 1.1345 0.5346 21 -298.1120 -1.3834 0.0400 0.9644 -0.2824 22 77.2448 0.3522 0.0429 1.1264 0.0745 23 -43.3686 -0.2032 0.0953 1.2003 -0.0660 24 150.8371 0.7264 0.1345 1.2030 0.2863 25 52.8648 0.2424 0.0546 1.1469 0.0582 26 -105.6681 -0.4911 0.0765 1.1556 -0.1413 27 -252.0138 -1.1923 0.0859 1.0556 -0.3656 28 161.3847 0.7444 0.0558 1.1003 0.1810 29 -115.1108 -0.5303 0.0591 1.1304 -0.1330 30 63.2238 0.3201 0.2241 1.3921 0.1720 31 -286.9022 -1.3865 0.1147 1.0451 -0.4991 32 596.3254 3.0037 0.0643 0.5690 0.7874 33 -66.0938 -0.3033 0.0554 1.1445 -0.0734 34 170.3818 0.7912 0.0670 1.1067 0.2121 35 65.9028 0.3039 0.0650 1.1563 0.0802 36 178.4025 0.8237 0.0552 1.0879 0.1991 37 193.1804 0.9164 0.1019 1.1288 0.3087 38 126.9413 0.5863 0.0625 1.1284 0.1514 39 283.9566 1.3166 0.0419 0.9811 0.2755 40 -108.8600 -0.5035 0.0670 1.1427 -0.1349 41 -199.3293 -0.9197 0.0506 1.0673 -0.2124 42 14.3613 0.0662 0.0659 1.1663 0.0176 43 -62.1614 -0.2846 0.0517 1.1411 -0.0664 The SAS System 11 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Output Statistics -------------------DFBETAS------------------- Obs Intercept area commis outlets 1 0.3002 -0.2322 -0.1656 -0.2990 2 -0.0704 0.0797 -0.0323 0.0633 3 -0.0409 -0.0083 0.0666 0.0516 4 0.0531 -0.0766 0.0491 -0.0432 5 0.0043 0.0076 0.0099 -0.0073 6 0.0211 -0.0192 0.0251 -0.0203 7 0.0500 -0.0928 0.0661 -0.0351 8 0.0262 -0.0183 -0.0361 -0.0267 9 -0.0049 0.0131 -0.0139 0.0024 10 0.0249 -0.0143 0.0188 -0.0261 11 0.1084 -0.0141 0.1151 -0.1734 12 -0.0596 0.0469 -0.0170 0.0591 13 -0.0396 0.0288 0.0587 0.0256 14 -0.0818 0.0155 -0.0247 0.0945 15 0.0709 -0.0661 0.1188 -0.1061 16 -0.0045 0.0622 0.0024 -0.0114 17 0.0224 0.0180 0.1103 -0.0684 18 0.0283 -0.0261 0.0085 -0.0270 19 0.5015 0.0804 -0.7649 -0.6264 20 -0.3516 0.4766 0.1685 0.2947 21 -0.0949 0.0216 -0.1155 0.1086 22 -0.0343 0.0179 0.0490 0.0365 23 -0.0410 0.0056 0.0489 0.0385 24 -0.1908 0.0436 0.1571 0.2183 25 0.0257 -0.0129 -0.0454 -0.0166 26 0.1029 -0.0959 -0.0741 -0.0981 27 -0.2827 0.1926 -0.0618 0.2886 28 0.0500 0.0183 -0.1427 -0.0317 29 0.0106 -0.0662 -0.0450 0.0052 30 -0.0603 0.1422 0.0262 0.0342 31 0.2797 -0.1498 0.1386 -0.3612 32 -0.0868 -0.0498 -0.4143 0.2543 33 -0.0453 0.0270 -0.0209 0.0473 34 0.1058 -0.0100 -0.1677 -0.0890 35 0.0494 -0.0272 -0.0617 -0.0384 36 0.0758 -0.1253 0.0924 -0.0574 37 -0.2464 0.1550 0.1707 0.2551 38 0.0690 -0.1044 0.0636 -0.0549 39 -0.0247 -0.0659 0.1742 0.0477 40 -0.0858 0.0482 0.1032 0.0675 41 -0.0356 0.0164 0.1533 -0.0030 42 0.0031 0.0052 -0.0131 -0.0021 43 -0.0072 0.0048 0.0458 -0.0055 The SAS System 12 The REG Procedure Model: MODEL1 Dependent Variable: profit Net profit margin for orders placed through rep Output Statistics Hat Diag Cov Obs Residual RStudent H Ratio DFFITS 44 129.8755 0.5973 0.0543 1.1173 0.1431 45 -267.1698 -1.2454 0.0558 1.0109 -0.3028 46 17.7971 0.0845 0.1187 1.2359 0.0310 47 500.6104 2.4472 0.0613 0.7116 0.6256 48 -48.0441 -0.2220 0.0698 1.1666 -0.0608 49 264.1524 1.2663 0.1062 1.0632 0.4366 50 35.2360 0.1612 0.0512 1.1461 0.0375 51 -7.5395 -0.0345 0.0547 1.1528 -0.0083 Output Statistics -------------------DFBETAS------------------- Obs Intercept area commis outlets 44 0.0836 -0.0862 0.0529 -0.0774 45 0.0390 -0.0364 0.1856 -0.0933 46 0.0044 0.0145 -0.0196 -0.0053 47 0.1425 -0.2111 -0.3844 -0.0037 48 -0.0341 0.0446 -0.0220 0.0291 49 -0.3100 0.1176 0.2496 0.3418 50 0.0118 -0.0041 -0.0290 -0.0058 51 0.0011 -0.0020 0.0054 -0.0023 Sum of Residuals 0 Sum of Squared Residuals 2317698 Predicted Residual SS (PRESS) 2692631