EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 1 15:31 Tuesday, August 14, 2001 The REG Procedure Correlation Variable X Y X 1.0000 0.8808 Y 0.8808 1.0000 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 2 15:31 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 40863 40863 86.54 <.0001 Error 25 11804 472.16256 Corrected Total 26 52667 Root MSE 21.72930 R-Square 0.7759 Dependent Mean 94.44444 Adj R-Sq 0.7669 Coeff Var 23.00750 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 14.44806 9.56201 1.51 0.1433 X 1 0.10536 0.01133 9.30 <.0001 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 3 15:31 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Consistent Covariance of Estimates Variable Intercept X Intercept 104.69356902 -0.167679941 X -0.167679941 0.0002881717 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 4 15:31 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Dep Var Predicted Std Error Obs Y Value Mean Predict 95% CL Predict Residual 1 30.0000 45.4242 6.7271 -1.4237 92.2721 -15.4242 2 32.0000 40.4722 7.1517 -6.6417 87.5862 -8.4722 3 37.0000 42.5795 6.9692 -4.4183 89.5772 -5.5795 4 44.0000 52.1673 6.1758 5.6426 98.6921 -8.1673 5 47.0000 59.0158 5.6561 12.7722 105.2594 -12.0158 6 49.0000 47.2154 6.5774 0.4577 93.9730 1.7846 7 56.0000 61.8606 5.4549 15.7196 108.0015 -5.8606 8 62.0000 70.7109 4.8986 24.8354 116.5863 -8.7109 9 68.0000 60.5962 5.5431 14.4107 106.7817 7.4038 10 78.0000 87.8847 4.2408 42.2881 133.4814 -9.8847 11 80.0000 86.9365 4.2590 41.3326 132.5403 -6.9365 12 84.0000 80.8255 4.4306 35.1524 126.4987 3.1745 13 88.0000 89.1491 4.2204 43.5605 134.7377 -1.1491 14 97.0000 80.5095 4.4420 34.8316 126.1873 16.4905 15 100.0000 79.2451 4.4896 33.5475 124.9427 20.7549 16 109.0000 119.7038 4.9860 73.7884 165.6191 -10.7038 17 114.0000 122.1271 5.1325 76.1433 168.1109 -8.1271 18 117.0000 121.3896 5.0869 75.4273 167.3519 -4.3896 19 106.0000 88.2008 4.2353 42.6063 133.7953 17.7992 20 128.0000 104.0050 4.3062 58.3823 149.6277 23.9950 21 130.0000 117.7019 4.8721 71.8384 163.5654 12.2981 22 160.0000 122.4432 5.1523 76.4500 168.4363 37.5568 23 97.0000 122.0217 5.1259 76.0411 168.0024 -25.0217 24 180.0000 140.8814 6.5119 94.1627 187.6001 39.1186 25 112.0000 146.1494 6.9555 99.1603 193.1386 -34.1494 26 210.0000 172.4897 9.3738 123.7507 221.2287 37.5103 27 135.0000 188.2939 10.9206 138.2076 238.3801 -53.2939 Sum of Residuals 0 Sum of Squared Residuals 11804 Predicted Residual SS (PRESS) 15937 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 5 15:31 Tuesday, August 14, 2001 The REG Procedure Correlation Variable X Y X 1.0000 0.9373 Y 0.9373 1.0000 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 6 15:31 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Weight: W Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.09286 0.09286 180.78 <.0001 Error 25 0.01284 0.00051369 Corrected Total 26 0.10571 Root MSE 0.02266 R-Square 0.8785 Dependent Mean 57.54471 Adj R-Sq 0.8737 Coeff Var 0.03939 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 3.80330 4.56975 0.83 0.4131 X 1 0.12099 0.00900 13.45 <.0001 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 7 15:31 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Consistent Covariance of Estimates Variable Intercept X Intercept 17.431873909 -0.034707499 X -0.034707499 0.000085462 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 8 15:31 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Weight Dep Var Predicted Std Error Obs Variable Y Value Mean Predict 95% CL Predict 1 0.0000116 30.0000 39.3744 2.5948 24.6470 54.1019 2 0.0000164 32.0000 33.6879 2.8381 20.7612 46.6146 3 0.0000140 37.0000 36.1077 2.7292 22.4355 49.7799 4 7.8025E-6 44.0000 47.1178 2.3469 29.7218 64.5139 5 5.5888E-6 47.0000 54.9822 2.2232 34.7130 75.2514 6 0.0000103 49.0000 41.4313 2.5185 26.0153 56.8473 7 4.9383E-6 56.0000 58.2489 2.2157 36.7534 79.7444 8 3.5069E-6 62.0000 68.4121 2.3579 43.0169 93.8073 9 5.2126E-6 68.0000 56.7970 2.2158 35.8486 77.7455 10 2.0584E-6 78.0000 88.1335 3.1753 54.9476 121.3195 11 2.1126E-6 80.0000 87.0446 3.1177 54.2938 119.7954 12 2.5195E-6 84.0000 80.0272 2.7753 50.0691 109.9853 13 1.9893E-6 88.0000 89.5854 3.2535 55.8185 123.3524 14 2.5437E-6 97.0000 79.6642 2.7592 49.8499 109.4785 15 2.6439E-6 100.0000 78.2123 2.6962 48.9726 107.4520 16 1.002E-6 109.0000 124.6726 5.4619 76.7027 172.6426 17 9.5741E-7 114.0000 127.4554 5.6518 78.3499 176.5609 18 9.7066E-7 117.0000 126.6085 5.5939 77.8487 175.3682 19 2.0408E-6 106.0000 88.4965 3.1947 55.1654 121.8277 20 1.3841E-6 128.0000 106.6451 4.2711 66.0045 147.2856 21 1.0412E-6 130.0000 122.3738 5.3061 75.3412 169.4064 22 9.5181E-7 160.0000 127.8184 5.6766 78.5647 177.0720 23 9.5929E-7 97.0000 127.3344 5.6435 78.2783 176.3905 24 6.9444E-7 180.0000 148.9917 7.1530 91.0720 206.9113 25 6.4E-7 112.0000 155.0412 7.5821 94.6390 215.4434 26 4.4444E-7 210.0000 185.2888 9.7557 112.4444 258.1331 27 3.6731E-7 135.0000 203.4373 11.0745 123.1107 283.7639 Output Statistics Obs Residual 1 -9.3744 2 -1.6879 3 0.8923 4 -3.1178 5 -7.9822 6 7.5687 7 -2.2489 8 -6.4121 9 11.2030 EXAMPLE 8. WEIGHTED LEAST SQUARES: SUPERVISOR DATA 9 15:31 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Obs Residual 10 -10.1335 11 -7.0446 12 3.9728 13 -1.5854 14 17.3358 15 21.7877 16 -15.6726 17 -13.4554 18 -9.6085 19 17.5035 20 21.3549 21 7.6262 22 32.1816 23 -30.3344 24 31.0083 25 -43.0412 26 24.7112 27 -68.4373 Sum of Residuals 0 Sum of Squared Residuals 0.01284 Predicted Residual SS (PRESS) 0.01493 NOTE: The above statistics use observation weights or frequencies.