FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 1 Obs AGE WEIGHT OXY RUNTIME RSTPULSE RUNPULSE MAXPULS E LOXY LRUNTIME RUNTMAGE 1 44 89.47 44.609 11.37 62 178 182 3.79794 2.43098 500.28 2 40 75.07 45.313 10.07 62 185 185 3.81359 2.30956 402.80 3 44 85.84 54.297 8.65 45 156 168 3.99447 2.15756 380.60 4 42 68.15 59.571 8.17 40 166 172 4.08717 2.10047 343.14 5 38 89.02 49.874 9.22 55 178 180 3.90950 2.22138 350.36 6 47 77.45 44.811 11.63 58 176 176 3.80245 2.45359 546.61 7 40 75.98 45.681 11.95 70 176 180 3.82168 2.48073 478.00 8 43 81.19 49.091 10.85 64 162 170 3.89368 2.38417 466.55 9 44 81.42 39.442 13.08 63 174 176 3.67483 2.57108 575.52 10 38 81.87 60.055 8.63 48 170 186 4.09526 2.15524 327.94 11 44 73.03 50.541 10.13 45 168 168 3.92278 2.31550 445.72 12 45 87.66 37.388 14.03 56 186 192 3.62135 2.64120 631.35 13 45 66.45 44.754 11.12 51 176 176 3.80118 2.40875 500.40 14 47 79.15 47.273 10.60 47 162 164 3.85594 2.36085 498.20 15 54 83.12 51.855 10.33 50 166 170 3.94845 2.33505 557.82 16 49 81.42 49.156 8.95 44 180 185 3.89500 2.19165 438.55 17 51 69.63 40.836 10.95 57 168 172 3.70956 2.39334 558.45 18 51 77.91 46.672 10.00 48 162 168 3.84314 2.30259 510.00 19 48 91.63 46.774 10.25 48 162 164 3.84533 2.32728 492.00 20 49 73.37 50.388 10.08 67 168 168 3.91975 2.31055 493.92 21 57 73.37 39.407 12.63 58 174 176 3.67394 2.53607 719.91 22 54 79.38 46.080 11.17 62 156 165 3.83038 2.41323 603.18 23 52 76.32 45.441 9.63 48 164 166 3.81641 2.26488 500.76 24 50 70.87 54.625 8.92 48 146 155 4.00049 2.18830 446.00 25 51 67.25 45.118 11.08 48 172 172 3.80928 2.40514 565.08 26 54 91.63 39.203 12.88 44 168 172 3.66875 2.55568 695.52 27 51 73.71 45.790 10.47 59 186 188 3.82407 2.34851 533.97 28 57 59.08 50.545 9.93 49 148 155 3.92286 2.29556 566.01 29 49 76.32 48.673 9.40 56 186 188 3.88512 2.24071 460.60 30 48 61.24 47.920 11.50 52 170 176 3.86953 2.44235 552.00 31 52 82.78 47.467 10.50 53 170 172 3.86003 2.35138 546.00 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 2 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Descriptive Statistics Uncorrected Standard Variable Sum Mean SS V ariance Deviation Intercept 31.00000 1.00000 31.00000 0 0 RUNTIME 328.17000 10.58613 3531.79750 1.92492 1.38741 AGE 1478.00000 47.67742 71282 2 7.15914 5.21144 WEIGHT 2400.78000 77.44452 188008 6 9.36504 8.32857 RUNPULSE 5259.00000 169.64516 895317 10 5.10323 10.25199 MAXPULSE 5387.00000 173.77419 938641 8 3.98065 9.16410 RSTPULSE 1657.00000 53.45161 90311 5 8.05591 7.61944 OXY 1468.65000 47.37581 70430 2 8.37938 5.32723 Uncorrected Sums of Squares and Crossproduc ts Variable Intercept RUNTIME A GE WEIGHT Intercept 31 328.17 14 78 2400.78 RUNTIME 328.17 3531.7975 15687. 24 25464.7145 AGE 1478 15687.24 712 82 114158.9 WEIGHT 2400.78 25464.7145 114158 .9 188008.1966 RUNPULSE 5259 55806.29 2501 94 407745.67 MAXPULSE 5387 57113.72 2562 18 417764.62 RSTPULSE 1657 17684.05 788 06 128409.28 OXY 1468.65 15356.14199 69767.7 54 113522.25709 Uncorrected Sums of Squares and Crossproduc ts Variable RUNPULSE MAXPULSE RSTPUL SE OXY Intercept 5259 5387 16 57 1468.65 RUNTIME 55806.29 57113.72 17684. 05 15356.14199 AGE 250194 256218 788 06 69767.754 WEIGHT 407745.67 417764.62 128409. 28 113522.25709 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 3 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Uncorrected Sums of Squares and Crossproduc ts Variable RUNPULSE MAXPULSE RSTPUL SE OXY RUNPULSE 895317 916499 2819 28 248497.309 MAXPULSE 916499 938641 2885 83 254866.745 RSTPULSE 281928 288583 903 11 78015.409 OXY 248497.309 254866.745 78015.4 09 70429.85969 Correlation Variable RUNTIME AGE WEIGHT RUNPULSE MAXPULSE RSTPULSE OXY RUNTIME 1.0000 0.1887 0.1435 0.3136 0.2261 0.4504 -0.8622 AGE 0.1887 1.0000 -0.2335 -0.3379 -0.4329 -0.1641 -0.3046 WEIGHT 0.1435 -0.2335 1.0000 0.1815 0.2494 0.0440 -0.1628 RUNPULSE 0.3136 -0.3379 0.1815 1.0000 0.9298 0.3525 -0.3980 MAXPULSE 0.2261 -0.4329 0.2494 0.9298 1.0000 0.3051 -0.2367 RSTPULSE 0.4504 -0.1641 0.0440 0.3525 0.3051 1.0000 -0.3994 OXY -0.8622 -0.3046 -0.1628 -0.3980 -0.2367 -0.3994 1.0000 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 4 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Model Crossproducts X'X X'Y Y'Y Variable Intercept RUNTIME A GE WEIGHT Intercept 31 328.17 14 78 2400.78 RUNTIME 328.17 3531.7975 15687. 24 25464.7145 AGE 1478 15687.24 712 82 114158.9 WEIGHT 2400.78 25464.7145 114158 .9 188008.1966 RUNPULSE 5259 55806.29 2501 94 407745.67 MAXPULSE 5387 57113.72 2562 18 417764.62 RSTPULSE 1657 17684.05 788 06 128409.28 OXY 1468.65 15356.14199 69767.7 54 113522.25709 Model Crossproducts X'X X'Y Y'Y Variable RUNPULSE MAXPULSE RSTPUL SE OXY Intercept 5259 5387 16 57 1468.65 RUNTIME 55806.29 57113.72 17684. 05 15356.14199 AGE 250194 256218 788 06 69767.754 WEIGHT 407745.67 417764.62 128409. 28 113522.25709 RUNPULSE 895317 916499 2819 28 248497.309 MAXPULSE 916499 938641 2885 83 254866.745 RSTPULSE 281928 288583 903 11 78015.409 OXY 248497.309 254866.745 78015.4 09 70429.85969 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 5 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY X'X Inverse, Parameter Estimates, and SSE Variable Intercept RUNTIME A GE WEIGHT Intercept 28.65754869 0.1430331574 -0.1680342 59 -0.033202236 RUNTIME 0.1430331574 0.0275486714 -0.0026436 35 -0.000822926 AGE -0.168034259 -0.002643635 0.00185675 52 0.000190362 WEIGHT -0.033202236 -0.000822926 0.0001903 62 0.0005551929 RUNPULSE 0.0523069253 -0.001685426 -0.0002242 66 0.0001796617 MAXPULSE -0.155127289 0.0008615381 0.00066732 85 -0.000255622 RSTPULSE -0.027561084 -0.002033294 0.0002775 12 0.0000707735 OXY 102.93447948 -2.628652818 -0.2269737 96 -0.074177414 X'X Inverse, Parameter Estimates, and SSE Variable RUNPULSE MAXPULSE RSTPUL SE OXY Intercept 0.0523069253 -0.155127289 -0.0275610 84 102.93447948 RUNTIME -0.001685426 0.0008615381 -0.0020332 94 -2.628652818 AGE -0.000224266 0.0006673285 0.0002775 12 -0.226973796 WEIGHT 0.0001796617 -0.000255622 0.00007077 35 -0.074177414 RUNPULSE 0.0026758691 -0.002785352 -0.0001424 13 -0.369627758 MAXPULSE -0.002785352 0.0034705808 0.00006381 46 0.3032171295 RSTPULSE -0.000142413 0.0000638146 0.00081277 32 -0.02153364 OXY -0.369627758 0.3032171295 -0.021533 64 128.83793783 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 6 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 722.54361 120.42393 22.43 <.0001 Error 24 128.83794 5.36825 Corrected Total 30 851.38154 Root MSE 2.31695 R-Square 0.8487 Dependent Mean 47.37581 Adj R-Sq 0.8108 Coeff Var 4.89057 Parameter Estimates Squared Parameter Standard Standardized Semi-partial Variable DF Estimate Error t Value Pr > ІtІ Type I SS Ty pe II SS Estimate Corr Type I Intercept 1 102.93448 12.40326 8.30 <.0001 69578 3 69.72831 0 . RUNTIME 1 -2.62865 0.38456 -6.84 <.0001 632.90010 2 50.82210 -0.68460 0.74338 AGE 1 -0.22697 0.09984 -2.27 0.0322 17.76563 27.74577 -0.22204 0.02087 WEIGHT 1 -0.07418 0.05459 -1.36 0.1869 5.60522 9.91059 -0.11597 0.00658 RUNPULSE 1 -0.36963 0.11985 -3.08 0.0051 38.87574 51.05806 -0.71133 0.04566 MAXPULSE 1 0.30322 0.13650 2.22 0.0360 26.82640 26.49142 0.52161 0.03151 RSTPULSE 1 -0.02153 0.06605 -0.33 0.7473 0.57051 0.57051 -0.03080 0.00067010 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 7 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Parameter Estimates Squared Squared Squared Partial Semi-partial Partial Variance Variable DF Corr Type I Corr Type II Corr Type II Tolerance I nflation 95% Confidence Limits Intercept 1 . . . . 0 77.33541 128.53355 RUNTIME 1 0.74338 0.29461 0.66065 0.62859 1.59087 -3.42235 -1.83496 AGE 1 0.08131 0.03259 0.17719 0.66101 1.51284 -0.43303 -0.02092 WEIGHT 1 0.02793 0.01164 0.07143 0.86555 1.15533 -0.18685 0.03850 RUNPULSE 1 0.19925 0.05997 0.28382 0.11852 8.43727 -0.61699 -0.12226 MAXPULSE 1 0.17171 0.03112 0.17055 0.11437 8.74385 0.02150 0.58493 RSTPULSE 1 0.00441 0.00067010 0.00441 0.70642 1.41559 -0.15786 0.11480 Covariance of Estimates Variable Intercept RUNTIME AGE WEIGHT R UNPULSE MAXPULSE RSTPULSE Intercept 153.84081152 0.7678373769 -0.902049478 -0.178237818 0.28 0796516 -0.832761667 -0.147954715 RUNTIME 0.7678373769 0.1478880839 -0.014191688 -0.004417672 -0.00 9047784 0.0046249498 -0.010915224 AGE -0.902049478 -0.014191688 0.009967521 0.0010219105 -0.00 1203914 0.0035823843 0.0014897532 WEIGHT -0.178237818 -0.004417672 0.0010219105 0.0029804131 0.000 9644683 -0.001372241 0.0003799295 RUNPULSE 0.280796516 -0.009047784 -0.001203914 0.0009644683 0.014 3647273 -0.014952457 -0.000764507 MAXPULSE -0.832761667 0.0046249498 0.0035823843 -0.001372241 -0.01 4952457 0.0186309364 0.0003425724 RSTPULSE -0.147954715 -0.010915224 0.0014897532 0.0003799295 -0.00 0764507 0.0003425724 0.0043631674 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 8 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Correlation of Estimates Variable Intercept RUNTIME AGE WEIGHT R UNPULSE MAXPULSE RSTPULSE Intercept 1.0000 0.1610 -0.7285 -0.2632 0.1889 -0.4919 -0.1806 RUNTIME 0.1610 1.0000 -0.3696 -0.2104 -0.1963 0.0881 -0.4297 AGE -0.7285 -0.3696 1.0000 0.1875 -0.1006 0.2629 0.2259 WEIGHT -0.2632 -0.2104 0.1875 1.0000 0.1474 -0.1842 0.1054 RUNPULSE 0.1889 -0.1963 -0.1006 0.1474 1.0000 -0.9140 -0.0966 MAXPULSE -0.4919 0.0881 0.2629 -0.1842 -0.9140 1.0000 0.0380 RSTPULSE -0.1806 -0.4297 0.2259 0.1054 -0.0966 0.0380 1.0000 Sequential Parameter Estimates Intercept RUNTIME AGE WEIGHT RUNP ULSE MAXPULSE RSTPULSE 47.375806 0 0 0 0 0 0 82.421773 -3.310555 0 0 0 0 0 88.462287 -3.203951 -0.150366 0 0 0 0 93.126150 -3.140387 -0.173877 -0.054437 0 0 0 115.662297 -2.772369 -0.276417 -0.049323 -0.12 9324 0 0 102.204275 -2.682523 -0.219621 -0.072302 -0.37 3401 0.304908 0 102.934479 -2.628653 -0.226974 -0.074177 -0.36 9628 0.303217 -0.021534 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 9 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Consistent Covariance of Estimates Variable Intercept RUNTIME AGE WEIGHT R UNPULSE MAXPULSE RSTPULSE Intercept 57.15651161 0.4031401002 -0.502827963 -0.17344742 0.157 4946096 -0.265912549 -0.088050065 RUNTIME 0.4031401002 0.0578211177 -0.00879021 -0.004458102 -0.00 7815908 0.0074146392 -0.004978143 AGE -0.502827963 -0.00879021 0.0071282949 0.0020193325 0.000 1899223 0.0000720652 0.0012393367 WEIGHT -0.17344742 -0.004458102 0.0020193325 0.0017268578 0.000 5647816 -0.000652952 0.0001616179 RUNPULSE 0.1574946096 -0.007815908 0.0001899223 0.0005647816 0.007 6336033 -0.008518188 0.0011798699 MAXPULSE -0.265912549 0.0074146392 0.0000720652 -0.000652952 -0.00 8518188 0.010115077 -0.001546469 RSTPULSE -0.088050065 -0.004978143 0.0012393367 0.0001616179 0.001 1798699 -0.001546469 0.0026391908 Test of First and Second Moment Specification DF Chi-Square Pr > ChiSq 27 23.38 0.6645 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 10 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Output Statistics Dep Var Predicted Std Error Std Error Student Obs OXY Value Mean Predict 95% CL Mean 95% CL Pr edict Residual Residual Residual 1 44.6090 44.4799 0.8734 42.6773 46.2825 39.3695 49.5903 0.1291 2.146 0.0602 2 45.3130 48.1954 1.0672 45.9928 50.3981 42.9306 53.4603 -2.8824 2.057 -1.402 3 54.2970 56.1519 1.1443 53.7903 58.5136 50.8186 61.4853 -1.8549 2.015 -0.921 4 59.5710 56.8041 1.2075 54.3119 59.2963 51.4117 62.1965 2.7669 1.977 1.399 5 49.8740 51.0710 1.1743 48.6474 53.4946 45.7100 56.4321 -1.1970 1.997 -0.599 6 44.8110 43.0132 0.6705 41.6294 44.3970 38.0351 47.9914 1.7978 2.218 0.811 7 45.6810 44.8244 1.1907 42.3668 47.2819 39.4479 50.2009 0.8566 1.988 0.431 8 49.0910 48.9203 1.0635 46.7255 51.1152 43.6587 54.1819 0.1707 2.058 0.0829 9 39.4420 40.2197 1.0438 38.0654 42.3740 34.9749 45.4645 -0.7777 2.069 -0.376 10 60.0550 58.0793 1.6245 54.7266 61.4321 52.2392 63.9195 1.9757 1.652 1.196 11 50.5410 48.7762 1.0925 46.5213 51.0311 43.4893 54.0631 1.7648 2.043 0.864 12 37.3880 37.5993 1.5015 34.5004 40.6982 31.9010 43.2976 -0.2113 1.765 -0.120 13 44.7540 45.7745 1.0219 43.6654 47.8835 40.5481 51.0008 -1.0205 2.079 -0.491 14 47.2730 47.3677 0.8839 45.5435 49.1919 42.2496 52.4858 -0.0947 2.142 -0.0442 15 51.8550 46.4703 0.8320 44.7531 48.1875 41.3894 51.5512 5.3847 2.162 2.490 16 49.1560 50.8615 1.1855 48.4147 53.3083 45.4899 56.2331 -1.7055 1.991 -0.857 17 40.8360 46.2386 0.6639 44.8684 47.6087 41.2642 51.2129 -5.4026 2.220 -2.434 18 46.6720 49.3203 0.6103 48.0607 50.5798 44.3752 54.2653 -2.6483 2.235 -1.185 19 46.7740 47.1135 1.1692 44.7003 49.5266 41.7571 52.4698 -0.3395 2.000 -0.170 20 50.3880 47.2738 1.2236 44.7485 49.7991 41.8660 52.6816 3.1142 1.968 1.583 21 39.4070 39.1567 1.0656 36.9574 41.3560 33.8933 44.4202 0.2503 2.057 0.122 22 46.0800 46.4614 1.2187 43.9463 48.9766 41.0584 51.8645 -0.3814 1.971 -0.194 23 45.4410 48.8382 0.7598 47.2701 50.4063 43.8057 53.8707 -3.3972 2.189 -1.552 24 54.6250 54.8806 1.1055 52.5990 57.1623 49.5822 60.1790 -0.2556 2.036 -0.126 25 45.1180 44.7887 0.9153 42.8996 46.6777 39.6471 49.9302 0.3293 2.128 0.155 26 39.2030 39.1324 1.4192 36.2033 42.0615 33.5246 44.7401 0.0706 1.831 0.0386 27 45.7900 45.3528 1.1495 42.9804 47.7252 40.0147 50.6909 0.4372 2.012 0.217 28 50.5450 50.7506 1.3230 48.0201 53.4812 45.2440 56.2573 -0.2056 1.902 -0.108 29 48.6730 48.4904 1.1986 46.0167 50.9641 43.1065 53.8743 0.1826 1.983 0.0921 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 11 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Output Statistics Cook's Hat Diag Cov Obs -2-1 0 1 2 D RStudent H Ratio DFFITS 1 І І І 0.000 0.0589 0.1421 1.5685 0.0240 2 І **І І 0.076 -1.4320 0.2122 0.9404 -0.7431 3 І *І І 0.039 -0.9177 0.2439 1.3851 -0.5212 4 І І** І 0.104 1.4293 0.2716 1.0193 0.8728 5 І *І І 0.018 -0.5911 0.2569 1.6311 -0.3475 6 І І* І 0.009 0.8046 0.0837 1.2105 0.2433 7 І І І 0.010 0.4236 0.2641 1.7336 0.2538 8 І І І 0.000 0.0812 0.2107 1.7032 0.0419 9 І І І 0.005 -0.3691 0.2030 1.6216 -0.1863 10 І І** І 0.198 1.2072 0.4916 1.7234 1.1870 11 І І* І 0.030 0.8590 0.2223 1.3887 0.4593 12 І І І 0.001 -0.1173 0.4200 2.3126 -0.0998 13 І І І 0.008 -0.4828 0.1945 1.5584 -0.2373 14 І І І 0.000 -0.0433 0.1455 1.5756 -0.0179 15 І І**** І 0.131 2.8306 0.1289 0.1908 1.0891 16 І *І І 0.037 -0.8518 0.2618 1.4682 -0.5073 17 І ****І І 0.076 -2.7453 0.0821 0.2018 -0.8210 18 І **І І 0.015 -1.1954 0.0694 0.9492 -0.3264 19 І І І 0.001 -0.1662 0.2547 1.7922 -0.0972 20 І І*** І 0.138 1.6373 0.2789 0.8634 1.0182 21 І І І 0.001 0.1191 0.2115 1.7011 0.0617 22 І І І 0.002 -0.1896 0.2767 1.8420 -0.1173 23 І ***І І 0.041 -1.6019 0.1075 0.7199 -0.5560 24 І І І 0.001 -0.1229 0.2277 1.7361 -0.0668 25 І І І 0.001 0.1515 0.1561 1.5850 0.0652 26 І І І 0.000 0.0378 0.3752 2.1550 0.0293 27 І І І 0.002 0.2130 0.2461 1.7624 0.1217 28 І І І 0.001 -0.1059 0.3261 1.9920 -0.0736 29 І І І 0.000 0.0902 0.2676 1.8347 0.0545 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 12 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Output Statistics -------------------------------------DFBETAS------------ ------------------------- Obs Intercept RUNTIME AGE WEIGHT RUNPULS E MAXPULSE RSTPULSE 1 -0.0085 -0.0011 -0.0009 0.0144 -0.000 1 0.0010 0.0101 2 -0.0463 0.2484 0.2592 0.1274 -0.335 8 0.2252 -0.2393 3 -0.1004 0.0974 0.0796 -0.1783 0.278 1 -0.1999 0.0660 4 0.4394 -0.1205 -0.3896 -0.3843 0.025 2 -0.0102 -0.4610 5 -0.0650 0.1382 0.1503 -0.1667 -0.150 4 0.1415 -0.0331 6 0.0246 0.0633 -0.0526 -0.0032 0.139 0 -0.1318 0.0184 7 0.0440 0.0597 -0.1240 -0.0561 -0.033 7 0.0116 0.1374 8 0.0107 0.0026 -0.0139 0.0051 -0.018 0 0.0078 0.0252 9 -0.0382 -0.1253 0.0912 -0.0060 -0.011 4 0.0359 -0.0214 10 -0.1569 -0.1115 -0.2117 -0.0879 -0.853 1 0.9145 -0.1245 11 0.3228 0.0926 -0.2779 -0.0907 0.257 7 -0.2929 -0.2532 12 0.0405 -0.0710 0.0105 -0.0051 0.031 9 -0.0429 0.0330 13 -0.0983 -0.0876 0.1136 0.1519 -0.092 3 0.0790 0.1012 14 -0.0121 -0.0052 0.0082 -0.0029 -0.007 4 0.0111 0.0080 15 -0.4336 -0.3386 0.7628 0.5961 0.075 3 -0.0318 0.0160 16 0.2769 0.2413 -0.2320 -0.0895 -0.018 4 -0.1342 0.1553 17 0.0659 -0.0294 -0.2586 0.4374 0.151 1 -0.1547 -0.2648 18 -0.0048 0.0472 -0.1195 -0.0573 0.078 4 -0.0526 0.0680 19 -0.0261 0.0072 0.0095 -0.0732 -0.039 4 0.0545 0.0148 20 0.1114 -0.5092 0.1474 0.0446 0.356 9 -0.4289 0.8106 21 -0.0338 0.0164 0.0402 -0.0093 -0.003 8 0.0112 0.0064 22 0.0250 0.0056 -0.0525 -0.0208 0.066 1 -0.0467 -0.0707 23 -0.0847 0.2344 -0.1930 -0.1132 -0.254 5 0.2664 0.0630 24 -0.0378 0.0100 0.0041 0.0099 0.024 6 -0.0051 -0.0064 25 0.0133 0.0187 -0.0012 -0.0346 0.027 5 -0.0219 -0.0329 26 -0.0065 0.0159 0.0055 0.0135 -0.000 8 0.0003 -0.0159 27 -0.0881 -0.0525 0.0747 -0.0172 0.010 1 0.0302 0.0343 28 -0.0213 -0.0014 -0.0199 0.0399 0.023 1 -0.0114 -0.0040 29 -0.0343 -0.0354 0.0291 0.0004 0.010 7 0.0074 0.0124 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 13 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Output Statistics Dep Var Predicted Std Error Std Error Student Obs OXY Value Mean Predict 95% CL Mean 95% CL Pr edict Residual Residual Residual 30 47.9200 46.6774 1.1923 44.2166 49.1381 41.2994 52.0553 1.2426 1.987 0.626 31 47.4670 45.5659 0.7433 44.0318 47.1001 40.5439 50.5879 1.9011 2.194 0.866 Output Statistics Cook's Hat Diag Cov Obs -2-1 0 1 2 D RStudent H Ratio DFFITS 30 І І* І 0.020 0.6174 0.2648 1.6331 0.3705 31 І І* І 0.012 0.8616 0.1029 1.2022 0.2919 Output Statistics -------------------------------------DFBETAS------------ ------------------------- Obs Intercept RUNTIME AGE WEIGHT RUNPULS E MAXPULSE RSTPULSE 30 0.0484 0.1819 -0.0651 -0.3146 -0.133 2 0.1441 -0.1011 31 -0.0981 -0.1063 0.1664 0.1676 0.107 1 -0.0885 0.0390 Sum of Residuals 0 Sum of Squared Residuals 128.837 94 Predicted Residual SS (PRESS) 192.788 22 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 14 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Partial Regression Residual Plot фтттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттътттт ттъттттттъттттттъттттттъттттттъттттттттх OXY щ щ 10 ъ ъ щ щ щ 1 щ щ 1 щ щ щ щ щ 5 ъ 11 ъ щ 1 щ щ 1 щ щ 1 1 1 1 1 1 1 щ щ 1 щ щ 2 щ 0 ъ 1 1 1 ъ щ щ щ щ щ 11 1 1 1 1 щ щ щ щ щ -5 ъ 11 ъ щ 1 1 щ щ 1 1 щ щ щ щ щ щ щ -10 ъ ъ щ щ штттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттътттт ттъттттттъттттттъттттттъттттттъттттттттю -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Intercept FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 15 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Partial Regression Residual Plot фтътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттъттт ттттттътттттттттътттттттттътттттттттъттх OXY щ щ 10 ъ ъ щ щ щ щ щ 1 1 щ щ щ щ 1 щ 5 ъ ъ щ 1 1 1 щ щ 1 щ щ 1 щ щ 1 щ щ 1 1 щ 0 ъ 1 1 11 1 1 1 ъ щ 1 1 1 щ щ 1 111 щ щ 1 щ щ 1 щ щ щ -5 ъ 1 ъ щ 1 1 щ щ щ щ 1 щ щ щ щ щ -10 ъ ъ щ щ штътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттъттт ттттттътттттттттътттттттттътттттттттъттю -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 RUNTIME FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 16 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Partial Regression Residual Plot фттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъ ттттттъттттттъттттттъттттттъттттттъттттх OXY щ щ 4 ъ 1 1 ъ щ щ щ 1 щ щ 1 1 щ щ щ 2 ъ 1 1 ъ щ 1 щ щ щ щ 1 1 1 щ щ 1 11 щ 0 ъ 1 1 1 1 1 ъ щ 1 щ щ щ щ 1 1 11 щ щ 1 1 щ -2 ъ 1 ъ щ щ щ 1 щ щ 1 щ щ щ -4 ъ 1 ъ щ щ щ щ щ щ щ щ -6 ъ 1 ъ шттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъ ттттттъттттттъттттттъттттттъттттттъттттю -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 AGE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 17 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Partial Regression Residual Plot фттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттъ тттттътттттътттттътттттътттттътттттътттх OXY щ щ 6 ъ ъ щ щ щ 1 щ щ щ 4 ъ ъ щ 1 щ щ 1 щ щ 1 щ 2 ъ 1 1 1 ъ щ 1 щ щ 1 1 1 щ щ 2 щ 0 ъ 1 1 1 1 ъ щ 1 1 1 1 щ щ 1 1 щ щ 1 щ -2 ъ 1 1 ъ щ 1 1 щ щ 1 щ щ 1 щ -4 ъ ъ щ щ щ 1 щ щ щ -6 ъ ъ щ щ шттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттъ тттттътттттътттттътттттътттттътттттътттю -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 WEIGHT FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 18 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Partial Regression Residual Plot фъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттт тттъттттттъттттттъттттттъттттттъттттттъх OXY щ щ 7.5 ъ ъ щ щ щ щ щ щ щ 1 щ 5.0 ъ 1 ъ щ щ щ щ щ щ щ щ 2.5 ъ 1 1 ъ щ 1 щ щ 1 11 1 щ щ 2 1 щ щ 1 1 щ 0.0 ъ 1 1 1 1 1 ъ щ 1 щ щ 1 1 1 щ щ щ щ 1 1 1 1 щ -2.5 ъ ъ щ 1 щ щ щ щ щ щ 1 1 щ -5.0 ъ 1 ъ шъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттт тттъттттттъттттттъттттттъттттттъттттттъю -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 RUNPULSE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 19 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Partial Regression Residual Plot фъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттт тттъттттттъттттттъттттттъттттттъттттттъх OXY щ щ 7.5 ъ ъ щ щ щ щ щ щ щ 1 щ 5.0 ъ 1 ъ щ щ щ щ щ щ щ щ 2.5 ъ 1 1 ъ щ 1 щ щ 1 щ щ 1 1 1 1 щ щ 1 2 1 щ 0.0 ъ 1 11 1 1 ъ щ 1 щ щ 1 1 1 щ щ 1 щ щ 1 1 щ -2.5 ъ 1 1 ъ щ щ щ 1 щ щ 1 щ щ щ -5.0 ъ 1 ъ шъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттт тттъттттттъттттттъттттттъттттттъттттттъю -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 MAXPULSE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 20 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Partial Regression Residual Plot фтттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттт тттъттттттъттттттъттттттъттттттътттттттх OXY щ щ 7.5 ъ ъ щ щ щ щ щ 1 щ 5.0 ъ ъ щ щ щ щ щ 1 щ 2.5 ъ 1 ъ щ 1 1 1 1 щ щ 1 щ щ 1 1 1 1 щ 0.0 ъ 1 1 1 1 2 1 1 1 ъ щ 1 1 1 щ щ 1 щ щ 1 1 щ -2.5 ъ 1 ъ щ 1 1 щ щ щ щ щ -5.0 ъ ъ щ 1 щ щ щ щ щ -7.5 ъ ъ щ щ штттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттт тттъттттттъттттттъттттттъттттттътттттттю -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 RSTPULSE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 21 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY фттттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттътт ттъттттъттттъттттъттттъттттъттттъттттттх STUDENT щ щ 3 ъ ъ щ щ S щ 1 щ t щ щ u 2 ъ ъ d щ щ e щ 1 1 щ n щ 1 щ t 1 ъ ъ i щ 1 1 1 1 щ z щ 1 щ e щ 2 щ d 0 ъ 1 1 1 1 1 1 2 ъ щ 1 1 1 щ R щ 1 1 1 щ e щ 1 щ s -1 ъ 1 ъ i щ 1 щ d щ 1 1 щ u щ щ a -2 ъ ъ l щ щ щ 1 щ щ щ -3 ъ ъ щ щ шттттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттътт ттъттттъттттъттттъттттъттттъттттъттттттю 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 AGE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 22 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY фттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттъ тттттътттттътттттътттттътттттътттттътттх STUDENT щ щ 3 ъ ъ щ щ S щ 1 щ t щ щ u 2 ъ ъ d щ щ e щ 1 1 щ n щ 1 щ t 1 ъ ъ i щ 1 1 1 1 щ z щ 1 щ e щ 1 1 щ d 0 ъ 1 1 1 1 1 1 1 1 ъ щ 1 1 1 щ R щ 1 1 1 щ e щ 1 щ s -1 ъ 1 ъ i щ 1 щ d щ 1 1 щ u щ щ a -2 ъ ъ l щ щ щ 1 щ щ щ -3 ъ ъ щ щ шттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттътттттъ тттттътттттътттттътттттътттттътттттътттю 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 WEIGHT FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 23 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY фтттттътттттттътттттттътттттттътттттттътттттттътттттттътттттттъттттттт ътттттттътттттттътттттттътттттттъттттттх STUDENT щ щ 3 ъ ъ щ щ S щ 1 щ t щ щ u 2 ъ ъ d щ щ e щ 1 1 щ n щ 1 щ t 1 ъ ъ i щ 1 1 1 1 щ z щ 1 щ e щ 1 1 щ d 0 ъ 1 1 1 1 1 1 1 1 ъ щ 1 1 1 щ R щ 1 1 1 щ e щ 1 щ s -1 ъ 1 ъ i щ 1 щ d щ 1 1 щ u щ щ a -2 ъ ъ l щ щ щ 1 щ щ щ -3 ъ ъ щ щ штттттътттттттътттттттътттттттътттттттътттттттътттттттътттттттъттттттт ътттттттътттттттътттттттътттттттъттттттю 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12 .0 12.5 13.0 13.5 14.0 RUNTIME FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 24 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY фтттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъ ттттъттттъттттъттттъттттъттттъттттъттттх STUDENT щ щ 3 ъ ъ щ щ S щ 1 щ t щ щ u 2 ъ ъ d щ щ e щ 1 1 щ n щ 1 щ t 1 ъ ъ i щ 1 2 1 щ z щ 1 щ e щ 1 1 щ d 0 ъ 1 2 1 1 1 2 ъ щ 1 1 1 щ R щ 1 1 1 щ e щ 1 щ s -1 ъ 1 ъ i щ 1 щ d щ 1 1 щ u щ щ a -2 ъ ъ l щ щ щ 1 щ щ щ -3 ъ ъ щ щ штттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъ ттттъттттъттттъттттъттттъттттъттттъттттю 146 148 150 152 154 156 158 160 162 164 166 168 170 17 2 174 176 178 180 182 184 186 RUNPULSE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 25 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY фттттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттътт ттъттттъттттъттттъттттъттттъттттъттттттх STUDENT щ щ 3 ъ ъ щ щ S щ 1 щ t щ щ u 2 ъ ъ d щ щ e щ 1 1 щ n щ 1 щ t 1 ъ ъ i щ 1 1 2 щ z щ 1 щ e щ 1 1 щ d 0 ъ 1 1 1 1 1 1 1 1 ъ щ 1 1 1 щ R щ 2 1 щ e щ 1 щ s -1 ъ 1 ъ i щ 1 щ d щ 1 1 щ u щ щ a -2 ъ ъ l щ щ щ 1 щ щ щ -3 ъ ъ щ щ шттттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттъттттътт ттъттттъттттъттттъттттъттттъттттъттттттю 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 MAXPULSE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 26 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY фтъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттътттт ттъттттттъттттттъттттттъттттттъттттттътх STUDENT щ щ 3 ъ ъ щ щ S щ 1 щ t щ щ u 2 ъ ъ d щ щ e щ 1 1 щ n щ 1 щ t 1 ъ ъ i щ 1 1 1 1 щ z щ 1 щ e щ 1 1 щ d 0 ъ 1 1 1 2 1 1 1 ъ щ 2 1 щ R щ 1 1 1 щ e щ 1 щ s -1 ъ 1 ъ i щ 1 щ d щ 1 1 щ u щ щ a -2 ъ ъ l щ щ щ 1 щ щ щ -3 ъ ъ щ щ штъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттъттттттътттт ттъттттттъттттттъттттттъттттттъттттттътю 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 RSTPULSE FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 27 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The UNIVARIATE Procedure Variable: RES (Residual) Moments N 31 Sum Weights 31 Mean 0 Sum Observations 0 Std Deviation 2.07234117 Variance 4.29459793 Skewness -0.0722231 Kurtosis 1.47046855 Uncorrected SS 128.837938 Corrected SS 128.837938 Coeff Variation . Std Error Mean 0.37220346 Basic Statistical Measures Location Variability Mean 0.000000 Std Deviation 2.07234 Median 0.070628 Variance 4.29460 Mode . Range 1 0.78725 Interquartile Range 2.26311 Tests for Location: Mu0=0 Test -Statistic- -----p Value-- ---- Student's t t 0 Pr > ІtІ 1. 0000 Sign M 0.5 Pr >= ІMІ 1. 0000 Signed Rank S 1 Pr >= ІSІ 0. 9847 Tests for Normality Test --Statistic--- -----p Va lue------ Shapiro-Wilk W 0.967787 Pr < W 0.4603 Kolmogorov-Smirnov D 0.136658 Pr > D 0.1439 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 28 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The UNIVARIATE Procedure Variable: RES (Residual) Tests for Normality Test --Statistic--- -----p Va lue------ Cramer-von Mises W-Sq 0.099941 Pr > W-Sq 0.1094 Anderson-Darling A-Sq 0.513679 Pr > A-Sq 0.1870 Quantiles (Definition 5) Quantile Estimate 100% Max 5.3846936 99% 5.3846936 95% 3.1141933 90% 1.9756510 75% Q3 1.2426484 50% Median 0.0706275 25% Q1 -1.0204638 10% -2.6482916 5% -3.3971716 1% -5.4025596 0% Min -5.4025596 Extreme Observations ------Lowest----- -----Highest---- - Value Obs Value Ob s -5.40256 17 1.90107 3 1 -3.39717 23 1.97565 1 0 -2.88244 2 2.76691 4 -2.64829 18 3.11419 2 0 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 29 MULTIVARIATE LINEAR REGRESSION OF ALL COVARIATES WITH OXY The UNIVARIATE Procedure Variable: RES (Residual) Extreme Observations ------Lowest----- -----Highest---- - Value Obs Value Ob s -1.85493 3 5.38469 1 5 Stem Leaf # Boxplot Normal Probability Plot 5 4 1 0 5.5+ * + 4 І +++++ 3 1 1 І І +*+++ 2 08 2 І І ++++* 1 2889 4 +-----+ І ++**** * 0 11223349 8 *--+--* І ******* -0 8433221 7 І І І ****** -1 9720 4 +-----+ І ****++ -2 96 2 І І *+*++ -3 4 1 І І +++*+ -4 І +++++ -5 4 1 0 -5.5++ * ----+----+----+----+ +----+----+ ----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 30 smoothed plot of RES versus ypred with smooth 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Predicted Value Statistic of OXY Minimum Value 37.59931 Maximum Value 58.07935 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 31 smoothed plot of RES versus ypred with smooth 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: RES Fit Summary Fit Method kd Tre e Blending Linea r Number of Observations 3 1 Number of Fitting Points 1 6 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.5000 0 Points in Local Neighborhood 1 5 Residual Sum of Squares 111.4764 6 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 32 smoothed plot of RES versus ypred with smooth 0.5 ------------------------------------------------ SmoothingParameter=0.5 -------- ---------------------------------------- Plot of DepVar*ypred. Symbol used is '*' . Plot of Pred*ypred. Symbol used is '+' . щ 7.50000 ъ щ щ щ * 5.00000 ъ щ щ щ * 2.50000 ъ * щ * * * * щ * + R щ + +* *+ +++ + + + E 0 ъ * * + * * * * * * S щ * * * ++ щ * + + ++* щ * * -2.50000 ъ * щ * * щ щ -5.00000 ъ щ * щ щ -7.50000 ъ щ шттъттттттттттъттттттттттъттттттттттъттттттттттъттттттттттътттттттт ттъттттттттттъттттттттттъттттттттттътт 37.50000 40.00000 42.50000 45.00000 47.50000 50.00000 52 .50000 55.00000 57.50000 60.00000 Predicted Value of OXY NOTE: 16 obs hidden. FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 33 smoothed plot of STDRES versus ypred with smoo th 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Predicted Value Statistic of OXY Minimum Value 37.59931 Maximum Value 58.07935 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 34 smoothed plot of STDRES versus ypred with smoo th 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: stdres Fit Summary Fit Method kd Tre e Blending Linea r Number of Observations 3 1 Number of Fitting Points 1 6 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.5000 0 Points in Local Neighborhood 1 5 Residual Sum of Squares 24.6815 1 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 35 smoothed plot of STDRES versus ypred with smoo th 0.5 ------------------------------------------------ SmoothingParameter=0.5 -------- ---------------------------------------- Plot of DepVar*ypred. Symbol used is '*' . Plot of Pred*ypred. Symbol used is '+' . щ 3.00000 ъ щ щ * щ 2.00000 ъ щ щ * * щ * 1.00000 ъ s щ * * * * + t щ * + + d щ + +* *+ +++ ++ + r 0 ъ * * + * * * * * e щ + * * ++ * s щ * * + + ++* щ * -1.00000 ъ * щ * щ * * щ -2.00000 ъ щ щ * щ -3.00000 ъ щ шттъттттттттттъттттттттттъттттттттттъттттттттттъттттттттттътттттттт ттъттттттттттъттттттттттъттттттттттътт 37.50000 40.00000 42.50000 45.00000 47.50000 50.00000 52 .50000 55.00000 57.50000 60.00000 Predicted Value of OXY NOTE: 12 obs hidden. FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 36 smoothed plot of STDRES versus ypred with smoo th 0.5 Obs predgrp meangroup vargroup 1 0 38.6295 0.0541 2 1 42.5709 1.7066 3 2 44.9886 0.0776 4 3 45.8596 13.5135 5 4 46.5364 8.8404 6 5 47.4876 6.0402 7 6 48.7016 6.9940 8 7 49.6638 2.3425 9 8 52.2710 0.5411 10 9 57.0118 6.1101 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 37 smoothed plot of STDRES versus ypred with smoo th 0.5 Plot of vargroup*meangroup. Legend: A = 1 obs, B = 2 obs, etc. щ щ 15 ъ щ щ A щ щ щ R щ e 10 ъ s щ i щ A d щ u щ A a щ A l щ A 5 ъ щ щ щ щ A щ A щ A 0 ъ A A щ штъттттттттттъттттттттттъттттттттттъттттттттттъттттттттттъттттттттттътттттт ттттъттттттттттъттттттттттъттттттттттътт 38 40 42 44 46 48 50 52 54 56 58 Predicted Value of OXY FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 38 VALUE ADDED PARTIAL REGRESSION PLOTS FOR A GE REGRESSION OF OXY ON OTHER VARIABLES LESS A GE The REG Procedure Model: MODEL1 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 694.79784 138.95957 22.19 <.0001 Error 25 156.58371 6.26335 Corrected Total 30 851.38154 Root MSE 2.50267 R-Square 0.8161 Dependent Mean 47.37581 Adj R-Sq 0.7793 Coeff Var 5.28259 Parameter Estimates Parameter Standard Variable DF Estimate Error t Val ue Pr > ІtІ Intercept 1 82.39361 9.17856 8. 98 <.0001 RUNTIME 1 -2.95182 0.38597 -7. 65 <.0001 WEIGHT 1 -0.05091 0.05792 -0. 88 0.3878 RUNPULSE 1 -0.39704 0.12880 -3. 08 0.0049 MAXPULSE 1 0.38479 0.14225 2. 71 0.0121 RSTPULSE 1 0.01239 0.06950 0. 18 0.8600 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 39 VALUE ADDED PARTIAL REGRESSION PLOTS FOR A GE REGRESSION OF age ON OTHER VARIABLES The REG Procedure Model: MODEL1 Dependent Variable: AGE Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 276.20022 55.24004 2.56 0.0527 Error 25 538.57397 21.54296 Corrected Total 30 814.77419 Root MSE 4.64144 R-Square 0.3390 Dependent Mean 47.67742 Adj R-Sq 0.2068 Coeff Var 9.73509 Parameter Estimates Parameter Standard Variable DF Estimate Error t Val ue Pr > ІtІ Intercept 1 90.49888 17.02253 5. 32 <.0001 RUNTIME 1 1.42379 0.71582 1. 99 0.0577 WEIGHT 1 -0.10252 0.10742 -0. 95 0.3490 RUNPULSE 1 0.12078 0.23888 0. 51 0.6175 MAXPULSE 1 -0.35941 0.26382 -1. 36 0.1852 RSTPULSE 1 -0.14946 0.12890 -1. 16 0.2572 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 40 smoothed plot of OXYRES versus AGERES with smoo th 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Statistic Residual Minimum Value -6.62033 Maximum Value 7.07175 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 41 smoothed plot of OXYRES versus AGERES with smoo th 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: OXYRES Fit Summary Fit Method kd Tre e Blending Linea r Number of Observations 3 1 Number of Fitting Points 1 6 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.5000 0 Points in Local Neighborhood 1 5 Residual Sum of Squares 110.8191 5 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 42 smoothed plot of OXYRES versus AGERES with smoo th 0.5 ------------------------------------------------ SmoothingParameter=0.5 -------- ---------------------------------------- Plot of DepVar*AGERES. Symbol used is '*' . Plot of Pred*AGERES. Symbol used is '+' . щ 4.00000 ъ * * щ щ * щ + * * щ 2.00000 ъ * * щ + + * щ ++ щ * +* * O щ * + + +++ + + ** X 0 ъ ** * * * ++ Y щ * + ++ R щ ++ + E щ + * + * ** S щ * + + + * -2.00000 ъ * щ щ * щ * щ -4.00000 ъ * щ щ щ щ -6.00000 ъ * штъттттттттттттъттттттттттттъттттттттттттъттттттттттттъттттттттттттът тттттттттттъттттттттттттъттттттттттттътт -8.00000 -6.00000 -4.00000 -2.00000 0 2.000 00 4.00000 6.00000 8.00000 Residual NOTE: 5 obs hidden. FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 43 MODEL WITH INTERACTION EFFECT The REG Procedure Model: MODEL1 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 653.74509 217.91503 29.77 <.0001 Error 27 197.63646 7.31987 Corrected Total 30 851.38154 Root MSE 2.70553 R-Square 0.7679 Dependent Mean 47.37581 Adj R-Sq 0.7421 Coeff Var 5.71077 Parameter Estimates Parameter Standard Variable DF Estimate Error t Val ue Pr > ІtІ Intercept 1 109.87914 33.46337 3. 28 0.0028 RUNTIME 1 -5.24330 3.16505 -1. 66 0.1092 AGE 1 -0.61397 0.72127 -0. 85 0.4021 RUNTMAGE 1 0.04402 0.06787 0. 65 0.5221 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 44 MODEL WITH INTERACTION EFFECT The REG Procedure Model: MODEL1 Test age Results for Dependent Variable OX Y Mean Source DF Square F Value Pr > F Numerator 2 10.42249 1.42 0.2583 Denominator 27 7.31987 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 45 MODEL WITH INTERACTION EFFECT The REG Procedure Model: MODEL1 Test runtime Results for Dependent Variable OXY Mean Source DF Square F Value Pr > F Numerator 2 287.37843 39.26 <.0001 Denominator 27 7.31987 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 46 MODEL WITH MULTIPLE INTERACTION EFFECTS -- PRO C GLM The GLM Procedure Number of observations 31 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 47 MODEL WITH MULTIPLE INTERACTION EFFECTS -- PRO C GLM The GLM Procedure Dependent Variable: OXY Sum of Source DF Squares Mean Square F Value Pr > F Model 10 732.0682019 73.2068202 12.27 <.0001 Error 20 119.3133430 5.9656671 Corrected Total 30 851.3815448 R-Square Coeff Var Root MSE OXY Mean 0.859859 5.155525 2.442472 47. 37581 Source DF Type I SS Mean Square F Value Pr > F RUNTIME 1 632.9000999 632.9000999 106.09 <.0001 AGE 1 17.7656325 17.7656325 2.98 0.0998 WEIGHT 1 5.6052170 5.6052170 0.94 0.3440 RUNPULSE 1 38.8757420 38.8757420 6.52 0.0190 RUNTIME*AGE 1 6.5000021 6.5000021 1.09 0.3090 RUNTIME*WEIGHT 1 4.8009570 4.8009570 0.80 0.3803 RUNTIME*RUNPULSE 1 2.0932373 2.0932373 0.35 0.5603 AGE*WEIGHT 1 2.4789069 2.4789069 0.42 0.5265 AGE*RUNPULSE 1 2.8715064 2.8715064 0.48 0.4958 WEIGHT*RUNPULSE 1 18.1769007 18.1769007 3.05 0.0962 Source DF Type III SS Mean Square F Value Pr > F RUNTIME 1 1.07174416 1.07174416 0.18 0.6762 AGE 1 31.22695470 31.22695470 5.23 0.0332 WEIGHT 1 21.56100669 21.56100669 3.61 0.0718 FITNESS DATA EXAMPLE FROM SAS MANUALS 12:21 Monday, March 1, 2004 48 MODEL WITH MULTIPLE INTERACTION EFFECTS -- PRO C GLM The GLM Procedure Dependent Variable: OXY Source DF Type III SS Mean Square F Value Pr > F RUNPULSE 1 26.29958974 26.29958974 4.41 0.0487 RUNTIME*AGE 1 9.68029962 9.68029962 1.62 0.2173 RUNTIME*WEIGHT 1 4.36791503 4.36791503 0.73 0.4023 RUNTIME*RUNPULSE 1 0.65682927 0.65682927 0.11 0.7435 AGE*WEIGHT 1 12.82200325 12.82200325 2.15 0.1582 AGE*RUNPULSE 1 12.04160145 12.04160145 2.02 0.1708 WEIGHT*RUNPULSE 1 18.17690075 18.17690075 3.05 0.0962 Standard Parameter Estimate Error t V alue Pr > ІtІ Intercept 703.5225202 261.2147193 2.69 0.0140 RUNTIME -3.8430174 9.0668472 - 0.42 0.6762 AGE -6.8210117 2.9813536 - 2.29 0.0332 WEIGHT -4.7858358 2.5174032 - 1.90 0.0718 RUNPULSE -2.9911920 1.4246209 - 2.10 0.0487 RUNTIME*AGE 0.0849427 0.0666824 1.27 0.2173 RUNTIME*WEIGHT -0.0673215 0.0786767 - 0.86 0.4023 RUNTIME*RUNPULSE 0.0142926 0.0430740 0.33 0.7435 AGE*WEIGHT 0.0312762 0.0213337 1.47 0.1582 AGE*RUNPULSE 0.0187882 0.0132243 1.42 0.1708 WEIGHT*RUNPULSE 0.0233859 0.0133975 1.75 0.0962