253 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 1 Statistics for Entry DF = 1,80 Model Variable Tolerance R-Square F Value Pr > F vol 1.000000 0.1126 10.15 0.0021 hp 1.000000 0.7344 221.21 <.0001 sp 1.000000 0.5486 97.24 <.0001 wt 1.000000 0.9005 724.27 <.0001 hp2 1.000000 0.5770 109.14 <.0001 sp2 1.000000 0.5091 82.98 <.0001 wt2 1.000000 0.8842 610.77 <.0001 vol2 1.000000 0.1589 15.11 0.0002 hpsp 1.000000 0.6219 131.61 <.0001 hpvol 1.000000 0.7036 189.88 <.0001 hpwt 1.000000 0.7925 305.47 <.0001 spvol 1.000000 0.3634 45.67 <.0001 spwt 1.000000 0.8784 578.15 <.0001 wtvol 1.000000 0.5606 102.08 <.0001 Variable wt Entered: R-Square = 0.9005 and C(p) = 87.5920 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 6.75750 6.75750 724.27 <.0001 Error 80 0.74641 0.00933 Corrected Total 81 7.50390 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 4.57248 0.04213 109.92158 11781.4 <.0001 wt -0.03548 0.00132 6.75750 724.27 <.0001 Bounds on condition number: 1, 1 ------------------------------------------------------------------------------ Stepwise Selection: Step 2 254 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 2 Statistics for Entry DF = 1,79 Model Variable Tolerance R-Square F Value Pr > F vol 0.851810 0.9016 0.84 0.3636 hp 0.307410 0.9152 13.70 0.0004 sp 0.539592 0.9179 16.71 0.0001 hp2 0.469377 0.9105 8.79 0.0040 sp2 0.570971 0.9153 13.83 0.0004 wt2 0.018083 0.9005 0.00 0.9948 vol2 0.785977 0.9026 1.68 0.1982 hpsp 0.429965 0.9126 10.95 0.0014 hpvol 0.276024 0.9041 2.93 0.0907 hpwt 0.215294 0.9119 10.24 0.0020 spvol 0.613225 0.9008 0.21 0.6496 spwt 0.100657 0.9144 12.76 0.0006 wtvol 0.326948 0.9032 2.21 0.1407 Variable sp Entered: R-Square = 0.9179 and C(p) = 60.6809 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 6.88781 3.44391 441.60 <.0001 Error 79 0.61609 0.00780 Corrected Total 81 7.50390 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 4.86906 0.08214 27.40243 3513.75 <.0001 sp -0.00389 0.00095156 0.13032 16.71 0.0001 wt -0.03093 0.00164 2.77082 355.30 <.0001 Bounds on condition number: 1.8533, 7.413 ------------------------------------------------------------------------------ Stepwise Selection: Step 3 255 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 3 Statistics for Removal DF = 1,79 Partial Model Variable R-Square R-Square F Value Pr > F sp 0.0174 0.9005 16.71 0.0001 wt 0.3693 0.5486 355.30 <.0001 Statistics for Entry DF = 1,78 Model Variable Tolerance R-Square F Value Pr > F vol 0.680239 0.9188 0.87 0.3539 hp 0.008132 0.9208 2.87 0.0944 hp2 0.073781 0.9208 2.82 0.0973 sp2 0.006428 0.9256 8.10 0.0057 wt2 0.017895 0.9181 0.18 0.6731 vol2 0.629844 0.9181 0.21 0.6511 hpsp 0.028332 0.9225 4.58 0.0355 hpvol 0.240304 0.9181 0.16 0.6861 hpwt 0.036708 0.9189 0.98 0.3253 spvol 0.607889 0.9187 0.78 0.3787 spwt 0.005401 0.9200 2.03 0.1582 wtvol 0.247017 0.9181 0.22 0.6436 Variable sp2 Entered: R-Square = 0.9256 and C(p) = 49.8280 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 6.94575 2.31525 323.55 <.0001 Error 78 0.55816 0.00716 Corrected Total 81 7.50390 256 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 3 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 6.34210 0.52364 1.04969 146.69 <.0001 sp -0.02819 0.00859 0.07708 10.77 0.0015 wt -0.02933 0.00167 2.20896 308.69 <.0001 sp2 0.00009428 0.00003313 0.05793 8.10 0.0057 Bounds on condition number: 164.61, 966.8 ------------------------------------------------------------------------------ Stepwise Selection: Step 4 Statistics for Removal DF = 1,78 Partial Model Variable R-Square R-Square F Value Pr > F sp 0.0103 0.9153 10.77 0.0015 wt 0.2944 0.6312 308.69 <.0001 sp2 0.0077 0.9179 8.10 0.0057 Statistics for Entry DF = 1,77 Model Variable Tolerance R-Square F Value Pr > F vol 0.631827 0.9257 0.05 0.8249 hp 0.002971 0.9263 0.74 0.3936 hp2 0.012324 0.9299 4.69 0.0334 wt2 0.016935 0.9257 0.05 0.8271 vol2 0.586856 0.9257 0.08 0.7841 hpsp 0.002929 0.9280 2.56 0.1139 hpvol 0.222609 0.9257 0.13 0.7214 hpwt 0.020694 0.9268 1.27 0.2626 spvol 0.546574 0.9256 0.00 0.9818 spwt 0.002305 0.9266 1.07 0.3034 wtvol 0.223825 0.9258 0.16 0.6889 257 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 4 Variable hp2 Entered: R-Square = 0.9299 and C(p) = 44.7184 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 6.97780 1.74445 255.31 <.0001 Error 77 0.52611 0.00683 Corrected Total 81 7.50390 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 7.61674 0.77988 0.65173 95.39 <.0001 sp -0.05763 0.01598 0.08892 13.01 0.0005 wt -0.02343 0.00318 0.37171 54.40 <.0001 hp2 -0.00000928 0.00000429 0.03205 4.69 0.0334 sp2 0.00025086 0.00007922 0.06852 10.03 0.0022 Bounds on condition number: 931.3, 6466.5 ------------------------------------------------------------------------------ Stepwise Selection: Step 5 Statistics for Removal DF = 1,77 Partial Model Variable R-Square R-Square F Value Pr > F sp 0.0118 0.9180 13.01 0.0005 wt 0.0495 0.8804 54.40 <.0001 hp2 0.0043 0.9256 4.69 0.0334 sp2 0.0091 0.9208 10.03 0.0022 258 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 5 Statistics for Entry DF = 1,76 Model Variable Tolerance R-Square F Value Pr > F vol 0.626185 0.9301 0.19 0.6663 hp 0.000544 0.9357 6.82 0.0108 wt2 0.006328 0.9353 6.34 0.0139 vol2 0.578923 0.9299 0.00 0.9752 hpsp 0.000197 0.9329 3.40 0.0691 hpvol 0.218889 0.9303 0.42 0.5168 hpwt 0.001638 0.9397 12.42 0.0007 spvol 0.545537 0.9299 0.01 0.9070 spwt 0.000242 0.9384 10.47 0.0018 wtvol 0.223111 0.9300 0.08 0.7727 Variable hpwt Entered: R-Square = 0.9397 and C(p) = 30.3270 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 7.05168 1.41034 237.02 <.0001 Error 76 0.45223 0.00595 Corrected Total 81 7.50390 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 12.87035 1.65906 0.35809 60.18 <.0001 sp -0.15484 0.03136 0.14509 24.38 <.0001 wt -0.04392 0.00653 0.26935 45.27 <.0001 hp2 -0.00005736 0.00001422 0.09685 16.28 0.0001 sp2 0.00072883 0.00015448 0.13245 22.26 <.0001 hpwt 0.00024677 0.00007003 0.07388 12.42 0.0007 Bounds on condition number: 4066.5, 41889 ------------------------------------------------------------------------------ Stepwise Selection: Step 6 259 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 6 Statistics for Removal DF = 1,76 Partial Model Variable R-Square R-Square F Value Pr > F sp 0.0193 0.9204 24.38 <.0001 wt 0.0359 0.9038 45.27 <.0001 hp2 0.0129 0.9268 16.28 0.0001 sp2 0.0177 0.9221 22.26 <.0001 hpwt 0.0098 0.9299 12.42 0.0007 Statistics for Entry DF = 1,75 Model Variable Tolerance R-Square F Value Pr > F vol 0.625613 0.9400 0.33 0.5700 hp 0.000493 0.9420 2.95 0.0898 wt2 0.001871 0.9401 0.41 0.5255 vol2 0.576249 0.9398 0.04 0.8382 hpsp 0.000196 0.9419 2.79 0.0989 hpvol 0.213604 0.9398 0.02 0.8782 spvol 0.543930 0.9398 0.10 0.7527 spwt 0.000117 0.9406 1.13 0.2918 wtvol 0.218713 0.9398 0.03 0.8553 Variable hp Entered: R-Square = 0.9420 and C(p) = 28.5242 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 7.06882 1.17814 203.09 <.0001 Error 75 0.43508 0.00580 Corrected Total 81 7.50390 260 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 6 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.89955 2.01917 0.31587 54.45 <.0001 hp 0.01153 0.00671 0.01714 2.95 0.0898 sp -0.17947 0.03412 0.16054 27.67 <.0001 wt -0.06028 0.01149 0.15957 27.51 <.0001 hp2 -0.00006495 0.00001472 0.11299 19.48 <.0001 sp2 0.00074261 0.00015274 0.13713 23.64 <.0001 hpwt 0.00020835 0.00007267 0.04769 8.22 0.0054 Bounds on condition number: 4077.7, 67391 ------------------------------------------------------------------------------ Stepwise Selection: Step 7 Statistics for Removal DF = 1,75 Partial Model Variable R-Square R-Square F Value Pr > F hp 0.0023 0.9397 2.95 0.0898 sp 0.0214 0.9206 27.67 <.0001 wt 0.0213 0.9208 27.51 <.0001 hp2 0.0151 0.9270 19.48 <.0001 sp2 0.0183 0.9237 23.64 <.0001 hpwt 0.0064 0.9357 8.22 0.0054 Statistics for Entry DF = 1,74 Model Variable Tolerance R-Square F Value Pr > F vol 0.617114 0.9425 0.61 0.4355 wt2 0.000488 0.9441 2.70 0.1045 vol2 0.571956 0.9421 0.13 0.7225 hpsp 0.000002784 0.9421 0.08 0.7792 hpvol 0.205242 0.9420 0.03 0.8531 spvol 0.531013 0.9423 0.35 0.5559 spwt 0.000043092 0.9422 0.23 0.6356 wtvol 0.217885 0.9421 0.08 0.7718 261 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 7 Variable wt2 Entered: R-Square = 0.9441 and C(p) = 27.1248 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 7 7.08414 1.01202 178.41 <.0001 Error 74 0.41976 0.00567 Corrected Total 81 7.50390 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 15.18386 2.00413 0.32560 57.40 <.0001 hp 0.02989 0.01299 0.03002 5.29 0.0242 sp -0.16310 0.03518 0.12194 21.50 <.0001 wt -0.11508 0.03522 0.06054 10.67 0.0016 hp2 -0.00004078 0.00002069 0.02203 3.88 0.0525 sp2 0.00054347 0.00019363 0.04468 7.88 0.0064 wt2 0.00114 0.00069665 0.01532 2.70 0.1045 hpwt -0.00019261 0.00025432 0.00325 0.57 0.4513 Bounds on condition number: 8443.5, 223414 ------------------------------------------------------------------------------ Stepwise Selection: Step 8 Statistics for Removal DF = 1,74 Partial Model Variable R-Square R-Square F Value Pr > F hp 0.0040 0.9401 5.29 0.0242 sp 0.0163 0.9278 21.50 <.0001 wt 0.0081 0.9360 10.67 0.0016 hp2 0.0029 0.9411 3.88 0.0525 sp2 0.0060 0.9381 7.88 0.0064 wt2 0.0020 0.9420 2.70 0.1045 hpwt 0.0004 0.9436 0.57 0.4513 262 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 8 Statistics for Entry DF = 1,73 Model Variable Tolerance R-Square F Value Pr > F vol 0.607975 0.9448 1.01 0.3194 vol2 0.550532 0.9444 0.48 0.4915 hpsp 0.000002742 0.9441 0.01 0.9337 hpvol 0.204630 0.9441 0.08 0.7822 spvol 0.526941 0.9445 0.56 0.4584 spwt 0.000025878 0.9444 0.51 0.4775 wtvol 0.211019 0.9443 0.35 0.5539 Variable hpwt Removed: R-Square = 0.9436 and C(p) = 25.8466 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 7.08089 1.18015 209.24 <.0001 Error 75 0.42301 0.00564 Corrected Total 81 7.50390 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 15.27776 1.99460 0.33091 58.67 <.0001 hp 0.02134 0.00641 0.06259 11.10 0.0013 sp -0.17489 0.03145 0.17436 30.91 <.0001 wt -0.09139 0.01616 0.18030 31.97 <.0001 hp2 -0.00005389 0.00001130 0.12826 22.74 <.0001 sp2 0.00065794 0.00012069 0.16763 29.72 <.0001 wt2 0.00063888 0.00019628 0.05976 10.59 0.0017 Bounds on condition number: 2799.9, 50504 ------------------------------------------------------------------------------ Stepwise Selection: Step 9 263 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Stepwise Selection: Step 9 Statistics for Removal DF = 1,75 Partial Model Variable R-Square R-Square F Value Pr > F hp 0.0083 0.9353 11.10 0.0013 sp 0.0232 0.9204 30.91 <.0001 wt 0.0240 0.9196 31.97 <.0001 hp2 0.0171 0.9265 22.74 <.0001 sp2 0.0223 0.9213 29.72 <.0001 wt2 0.0080 0.9357 10.59 0.0017 Statistics for Entry DF = 1,74 Model Variable Tolerance R-Square F Value Pr > F vol 0.616676 0.9442 0.82 0.3674 vol2 0.568008 0.9439 0.30 0.5845 hpsp 0.000003216 0.9437 0.05 0.8323 hpvol 0.204777 0.9437 0.07 0.7971 hpwt 0.000118 0.9441 0.57 0.4513 spvol 0.530578 0.9440 0.47 0.4974 spwt 0.000064848 0.9436 0.02 0.8937 wtvol 0.215135 0.9438 0.24 0.6286 All variables left in the model are significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model. Summary of Stepwise Selection Variable Variable Number Partial Model Step Entered Removed Vars In R-Square R-Square C(p) F Value Pr > F 1 wt 1 0.9005 0.9005 87.5920 724.27 <.0001 2 sp 2 0.0174 0.9179 60.6809 16.71 0.0001 3 sp2 3 0.0077 0.9256 49.8280 8.10 0.0057 4 hp2 4 0.0043 0.9299 44.7184 4.69 0.0334 5 hpwt 5 0.0098 0.9397 30.3270 12.42 0.0007 6 hp 6 0.0023 0.9420 28.5242 2.95 0.0898 7 wt2 7 0.0020 0.9441 27.1248 2.70 0.1045 264 The REG Procedure Model: MODEL1 Dependent Variable: lmpg Summary of Stepwise Selection Variable Variable Number Partial Model Step Entered Removed Vars In R-Square R-Square C(p) F Value Pr > F 8 hpwt 6 0.0004 0.9436 25.8466 0.57 0.4513