MODEL SELECTION for apple taste on 5 covariates - YOURNAME 1 PROC REG of taste on 5 variables 23:57 Monday, October 10, 2005 MODEL RSQUARE=0.8793 (P=0.0016), but NOTHING is significant in the Parameter Estimate table. The REG Procedure Model: MODEL1 Dependent Variable: yy AppleTaste Number of Observations Read 14 Number of Observations Used 14 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 3577641 715528 11.65 0.0016 Error 8 491317 61415 Corrected Total 13 4068957 Root MSE 247.81967 R-Square 0.8793 Dependent Mean 2195.42857 Adj R-Sq 0.8038 Coeff Var 11.28799 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 299.64546 988.08291 0.30 0.7694 Nat Sodium 1 -10.77226 76.56324 -0.14 0.8916 Kk Potassium 1 43.61828 60.00005 0.73 0.4880 Pp Phosphorus 1 0.34494 0.74392 0.46 0.6552 Shade Shade 1 -179.09980 1800.82748 -0.10 0.9232 Water Water 1 1.75238 3.52645 0.50 0.6326 MODEL SELECTION for apple taste on 5 covariates - YOURNAME 2 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL1 Dependent Variable: yy R-Square Selection Method Number of Observations Read 14 Number of Observations Used 14 Number in Model R-Square Variables in Model 1 0.8410 Shade 1 0.5678 Pp 1 0.5417 Water 1 0.1728 Kk 1 0.1687 Nat ----------------------------------------------- 2 0.8743 Kk Pp 2 0.8705 Nat Shade 2 0.8665 Pp Shade 2 0.8664 Shade Water 2 0.8635 Kk Water 2 0.8612 Kk Shade 2 0.8362 Nat Pp 2 0.8156 Nat Water 2 0.5679 Pp Water 2 0.1751 Nat Kk ----------------------------------------------- 3 0.8775 Kk Pp Water 3 0.8752 Nat Kk Pp 3 0.8744 Kk Pp Shade 3 0.8727 Nat Kk Shade 3 0.8709 Nat Pp Shade 3 0.8705 Nat Shade Water 3 0.8688 Kk Shade Water 3 0.8670 Pp Shade Water 3 0.8667 Nat Kk Water 3 0.8368 Nat Pp Water ----------------------------------------------- 4 0.8791 Nat Kk Pp Water 4 0.8790 Kk Pp Shade Water 4 0.8760 Nat Kk Shade Water 4 0.8755 Nat Kk Pp Shade 4 0.8713 Nat Pp Shade Water ----------------------------------------------- 5 0.8793 Nat Kk Pp Shade Water MODEL SELECTION for apple taste on 5 covariates - YOURNAME 3 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL2 Dependent Variable: yy Adjusted R-Square Selection Method Number of Observations Read 14 Number of Observations Used 14 Number in Adjusted Model R-Square R-Square Variables in Model 2 0.8514 0.8743 Kk Pp 2 0.8469 0.8705 Nat Shade 2 0.8422 0.8665 Pp Shade 2 0.8421 0.8664 Shade Water 3 0.8407 0.8775 Kk Pp Water 2 0.8386 0.8635 Kk Water 3 0.8378 0.8752 Nat Kk Pp 3 0.8367 0.8744 Kk Pp Shade 2 0.8359 0.8612 Kk Shade 3 0.8345 0.8727 Nat Kk Shade 3 0.8321 0.8709 Nat Pp Shade 3 0.8316 0.8705 Nat Shade Water 3 0.8294 0.8688 Kk Shade Water 1 0.8277 0.8410 Shade 3 0.8270 0.8670 Pp Shade Water 3 0.8267 0.8667 Nat Kk Water 4 0.8254 0.8791 Nat Kk Pp Water 4 0.8252 0.8790 Kk Pp Shade Water 4 0.8209 0.8760 Nat Kk Shade Water 4 0.8202 0.8755 Nat Kk Pp Shade 4 0.8141 0.8713 Nat Pp Shade Water 2 0.8064 0.8362 Nat Pp 5 0.8038 0.8793 Nat Kk Pp Shade Water 3 0.7878 0.8368 Nat Pp Water 2 0.7820 0.8156 Nat Water 1 0.5318 0.5678 Pp 1 0.5035 0.5417 Water 2 0.4893 0.5679 Pp Water 1 0.1039 0.1728 Kk 1 0.0994 0.1687 Nat 2 0.0251 0.1751 Nat Kk MODEL SELECTION for apple taste on 5 covariates - YOURNAME 4 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL3 Dependent Variable: yy AppleTaste Number of Observations Read 14 Number of Observations Used 14 Forward Selection: Step 1 Variable Shade Entered: R-Square = 0.8410 and C(p) = 0.5367 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 3421848 3421848 63.45 <.0001 Error 12 647110 53926 Corrected Total 13 4068957 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 645.72764 204.20305 539226 10.00 0.0082 Shade 811.96905 101.93130 3421848 63.45 <.0001 Bounds on condition number: 1, 1 --------------------------------------------------------------------------- Forward Selection: Step 2 Variable Nat Entered: R-Square = 0.8705 and C(p) = 0.5814 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 3541934 1770967 36.96 <.0001 Error 11 527023 47911 Corrected Total 13 4068957 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 798.46545 215.30332 658943 13.75 0.0034 Nat -26.08884 16.47880 120087 2.51 0.1417 Shade 925.46000 119.87479 2855594 59.60 <.0001 MODEL SELECTION for apple taste on 5 covariates - YOURNAME 5 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL3 Dependent Variable: yy AppleTaste Forward Selection: Step 2 Bounds on condition number: 1.5567, 6.2267 --------------------------------------------------------------------------- No other variable met the 0.5000 significance level for entry into the model. Summary of Forward Selection Variable Number Partial Model Step Entered Label Vars In R-Square R-Square C(p) F Value Pr > F 1 Shade Shade 1 0.8410 0.8410 0.5367 63.45 <.0001 2 Nat Sodium 2 0.0295 0.8705 0.5814 2.51 0.1417 MODEL SELECTION for apple taste on 5 covariates - YOURNAME 6 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL4 Dependent Variable: yy AppleTaste Number of Observations Read 14 Number of Observations Used 14 Stepwise Selection: Step 1 Variable Shade Entered: R-Square = 0.8410 and C(p) = 0.5367 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 3421848 3421848 63.45 <.0001 Error 12 647110 53926 Corrected Total 13 4068957 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 645.72764 204.20305 539226 10.00 0.0082 Shade 811.96905 101.93130 3421848 63.45 <.0001 Bounds on condition number: 1, 1 --------------------------------------------------------------------------- Stepwise Selection: Step 2 Variable Nat Entered: R-Square = 0.8705 and C(p) = 0.5814 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 3541934 1770967 36.96 <.0001 Error 11 527023 47911 Corrected Total 13 4068957 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 798.46545 215.30332 658943 13.75 0.0034 Nat -26.08884 16.47880 120087 2.51 0.1417 Shade 925.46000 119.87479 2855594 59.60 <.0001 MODEL SELECTION for apple taste on 5 covariates - YOURNAME 7 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL4 Dependent Variable: yy AppleTaste Stepwise Selection: Step 2 Bounds on condition number: 1.5567, 6.2267 --------------------------------------------------------------------------- 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 Label Vars In R-Square R-Square C(p) 1 Shade Shade 1 0.8410 0.8410 0.5367 2 Nat Sodium 2 0.0295 0.8705 0.5814 Summary of Stepwise Selection Step F Value Pr > F 1 63.45 <.0001 2 2.51 0.1417 MODEL SELECTION for apple taste on 5 covariates - YOURNAME 8 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL5 Dependent Variable: yy AppleTaste Number of Observations Read 14 Number of Observations Used 14 Backward Elimination: Step 0 All Variables Entered: R-Square = 0.8793 and C(p) = 6.0000 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 3577641 715528 11.65 0.0016 Error 8 491317 61415 Corrected Total 13 4068957 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 299.64546 988.08291 5648.07120 0.09 0.7694 Nat -10.77226 76.56324 1215.75074 0.02 0.8916 Kk 43.61828 60.00005 32457 0.53 0.4880 Pp 0.34494 0.74392 13204 0.22 0.6552 Shade -179.09980 1800.82748 607.45977 0.01 0.9232 Water 1.75238 3.52645 15165 0.25 0.6326 Bounds on condition number: 274.07, 2783.9 --------------------------------------------------------------------------- Backward Elimination: Step 1 Variable Shade Removed: R-Square = 0.8791 and C(p) = 4.0099 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 3577033 894258 16.36 0.0004 Error 9 491924 54658 Corrected Total 13 4068957 MODEL SELECTION for apple taste on 5 covariates - YOURNAME 9 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL5 Dependent Variable: yy AppleTaste Backward Elimination: Step 1 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 391.72312 325.63626 79095 1.45 0.2597 Nat -16.51251 47.45755 6617.15339 0.12 0.7359 Kk 38.09669 21.46412 172188 3.15 0.1097 Pp 0.27749 0.28833 50626 0.93 0.3610 Water 1.59125 2.95493 15850 0.29 0.6033 Bounds on condition number: 24.778, 288.31 --------------------------------------------------------------------------- Backward Elimination: Step 2 Variable Nat Removed: R-Square = 0.8775 and C(p) = 2.1176 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 3570416 1190139 23.87 <.0001 Error 10 498541 49854 Corrected Total 13 4068957 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 317.02761 233.84411 91631 1.84 0.2050 Kk 30.97381 6.16202 1259634 25.27 0.0005 Pp 0.29157 0.27264 57019 1.14 0.3100 Water 1.42377 2.78440 13035 0.26 0.6202 Bounds on condition number: 24.121, 147.33 --------------------------------------------------------------------------- Backward Elimination: Step 3 Variable Water Removed: R-Square = 0.8743 and C(p) = 0.3299 MODEL SELECTION for apple taste on 5 covariates - YOURNAME 10 MODEL SELECTION of taste on 5 variables 23:57 Monday, October 10, 2005 The REG Procedure Model: MODEL5 Dependent Variable: yy AppleTaste Backward Elimination: Step 3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 3557381 1778690 38.25 <.0001 Error 11 511577 46507 Corrected Total 13 4068957 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 337.00028 222.68472 106512 2.29 0.1584 Kk 30.61040 5.91185 1246835 26.81 0.0003 Pp 0.42795 0.05463 2854105 61.37 <.0001 Bounds on condition number: 1.0305, 4.1219 --------------------------------------------------------------------------- All variables left in the model are significant at the 0.1000 level. Summary of Backward Elimination Variable Number Partial Model Step Removed Label Vars In R-Square R-Square C(p) F Value Pr > F 1 Shade Shade 4 0.0001 0.8791 4.0099 0.01 0.9232 2 Nat Sodium 3 0.0016 0.8775 2.1176 0.12 0.7359 3 Water Water 2 0.0032 0.8743 0.3299 0.26 0.6202