> hormone.reg1 <- lm(growrate ~ X1 + X2 + X3 + X1X2 + X1X3) > summary(hormone.reg1) Call: lm(formula = growrate ~ X1 + X2 + X3 + X1X2 + X1X3) Residuals: Min 1Q Median 3Q Max -0.6 -0.2 0.0 0.2 0.4 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.700e+00 1.164e-01 14.609 4.73e-07 *** X1 -1.000e-01 1.164e-01 -0.859 0.4152 X2 5.000e-01 1.778e-01 2.813 0.0227 * X3 3.000e-01 1.576e-01 1.904 0.0934 . X1X2 -1.000e-01 1.778e-01 -0.563 0.5891 X1X3 4.340e-17 1.576e-01 0.000 1.0000 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.4031 on 8 degrees of freedom Multiple R-squared: 0.7749, Adjusted R-squared: 0.6342 F-statistic: 5.507 on 5 and 8 DF, p-value: 0.01722 > anova(hormone.reg1) Analysis of Variance Table Response: growrate Df Sum Sq Mean Sq F value Pr(>F) X1 1 0.0029 0.0029 0.0176 0.897785 X2 1 3.6509 3.6509 22.4668 0.001464 ** X3 1 0.7451 0.7451 4.5855 0.064638 . X1X2 1 0.0754 0.0754 0.4642 0.514913 X1X3 1 0.0000 0.0000 0.0000 1.000000 Residuals 8 1.3000 0.1625 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > drop1(hormone.reg1) Single term deletions Model: growrate ~ X1 + X2 + X3 + X1X2 + X1X3 Df Sum of Sq RSS AIC 1.3000 -21.274 X1 1 0.12000 1.4200 -22.038 X2 1 1.28571 2.5857 -13.647 X3 1 0.58909 1.8891 -18.041 X1X2 1 0.05143 1.3514 -22.730 X1X3 1 0.00000 1.3000 -23.274 > > > hormone.reg2 <- lm(growrate ~ X1 + X2 + X3) > summary(hormone.reg2) Call: lm(formula = growrate ~ X1 + X2 + X3) Residuals: Min 1Q Median 3Q Max -0.65714 -0.18714 0.03714 0.27286 0.41143 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.67619 0.09973 16.808 1.17e-08 *** X1 -0.08571 0.10448 -0.820 0.4311 X2 0.46667 0.15418 3.027 0.0127 * X3 0.32667 0.14035 2.328 0.0422 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.3709 on 10 degrees of freedom Multiple R-squared: 0.7618, Adjusted R-squared: 0.6903 F-statistic: 10.66 on 3 and 10 DF, p-value: 0.001858 > anova(hormone.reg2) Analysis of Variance Table Response: growrate Df Sum Sq Mean Sq F value Pr(>F) X1 1 0.0029 0.0029 0.0208 0.8882630 X2 1 3.6509 3.6509 26.5435 0.0004302 *** X3 1 0.7451 0.7451 5.4175 0.0422260 * Residuals 10 1.3754 0.1375 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > drop1(hormone.reg2) Single term deletions Model: growrate ~ X1 + X2 + X3 Df Sum of Sq RSS AIC 1.3754 -24.484 X1 1 0.09257 1.4680 -25.572 X2 1 1.26000 2.6354 -17.380 X3 1 0.74514 2.1206 -20.423 > > hormone.reg3 <- lm(growrate ~ X2 + X3 + X1X2 + X1X3) > summary(hormone.reg3) Call: lm(formula = growrate ~ X2 + X3 + X1X2 + X1X3) Residuals: Min 1Q Median 3Q Max -0.66667 -0.28333 0.08333 0.18333 0.46667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.68889 0.11396 14.821 1.25e-07 *** X2 0.44444 0.16316 2.724 0.0235 * X3 0.32778 0.15196 2.157 0.0594 . X1X2 -0.06667 0.17093 -0.390 0.7056 X1X3 -0.01667 0.15408 -0.108 0.9162 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.3972 on 9 degrees of freedom Multiple R-squared: 0.7541, Adjusted R-squared: 0.6448 F-statistic: 6.899 on 4 and 9 DF, p-value: 0.007968 > anova(hormone.reg3) Analysis of Variance Table Response: growrate Df Sum Sq Mean Sq F value Pr(>F) X2 1 3.4410 3.4410 21.8092 0.001169 ** X3 1 0.8653 0.8653 5.4842 0.043889 * X1X2 1 0.0462 0.0462 0.2925 0.601735 X1X3 1 0.0018 0.0018 0.0117 0.916233 Residuals 9 1.4200 0.1578 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > drop1(hormone.reg3) Single term deletions Model: growrate ~ X2 + X3 + X1X2 + X1X3 Df Sum of Sq RSS AIC 1.4200 -22.038 X2 1 1.17073 2.5907 -15.620 X3 1 0.73413 2.1541 -18.203 X1X2 1 0.02400 1.4440 -23.803 X1X3 1 0.00185 1.4219 -24.019 > > hormone.reg4 <- lm(growrate ~ X1 + X1X2 + X1X3) > summary(hormone.reg4) Call: lm(formula = growrate ~ X1 + X1X2 + X1X3) Residuals: Min 1Q Median 3Q Max -1.07429 -0.51571 0.09714 0.60571 0.85714 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.62857 0.20873 7.802 1.47e-05 *** X1 0.01905 0.19924 0.096 0.926 X1X2 0.06667 0.30803 0.216 0.833 X1X3 -0.19333 0.28039 -0.690 0.506 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.7409 on 10 degrees of freedom Multiple R-squared: 0.04928, Adjusted R-squared: -0.2359 F-statistic: 0.1728 on 3 and 10 DF, p-value: 0.9124 > anova(hormone.reg4) Analysis of Variance Table Response: growrate Df Sum Sq Mean Sq F value Pr(>F) X1 1 0.0029 0.00286 0.0052 0.9439 X1X2 1 0.0207 0.02071 0.0377 0.8499 X1X3 1 0.2610 0.26100 0.4754 0.5062 Residuals 10 5.4897 0.54897 > drop1(hormone.reg4) Single term deletions Model: growrate ~ X1 + X1X2 + X1X3 Df Sum of Sq RSS AIC 5.4897 -5.1065 X1 1 0.005017 5.4947 -7.0937 X1X2 1 0.025714 5.5154 -7.0411 X1X3 1 0.261000 5.7507 -6.4563 > > anova(hormone.reg2,hormone.reg1) Analysis of Variance Table Model 1: growrate ~ X1 + X2 + X3 Model 2: growrate ~ X1 + X2 + X3 + X1X2 + X1X3 Res.Df RSS Df Sum of Sq F Pr(>F) 1 10 1.3754 2 8 1.3000 2 0.075429 0.2321 0.798 > anova(hormone.reg3,hormone.reg1) Analysis of Variance Table Model 1: growrate ~ X2 + X3 + X1X2 + X1X3 Model 2: growrate ~ X1 + X2 + X3 + X1X2 + X1X3 Res.Df RSS Df Sum of Sq F Pr(>F) 1 9 1.42 2 8 1.30 1 0.12 0.7385 0.4152 > anova(hormone.reg4,hormone.reg1) Analysis of Variance Table Model 1: growrate ~ X1 + X1X2 + X1X3 Model 2: growrate ~ X1 + X2 + X3 + X1X2 + X1X3 Res.Df RSS Df Sum of Sq F Pr(>F) 1 10 5.4897 2 8 1.3000 2 4.1897 12.891 0.003145 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > >