> kb.mod1 <- lm(Y ~ X1 + X2 + X3 + X4 + X1X4 + X2X4 + X3X4) > anova(kb.mod1) Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) X1 1 32086 32086 10.1581 0.001575 ** X2 1 1696 1696 0.5371 0.464174 X3 1 11308 11308 3.5801 0.059358 . X4 1 116341 116341 36.8329 3.552e-09 *** X1X4 1 0 0 0.0001 0.994104 X2X4 1 1361 1361 0.4308 0.512054 X3X4 1 81 81 0.0256 0.872957 Residuals 328 1036027 3159 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > kb.mod2 <- lm(Y ~ X1 + X2 + X3 + X4) > anova(kb.mod2) Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) X1 1 32086 32086 10.2368 0.00151 ** X2 1 1696 1696 0.5412 0.46245 X3 1 11308 11308 3.6078 0.05838 . X4 1 116341 116341 37.1181 3.087e-09 *** Residuals 331 1037469 3134 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > kb.mod3 <- lm(Y ~ X4 + X1X4 + X2X4 + X3X4) > anova(kb.mod3) Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) X4 1 115482 115482 35.3528 6.985e-09 *** X1X4 1 24 24 0.0072 0.9324 X2X4 1 1652 1652 0.5059 0.4774 X3X4 1 509 509 0.1558 0.6933 Residuals 331 1081233 3267 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > kb.mod4 <- lm(Y ~ X1 + X2 + X3 + X1X4 + X2X4 + X3X4) > anova(kb.mod4) Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) X1 1 32086 32086 9.1694 0.002656 ** X2 1 1696 1696 0.4848 0.486752 X3 1 11308 11308 3.2316 0.073148 . X1X4 1 40 40 0.0114 0.915061 X2X4 1 2505 2505 0.7158 0.398140 X3X4 1 23 23 0.0065 0.935843 Residuals 329 1151243 3499 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > anova(kb.mod2,kb.mod1) Analysis of Variance Table Model 1: Y ~ X1 + X2 + X3 + X4 Model 2: Y ~ X1 + X2 + X3 + X4 + X1X4 + X2X4 + X3X4 Res.Df RSS Df Sum of Sq F Pr(>F) 1 331 1037469 2 328 1036027 3 1441.8 0.1522 0.9283 > anova(kb.mod3,kb.mod1) Analysis of Variance Table Model 1: Y ~ X4 + X1X4 + X2X4 + X3X4 Model 2: Y ~ X1 + X2 + X3 + X4 + X1X4 + X2X4 + X3X4 Res.Df RSS Df Sum of Sq F Pr(>F) 1 331 1081233 2 328 1036027 3 45206 4.7706 0.002865 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(kb.mod4,kb.mod1) Analysis of Variance Table Model 1: Y ~ X1 + X2 + X3 + X1X4 + X2X4 + X3X4 Model 2: Y ~ X1 + X2 + X3 + X4 + X1X4 + X2X4 + X3X4 Res.Df RSS Df Sum of Sq F Pr(>F) 1 329 1151243 2 328 1036027 1 115216 36.477 4.187e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > kb.mod5 <- aov(Y ~ factor(Wood) + factor(Board)) > anova(kb.mod5) Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) factor(Wood) 3 45090 15030 4.7953 0.002768 ** factor(Board) 1 116341 116341 37.1181 3.087e-09 *** Residuals 331 1037469 3134 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > drop1(kb.mod5) Single term deletions Model: Y ~ factor(Wood) + factor(Board) Df Sum of Sq RSS AIC 1037469 2709.8 factor(Wood) 3 45949 1083418 2718.4 factor(Board) 1 116341 1153810 2743.5 > TukeyHSD(kb.mod5) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = Y ~ factor(Wood) + factor(Board)) $`factor(Wood)` diff lwr upr p adj 2-1 -7.736434 -30.11942 14.646551 0.8087699 3-1 -25.284957 -47.81338 -2.756539 0.0207886 4-1 -27.069768 -48.86881 -5.270729 0.0080034 3-2 -17.548523 -40.40743 5.310383 0.1967522 4-2 -19.333334 -41.47375 2.807083 0.1109697 4-3 -1.784811 -24.07224 20.502622 0.9968681 $`factor(Board)` diff lwr upr p adj 2-1 -37.25503 -49.30216 -25.2079 0