> names(karate) [1] "Trt" "Wood" "Board" "Y" "X1" "X2" "X3" "X4" "X1X4" [10] "X2X4" "X3X4" > > 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 32085 32085 10.1578 0.001575 ** X2 1 1696 1696 0.5371 0.464181 X3 1 11307 11307 3.5798 0.059365 . X4 1 116342 116342 36.8329 3.552e-09 *** X1X4 1 0 0 0.0001 0.994156 X2X4 1 1360 1360 0.4306 0.512132 X3X4 1 81 81 0.0256 0.872927 Residuals 328 1036035 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 32085 32085 10.2365 0.00151 ** X2 1 1696 1696 0.5412 0.46245 X3 1 11307 11307 3.6076 0.05839 . X4 1 116342 116342 37.1181 3.088e-09 *** Residuals 331 1037476 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 115483 115483 35.3528 6.985e-09 *** X1X4 1 23 23 0.0072 0.9325 X2X4 1 1652 1652 0.5057 0.4775 X3X4 1 509 509 0.1558 0.6933 Residuals 331 1081239 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 32085 32085 9.1691 0.002656 ** X2 1 1696 1696 0.4848 0.486758 X3 1 11307 11307 3.2314 0.073156 . X1X4 1 40 40 0.0114 0.915111 X2X4 1 2504 2504 0.7156 0.398205 X3X4 1 23 23 0.0065 0.935872 Residuals 329 1151251 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 1037476 2 328 1036035 3 1441.4 0.1521 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 1081239 2 328 1036035 3 45205 4.7705 0.002866 ** --- 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 1151251 2 328 1036035 1 115217 36.477 4.187e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > Wood.f <- factor(Wood) > Board.f <- factor(Board) > > options(contrasts=c("contr.sum","contr.poly")) > kb.mod5 <- aov(Y ~ Wood.f + Board.f + Wood.f:Board.f) > anova(kb.mod5) Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) Wood.f 3 45089 15030 4.7582 0.002913 ** Board.f 1 116342 116342 36.8329 3.552e-09 *** Wood.f:Board.f 3 1441 480 0.1521 0.928296 Residuals 328 1036035 3159 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > install.packages("car") Warning: package ‘car’ is in use and will not be installed > library(car) > > Anova(kb.mod5,type="III") Anova Table (Type III tests) Response: Y Sum Sq Df F value Pr(>F) (Intercept) 2308824 1 730.9544 < 2.2e-16 *** Wood.f 45205 3 4.7705 0.002866 ** Board.f 115217 1 36.4766 4.187e-09 *** Wood.f:Board.f 1441 3 0.1521 0.928296 Residuals 1036035 328 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >