> boxplot(SUGARS ~ factor(SHELF)) > cereal[1:20,] NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF 1 100%_Bran 70 4 1 130 10.0 5.0 6 3 2 100%_Natural_Bran 120 3 5 15 2.0 8.0 8 3 3 All-Bran 70 4 1 260 9.0 7.0 5 3 4 All-Bran_with_Extra_Fiber 50 4 0 140 14.0 8.0 0 3 5 Almond_Delight 110 2 2 200 1.0 14.0 8 3 6 Apple_Cinnamon_Cheerios 110 2 2 180 1.5 10.5 10 1 7 Apple_Jacks 110 2 0 125 1.0 11.0 14 2 8 Basic_4 130 3 2 210 2.0 18.0 8 3 9 Bran_Chex 90 2 1 200 4.0 15.0 6 1 10 Bran_Flakes 90 3 0 210 5.0 13.0 5 3 11 Cap'n'Crunch 120 1 2 220 0.0 12.0 12 2 12 Cheerios 110 6 2 290 2.0 17.0 1 1 13 Cinnamon_Toast_Crunch 120 1 3 210 0.0 13.0 9 2 14 Clusters 110 3 2 140 2.0 13.0 7 3 15 Cocoa_Puffs 110 1 1 180 0.0 12.0 13 2 16 Corn_Chex 110 2 0 280 0.0 22.0 3 1 17 Corn_Flakes 100 2 0 290 1.0 21.0 2 1 18 Corn_Pops 110 1 0 90 1.0 13.0 12 2 19 Count_Chocula 110 1 1 180 0.0 12.0 13 2 20 Cracklin'_Oat_Bran 110 3 3 140 4.0 10.0 7 3 > anova(lm(SUGARS ~ factor(SHELF))) Analysis of Variance Table Response: SUGARS Df Sum Sq Mean Sq F value Pr(>F) factor(SHELF) 2 248.41 124.204 7.3345 0.001242 ** Residuals 74 1253.12 16.934 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(lm(SUGARS ~ (FAT>0))) Analysis of Variance Table Response: SUGARS Df Sum Sq Mean Sq F value Pr(>F) FAT > 0 1 204.62 204.623 11.833 0.0009536 *** Residuals 75 1296.91 17.292 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > boxplot(residuals(lm(SUGARS ~ factor(SHELF))) ~ (FAT>0)) > hist(residuals(lm(SUGARS ~ factor(SHELF) + (FAT>0)))) > hist(residuals(lm(SUGARS ~ factor(SHELF) + (FAT>0)))[FAT>0]) > hist(residuals(lm(SUGARS ~ factor(SHELF) + (FAT>0)))[FAT==0]) > anova(lm(SUGARS ~ factor(SHELF) + (FAT>0))) Analysis of Variance Table Response: SUGARS Df Sum Sq Mean Sq F value Pr(>F) factor(SHELF) 2 248.41 124.204 8.0540 0.0006908 *** FAT > 0 1 127.36 127.364 8.2589 0.0053083 ** Residuals 73 1125.76 15.421 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > (lm(SUGARS ~ factor(SHELF) + (FAT>0))) Call: lm(formula = SUGARS ~ factor(SHELF) + (FAT > 0)) Coefficients: (Intercept) factor(SHELF)2 factor(SHELF)3 FAT > 0TRUE 3.546 3.950 1.047 2.787 > anova(lm(SUGARS ~ (FAT>0) + factor(SHELF))) Analysis of Variance Table Response: SUGARS Df Sum Sq Mean Sq F value Pr(>F) FAT > 0 1 204.62 204.623 13.2688 0.0005016 *** factor(SHELF) 2 171.15 85.574 5.5491 0.0057093 ** Residuals 73 1125.76 15.421 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > cereal[1:10,] NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF 1 100%_Bran 70 4 1 130 10.0 5.0 6 3 2 100%_Natural_Bran 120 3 5 15 2.0 8.0 8 3 3 All-Bran 70 4 1 260 9.0 7.0 5 3 4 All-Bran_with_Extra_Fiber 50 4 0 140 14.0 8.0 0 3 5 Almond_Delight 110 2 2 200 1.0 14.0 8 3 6 Apple_Cinnamon_Cheerios 110 2 2 180 1.5 10.5 10 1 7 Apple_Jacks 110 2 0 125 1.0 11.0 14 2 8 Basic_4 130 3 2 210 2.0 18.0 8 3 9 Bran_Chex 90 2 1 200 4.0 15.0 6 1 10 Bran_Flakes 90 3 0 210 5.0 13.0 5 3 > plot(lm(SUGARS ~ factor(SHELF) + (FAT>0))) Hit to see next plot: Hit to see next plot: Hit to see next plot: Hit to see next plot: > interaction.plot(factor(SHELF), FAT>0, SUGARS) > anova(lm(SUGARS ~ factor(SHELF) + (FAT>0) + factor(SHELF)*(FAT>0))) Analysis of Variance Table Response: SUGARS Df Sum Sq Mean Sq F value Pr(>F) factor(SHELF) 2 248.41 124.204 8.1359 0.0006587 *** FAT > 0 1 127.36 127.364 8.3428 0.0051297 ** factor(SHELF):FAT > 0 2 41.86 20.929 1.3709 0.2605117 Residuals 71 1083.90 15.266 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(lm(SUGARS ~ factor(SHELF) + (FAT>0) )) Analysis of Variance Table Response: SUGARS Df Sum Sq Mean Sq F value Pr(>F) factor(SHELF) 2 248.41 124.204 8.0540 0.0006908 *** FAT > 0 1 127.36 127.364 8.2589 0.0053083 ** Residuals 73 1125.76 15.421 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >