A manufacturing engineer is studying the dimensional variability of a particular component that is produced on three machines. Each machine has two spindles, and four components are randomly selected from each spindle. The results follow. Analyze the data, assuming that machines and spindles are fixed factors
Based on the p-values, the machine and spindle factors are significant. To work with the fixed factors we used the aov function instead GAD.machine <- c(rep(1,8),rep(2,8),rep(3,8))
spindle <- rep(c(rep(1,4),rep(2,4)),3)
obs <- c(12,9,11,12,8,9,10,8,14,15,13,14,12,10,11,13,14,10,12,11,16,15,15,14)
#df <- data.frame(machine,spindle,obs)
machine <- as.factor(machine)
spindle <- as.factor(spindle)
model <- lm(obs~machine+spindle%in%machine)
aov <- aov(model)
summary(aov)## Df Sum Sq Mean Sq F value Pr(>F)
## machine 2 55.75 27.875 18.934 3.74e-05 ***
## machine:spindle 3 43.75 14.583 9.906 0.000443 ***
## Residuals 18 26.50 1.472
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#plot(aov)