本文是实验设计与分析（第6版，Montgomery著，傅珏生译) 第5章析因设计引导5.7节思考题5.13 R语言解题。主要涉及方差分析，正态假设检验，残差分析，交互作用图。

dataframe<-data.frame(

y=c(36,18,30,39,20,37,36,22,33,32,20,34),

column=gl(4,3,12),

row=gl(3,1,12))

summary (dataframe)

dataframe.aov2 <- aov(y~column+row,data=dataframe)

summary (dataframe.aov2)

> summary (dataframe.aov2)

            Df Sum Sq Mean Sq F value   Pr(>F)   

column       3   28.9    9.64   2.006 0.214717   

row          2  580.5  290.25  60.399 0.000106 ***

Residuals    6   28.8    4.81                    

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

with(dataframe,interaction.plot(column,row,y,type="b",pch=19,fixed=T,xlab="column",ylab="y"))

plot.design(y~column*row,data=dataframe)

fit <-lm(y~column+row,data=dataframe)

anova(fit)

summary(fit)

par(mfrow=c(2,2))

plot(fit)

par(mfrow=c(2,2))

plot(as.numeric(dataframe$column), fit$residuals, xlab="column", ylab="Residuals", type="p", pch=16)

plot(as.numeric(dataframe$row), fit$residuals, xlab="row", ylab="Residuals", pch=16)