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5.8 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。

(a)

            

dataframe<-data.frame(

Light=c(580,568,570,550,530,579,546,575,599,1090,1087,1085,1070,1035,1000,1045,1053,1066,1392,1380,1386,1328,1312,1299,867,904,889),

Temperature=gl(3,9,27),

Material=gl(3,3,27))

summary (dataframe)

dataframe.aov2 <- aov(Light~Material*Temperature,data=dataframe)

summary (dataframe.aov2)

> summary (dataframe.aov2)

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

Material              2  150865   75432   206.4 3.89e-13 ***

Temperature           2 1970335  985167  2695.3  < 2e-16 ***

Material:Temperature  4  290552   72638   198.7 1.25e-14 ***

Residuals            18    6579     366                    

---

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

with(dataframe,interaction.plot(Temperature,Material,Light,type="b",pch=19,fixed=T,xlab="Temperature (°F)",ylab="Light"))

plot.design(Light~Material*Temperature,data=dataframe)

(b)

fit <-lm(Light~Material*Temperature,data=dataframe)

anova(fit)

> anova(fit)

Analysis of Variance Table

Response: Light

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

Material              2  150865   75432  206.37 3.886e-13 ***

Temperature           2 1970335  985167 2695.26 < 2.2e-16 ***

Material:Temperature  4  290552   72638  198.73 1.254e-14 ***

Residuals            18    6579     366                     

---

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

summary(fit)

> summary(fit)

Call:

lm(formula = Light ~ Material * Temperature, data = dataframe)

Residuals:

    Min      1Q  Median      3Q     Max

-35.000  -5.333  -0.333   6.667  35.000

Coefficients:

                        Estimate Std. Error t value Pr(>|t|)   

(Intercept)             572.6667    11.0381  51.881  < 2e-16 ***

Material2               -19.6667    15.6102  -1.260   0.2238   

Material3                 0.6667    15.6102   0.043   0.9664   

Temperature2            514.6667    15.6102  32.970  < 2e-16 ***

Temperature3            813.3333    15.6102  52.103  < 2e-16 ***

Material2:Temperature2  -32.6667    22.0762  -1.480   0.1562   

Material3:Temperature2  -33.3333    22.0762  -1.510   0.1484   

Material2:Temperature3  -53.3333    22.0762  -2.416   0.0265 * 

Material3:Temperature3 -500.0000    22.0762 -22.649 1.11e-14 ***

---

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

Residual standard error: 19.12 on 18 degrees of freedom

Multiple R-squared:  0.9973,    Adjusted R-squared:  0.9961

F-statistic: 824.8 on 8 and 18 DF,  p-value: < 2.2e-16

(c)

par(mfrow=c(2,2))

plot(fit)

par(mfrow=c(2,2))

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

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