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5.5 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(

wrap=c(17,20,12,9,16,12,21,17,16,21,18,13,18,21,23,21,24,22,17,12,25,23,23,22,28,27,27,31,30,23,29,31),

Temperature=gl(4,2,32),

copper=gl(4,8, 32))

summary (dataframe)

dataframe.aov2 <- aov(wrap~copper*Temperature,data=dataframe)

summary (dataframe.aov2)

> summary (dataframe.aov2)

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

copper              3  698.3  232.78  34.327 3.35e-07 ***

Temperature         3  156.1   52.03   7.673  0.00213 **

copper:Temperature  9  113.8   12.64   1.864  0.13275   

Residuals          16  108.5    6.78                    

---

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

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

plot.design(wrap~copper*Temperature,data=dataframe)

fit <-lm(wrap~copper*Temperature,data=dataframe)

anova(fit)

> anova(fit)

Analysis of Variance Table

Response: wrap

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

copper              3 698.34 232.781 34.3272 3.35e-07 ***

Temperature         3 156.09  52.031  7.6728 0.002127 **

copper:Temperature  9 113.78  12.642  1.8643 0.132748   

Residuals          16 108.50   6.781                    

---

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

summary(fit)

> summary(fit)

Call:

lm(formula = wrap ~ copper * Temperature, data = dataframe)

Residuals:

   Min     1Q Median     3Q    Max

  -3.5   -1.5    0.0    1.5    3.5

Coefficients:

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

(Intercept)           1.850e+01  1.841e+00  10.047 2.57e-08 ***

copper2               8.521e-15  2.604e+00   0.000  1.00000   

copper3               4.500e+00  2.604e+00   1.728  0.10323   

copper4               9.000e+00  2.604e+00   3.456  0.00325 **

Temperature2         -8.000e+00  2.604e+00  -3.072  0.00729 **

Temperature3         -4.500e+00  2.604e+00  -1.728  0.10323   

Temperature4          5.000e-01  2.604e+00   0.192  0.85015   

copper2:Temperature2  5.000e+00  3.683e+00   1.358  0.19340   

copper3:Temperature2 -5.000e-01  3.683e+00  -0.136  0.89370   

copper4:Temperature2  9.500e+00  3.683e+00   2.580  0.02016 * 

copper2:Temperature3  5.500e+00  3.683e+00   1.493  0.15477   

copper3:Temperature3  5.500e+00  3.683e+00   1.493  0.15477   

copper4:Temperature3  3.500e+00  3.683e+00   0.950  0.35605   

copper2:Temperature4  3.000e+00  3.683e+00   0.815  0.42725   

copper3:Temperature4 -1.000e+00  3.683e+00  -0.272  0.78945   

copper4:Temperature4  2.000e+00  3.683e+00   0.543  0.59456   

---

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

Residual standard error: 2.604 on 16 degrees of freedom

Multiple R-squared:  0.8992,    Adjusted R-squared:  0.8048

F-statistic: 9.519 on 15 and 16 DF,  p-value: 2.57e-05

par(mfrow=c(2,2))

plot(fit)

par(mfrow=c(2,2))

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

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