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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5.4 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(
Light=c(280,290,285,230,235,240,300,310,295,260,240,235,290,285,290,220,225,230),
phospor=gl(3, 6,18),
glass=gl(2, 3, 18))
summary (battery)
battery.aov2 <- aov(Light ~ phospor * glass,data= dataframe)
summary (battery.aov2)
> summary (battery.aov2)
Df Sum Sq Mean Sq F value Pr(>F)
phospor 2 933 467 8.842 0.00436 **
glass 1 14450 14450 273.789 1.26e-09 ***
phospor:glass 2 133 67 1.263 0.31780
Residuals 12 633 53
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
with(dataframe,interaction.plot(phospor,glass,Light,type="b",pch=19,fixed=T,xlab="phosphor",ylab="Light"))
plot.design(Light~glass*phospor,data=dataframe)
fit <-lm(Light~glass*phospor,data=dataframe)
anova(fit)
> anova(fit)
Analysis of Variance Table
Response: Light
Df Sum Sq Mean Sq F value Pr(>F)
glass 1 14450.0 14450.0 273.7895 1.259e-09 ***
phospor 2 933.3 466.7 8.8421 0.004364 **
glass:phospor 2 133.3 66.7 1.2632 0.317801
Residuals 12 633.3 52.8
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
summary(fit)
> summary(fit)
Call:
lm(formula = Light ~ glass * phospor, data = dataframe)
Residuals:
Min 1Q Median 3Q Max
-10.000 -5.000 0.000 4.167 15.000
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 285.000 4.194 67.949 < 2e-16 ***
glass2 -50.000 5.932 -8.429 2.19e-06 ***
phospor2 16.667 5.932 2.810 0.0158 *
phospor3 3.333 5.932 0.562 0.5845
glass2:phospor2 -6.667 8.389 -0.795 0.4422
glass2:phospor3 -13.333 8.389 -1.589 0.1379
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.265 on 12 degrees of freedom
Multiple R-squared: 0.9608, Adjusted R-squared: 0.9444
F-statistic: 58.8 on 5 and 12 DF, p-value: 5.067e-08
par(mfrow=c(2,2))
plot(fit)
par(mfrow=c(2,2))
plot(as.numeric(dataframe$glass), fit$residuals, xlab="glass", ylab="Residuals", type="p", pch=16)
plot(as.numeric(dataframe$phospor), fit$residuals, xlab="phospor", ylab="Residuals", pch=16)
