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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5.5 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)
