本文是实验设计与分析（第6版，Montgomery著，傅珏生译) 第10章拟合回归模型10.9节思考题10.12 R语言解题。主要涉及线性回归、回归的显著性、残差分析。
10-12
vial <- seq(1, 12, 1)
Viscosity <- c(26,24,175,160,163,55,62,100,26,30,70,71)
Temperature <- c(1.0,1.0,1.5,1.5,1.5,0.5,1.5,0.5,1.0,0.5,1.0,0.5)
Catalyst <- c(1.0,1.0,4.0,4.0,4.0,2.0,2.0,3.0,1.5,1.5,2.5,2.5)
visc <- data.frame(vial, Viscosity, Temperature,Catalyst)
visc
lm.fit <- lm(Viscosity ~ (Temperature)^2+(Catalyst)^2, data=visc)
summary (lm.fit)
> summary (lm.fit)
Call:
lm.default(formula = Viscosity ~ (Temperature)^2 + (Catalyst)^2,
data = visc)
Residuals:
Min 1Q Median 3Q Max
-14.0097 -4.9064 0.9614 4.7104 12.6390
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -49.635 7.988 -6.214 0.000156 ***
Temperature 18.355 7.615 2.410 0.039218 *
Catalyst 46.116 2.887 15.975 6.52e-08 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.483 on 9 degrees of freedom
Multiple R-squared: 0.9771, Adjusted R-squared: 0.972
F-statistic: 191.8 on 2 and 9 DF, p-value: 4.178e-08
summary (aov(lm.fit))
> summary (aov(lm.fit))
Df Sum Sq Mean Sq F value Pr(>F)
Temperature 1 11552 11552 128.5 1.25e-06 ***
Catalyst 1 22950 22950 255.2 6.52e-08 ***
Residuals 9 809 90
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
op <- par(mfrow=c(2,2), las=1)
plot(lm.fit)
par(op)
library(car)
carPlots(lm.fit)
