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

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)