LMR 7.3
library(MASS)
library(faraway)
data(ozone)
head(ozone,n=10)
## O3 vh wind humidity temp ibh dpg ibt vis doy
## 1 3 5710 4 28 40 2693 -25 87 250 33
## 2 5 5700 3 37 45 590 -24 128 100 34
## 3 5 5760 3 51 54 1450 25 139 60 35
## 4 6 5720 4 69 35 1568 15 121 60 36
## 5 4 5790 6 19 45 2631 -33 123 100 37
## 6 4 5790 3 25 55 554 -28 182 250 38
## 7 6 5700 3 73 41 2083 23 114 120 39
## 8 7 5700 3 59 44 2654 -2 91 120 40
## 9 4 5770 8 27 54 5000 -19 92 120 41
## 10 6 5720 3 44 51 111 9 173 150 42
g<-lm(O3~temp+humidity+ibh,ozone)
summary(g)
##
## Call:
## lm(formula = O3 ~ temp + humidity + ibh, data = ozone)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.5291 -3.0137 -0.2249 2.8239 13.9303
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.049e+01 1.616e+00 -6.492 3.16e-10 ***
## temp 3.296e-01 2.109e-02 15.626 < 2e-16 ***
## humidity 7.738e-02 1.339e-02 5.777 1.77e-08 ***
## ibh -1.004e-03 1.639e-04 -6.130 2.54e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.524 on 326 degrees of freedom
## Multiple R-squared: 0.684, Adjusted R-squared: 0.6811
## F-statistic: 235.2 on 3 and 326 DF, p-value: < 2.2e-16
plot(g)
bc<-boxcox(g,plotit = T,lambda=seq(0.15,0.35,by=0.05))
(best.lam<-bc$x[which(bc$y==max(bc$y))])
## [1] 0.2772727
gbc<-lm(O3^best.lam~temp+humidity+ibh,ozone)
summary(gbc)
##
## Call:
## lm(formula = O3^best.lam ~ temp + humidity + ibh, data = ozone)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.63030 -0.12606 0.01037 0.14553 0.57837
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.738e-01 7.283e-02 11.999 < 2e-16 ***
## temp 1.544e-02 9.504e-04 16.246 < 2e-16 ***
## humidity 3.533e-03 6.034e-04 5.854 1.17e-08 ***
## ibh -5.691e-05 7.382e-06 -7.709 1.55e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2038 on 326 degrees of freedom
## Multiple R-squared: 0.7162, Adjusted R-squared: 0.7136
## F-statistic: 274.2 on 3 and 326 DF, p-value: < 2.2e-16
plot(gbc)
