software ex2.1 #8

library(ISLR2)
fit <- lm(mpg ~ horsepower, data = Auto)
summary(fit)

## 
## Call:
## lm(formula = mpg ~ horsepower, data = Auto)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.5710  -3.2592  -0.3435   2.7630  16.9240 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.935861   0.717499   55.66   <2e-16 ***
## horsepower  -0.157845   0.006446  -24.49   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.906 on 390 degrees of freedom
## Multiple R-squared:  0.6059, Adjusted R-squared:  0.6049 
## F-statistic: 599.7 on 1 and 390 DF,  p-value: < 2.2e-16

predict(fit, data.frame(horsepower = 98), interval = "confidence")

##        fit      lwr      upr
## 1 24.46708 23.97308 24.96108

predict(fit, data.frame(horsepower = 98), interval = "prediction")

##        fit     lwr      upr
## 1 24.46708 14.8094 34.12476

plot(Auto$horsepower, Auto$mpg, xlab = "horsepower", ylab = "mpg")
abline(fit)

par(mfrow = c(2, 2))
plot(fit, cex = 0.2)