Assignment 11

Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.)

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00
cars%>%
  ggplot(aes(speed, dist))+
  geom_point()+
  geom_smooth(method = lm, se = F)+
  labs(title = "Original Data", x="Speed", y="Distance")+
  theme_minimal()
## `geom_smooth()` using formula 'y ~ x'

cars_lm<-lm(cars$dist ~ cars$speed)
summary(cars_lm)
## 
## Call:
## lm(formula = cars$dist ~ cars$speed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.5791     6.7584  -2.601   0.0123 *  
## cars$speed    3.9324     0.4155   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
## F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12
plot(fitted(cars_lm),resid(cars_lm))

cars_lm %>%
  ggplot(aes(fitted(cars_lm),resid(cars_lm)))+
  geom_point()+
  geom_smooth(method = lm, se = F)+
  labs(title = "Residual Data", x="Fitted", y="Residual")+
  theme_minimal()
## `geom_smooth()` using formula 'y ~ x'

cars_lm %>%
  ggplot(aes(sample=resid(cars_lm)))+
  stat_qq()+
  stat_qq_line()+
  labs(title = "Q-Q Plot")+
  theme_minimal()