library(e1071)
data(cars)
attach(cars); 
str(cars)
## 'data.frame':    50 obs. of  2 variables:
##  $ speed: num  4 4 7 7 8 9 10 10 10 11 ...
##  $ dist : num  2 10 4 22 16 10 18 26 34 17 ...
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 dataset has only two variables - let’s explore them…

hist(speed, breaks = 50)

hist(dist,  breaks = 50)

qqnorm(speed); qqline(speed, col = 2)

qqnorm(dist); qqline(dist, col = 2)

shapiro.test(speed)
## 
##  Shapiro-Wilk normality test
## 
## data:  speed
## W = 0.9776, p-value = 0.4576
shapiro.test(dist)
## 
##  Shapiro-Wilk normality test
## 
## data:  dist
## W = 0.9514, p-value = 0.0391

There seems to be a linear relation between the variables…

boxplot(cars)

library(corrplot)
correlations <- cor(cars); 
correlations
##           speed      dist
## speed 1.0000000 0.8068949
## dist  0.8068949 1.0000000
corrplot(correlations)

There is a pronounced correlation too, let’s create a linear model…

model <- lm(speed ~ dist)
summary(model)
## 
## Call:
## lm(formula = speed ~ dist)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.5293 -2.1550  0.3615  2.4377  6.4179 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.28391    0.87438   9.474 1.44e-12 ***
## dist         0.16557    0.01749   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.156 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(model)

And finally, we can add the fitted line to the original scatter plot.

plot(speed ~ dist); abline(model, col = "red")