Load in Packages

library(ggplot2)
library(tidyverse)

## Warning: package 'tidyverse' was built under R version 3.5.3

## -- Attaching packages ------------------------------------------------------------------------------------ tidyverse 1.2.1 --

## v tibble  2.0.1     v purrr   0.2.5
## v tidyr   0.8.2     v dplyr   0.7.8
## v readr   1.3.1     v stringr 1.3.1
## v tibble  2.0.1     v forcats 0.3.0

## -- Conflicts --------------------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

cars <- cars

Build and Evaluate the Model

ggplot(data = cars, aes(x = speed, y = dist)) + 
  geom_point(color='blue') +
  geom_smooth(method = "lm", se = FALSE)#+xlim(0,25000)

linear_model <- lm(dist~speed,cars)

plot(linear_model)

linear_model

## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## Coefficients:
## (Intercept)        speed  
##     -17.579        3.932

summary(linear_model)

## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## 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 *  
## 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

Conclusion

The relationship between stopping distance and speed is statistically significant which makes sense because the faster a car is going the harder it is for the car to stop. Based on the mnodel for every additional mpg of speed the distance to stop but increase 3.932 units of distance. The quantile quantile plot is pretty close to a straight line meaning that the residuals are indeed appoximately distributed. The adjusted R-squared value is .64 which means that around 64% of the variance in stopping distance can be explained with just the speed of the car