Predicting Car Stopping Distance

Asier Goikoetxea
2016/08/20

Introduction

  • We want to create a prediction model to determine the stopping distance of a car knowing the speed.
  • We will use the “Cars” dataset from the “Datasets” package
  • The Data has 50 observations and 2 variables: speed (mph) and dist (distance, ft)
library(datasets)
data("cars")
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

Fitting a Model

  • For our prediction algorithm we will fit a basic linear model which relates Speed and Distance
  • We can take a look a the coefficients to analyze the model
  • in the next slide we will analyze some plots
mdl <- lm(dist ~ speed, data = cars)
summary(mdl)$coef

              Estimate Std. Error   t value     Pr(>|t|)
(Intercept) -17.579095  6.7584402 -2.601058 1.231882e-02
speed         3.932409  0.4155128  9.463990 1.489836e-12

Model Analysis

par(mfrow=c(2,2))
plot(mdl)

plot of chunk unnamed-chunk-3

Predicting new values

  • We use the predict function to calculate new values using our linear model. For example, with a speed of 20 mph we would get these results
userspeed <- 20; 
dist <- predict(mdl, newdata = data.frame(speed=userspeed))
print(dist)

       1 
61.06908

Ploting the Results

plot(cars$speed, cars$dist, xlab="Car Speed (mph)", ylab = "Distance (ft)",
     col="blue") 
abline(mdl); lines(c(userspeed, userspeed), c(0, 200),col="red",lwd=3)
text(10, 120, paste("Distance = ", round(dist, digits = 3)))

plot of chunk unnamed-chunk-5