Vehicle speed and braking distance
I am creating a simple model to show if there is a direct
correlation between vehicle speed and braking distance to stop using the
cars dataset.
head(cars)
## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
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
plot(cars[,'speed'],cars[,'dist'],main="Stopping Distance by speed",xlab="Speed (mph)",ylab="Distance (ft)")
After creating a simple plot of the distance by the vehicle speed,
one will notice the right upward trend of distance as vehicle speed
increases.
(cars_lm <- lm(dist ~ speed, data = cars))
##
## Call:
## lm(formula = dist ~ speed, data = cars)
##
## Coefficients:
## (Intercept) speed
## -17.579 3.932
Use the linear model function to calculate the y-intercept, the
slope and the residuals. We fit the plot with an abline to illustrate if
the data fits the model well.
plot(dist ~ speed, data = cars)
abline(cars_lm, col='red')
summary(cars_lm)
##
## 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
The t-value ratio of 9.464 and a very small p-value of 1.49e-12
there is strong evidence of a correlation between the speed of a vehicle
and the braking distance that it travels.