Question

Data were collected in the 1920s to determine the relationship between speed (km/h) and stopping distance (m) of cars. A linear regression was fitted, giving a line of best fit for dist.m in terms of speed.kph as

dist.m = -5.3581 + 0.7448 speed.kph

with an R² value of 0.6511.

(a) Before using the results of this linear regression, what plot should you look at to assess whether the regression model is appropriate for explaining the relationship between stopping distance and speed?

(b) What is the correlation between stopping distance and speed?

(c) Suppose that guidelines required an expected stopping distance of 20 m (or less) in a residential area. Based on this, what does the model predict as an appropriate speed limit?

Answer 1

The given model is: dist.m = -5.3581 + 0.7448 speed.kph

a) To assess whether the regression model is appropriate to explain the relationship between stopping distance and speed, we should look at the scatter plot between the 2 variables. The scatter plot gives a good estimate of how the stopping distance varies with speed.

b) Correlation between stopping distance and speed

= SQRT(R²)

= 0.807

c) An appropriate speed limit for an expected stopping distance of 20m or less

=  ( dist.m + 5.3581 ) / 0.7448 (by re-arranging the given regression equation)

= 34.05 km/h