If you are driving and spot an object in the road, the distance it will take you to stop is equal to the sum of the following:

• The reaction distance is the distance you will continue to travel before you hit the brakes.

• The braking distance is the distance you will travel as you are braking.

The reaction and braking distances are shown in Table 51 for various driving speeds.

Let B be the braking distance (in feet) when driving at s miles per hour.

a. Construct a scatterplot that compares the values of s and B.

b. Describe the four characteristics of the association between s and B.

c. Construct a residual plot for the regression line that models the association between s and B. Does it support any of the conclusions you made in part (b)? If yes, which one(s)?

d. Estimate the driving speed and the residual represented by the lowest point in the residual plot. What does this tell you about the corresponding data point in the scatterplot and the regression line?

e. A student computes that r = 0.99 and concludes that there is a strong, linear association. What would you tell the student?

Table 51 Reaction and Braking Distances Driving Speed mles per hour) feet) Reaction Distance Braking Distance (feet 25 57 101 158 227 310 20 30 40 110 132 154 176 70 80