Question

Leonard is studying the relationship between the fuel efficiency in miles per gallon (mpg), y, and the speed in miles per hour (mph), x, of his car. He collected data for 8 different speeds and found a linear model that best fit his data: y = 18.46 + 0.16x. To analyze the fit, he found the residuals and created the following residual plot.

Using the residual plot, what conclusion can he make about the linear model he found?
A. There is a negative linear relationship between the speed and fuel efficiency.
B. There is a positive linear relationship between the speed and fuel efficiency.
C. There is a quadratic relationship between the speed and fuel efficiency.
D. There is a nonlinear relationship between the speed and fuel efficiency.

Answer 1

D. There is a nonlinear relationship between the speed and fuel efficiency.

Explanation:

A desirable residual plot should show a horizontal band with points randomly distributed about the horizontal axis.

Leonard's plot is definitely nonlinear.

The residuals show a good fit to a parabola.

This suggests that the relation between speed and fuel efficiency may be parabolic.