Question

Driving speed and fuel consumption Exercise 9 (page 171) gives data on the fuel consumption y of a car at various speeds x. Fuel consumption is measured in liters of gasoline per 100 kilometers driven, and speed is measured in kilometers per hour. A statistical software package gives the least-squares regression line y^=11.058–0.01466x. Use the residual plot to determine if this linear model is appropriate.

Short answer

No, it is not appropriate.

Step-by-step solution

Given information

The figure is:

Concept

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

Explanation

The regression equation is:

$\stackrel{⏜}{y}=11.058-0.01466x$

The data points on the residual plot should follow a linear pattern, which is an important property of an adequate linear regression model. The data points in the presented residual plot do not form a linear pattern, making the model incorrect. Simply put, the existence of curvature in the residual plot indicates that the model is ineffective.