Quarterly figures for e-commerce retail sales were obtained from the first quarter of 2009 through the fourth quarter of 2015. A regression model was estimated to describe the trend in e-commerce retail sales over time. What does the plot of residuals versus predicted values suggest?
A) The relationship seems reasonably straight.
B) There is no reason to be alert for autocorrelation.
C) The Equal Spread condition is satisfied.
D) The Linearity condition is satisfied.
E) The Linearity condition is not satisfied, and the Equal Spread condition is not satisfied as well.

Question

Quarterly figures for e-commerce retail sales were obtained from the first quarter of 2009 through the fourth quarter of 2015. A regression model was estimated to describe the trend in e-commerce retail sales over time. What does the plot of residuals versus predicted values suggest? 
A) The relationship seems reasonably straight. 
B) There is no reason to be alert for autocorrelation. 
C) The Equal Spread condition is satisfied. 
D) The Linearity condition is satisfied. 
E) The Linearity condition is not satisfied, and the Equal Spread condition is not satisfied as well.

Quizplus · Accepted Answer

The plot of residuals versus predicted values is used to assess the Linearity and Equal Spread conditions of the regression model. If the points on the plot are randomly scattered around the horizontal axis, then we can conclude that the Linearity condition is satisfied. If, on the other hand, the points show a clear pattern, then the Linearity condition is not satisfied. In this case, the plot suggests that the points follow a bow-shaped pattern, which indicates that the Linearity condition is not satisfied. Additionally, if there is a clear trend or pattern in the spread of the residuals across the predicted values, then the Equal Spread condition is not satisfied. The plot shows that the spread of the residuals increases as the predicted values increase, which indicates that the Equal Spread condition is not satisfied as well. Therefore, the best choice is E.

Quarterly Figures for E-Commerce Retail Sales Were Obtained from the First