A manager of the restaurant chain examines how waiters' hourly wages affect the average service rating from visitors. A scatterplot of the data, a residual plot, and a histogram of standardized residuals are shown below. Are the assumptions of the simple linear regression model reasonable?
A) No, because the histogram of standardized residuals is skewed.
B) No, because the residual plot shows a curved pattern.
C) No, because the spread around the line on the residual plot does not appear to be constant.
D) No, because the residual plot indicates a large residual.
E) Yes, all the conditions for a linear regression are met.

Question

A manager of the restaurant chain examines how waiters' hourly wages affect the average service rating from visitors. A scatterplot of the data, a residual plot, and a histogram of standardized residuals are shown below. Are the assumptions of the simple linear regression model reasonable? ​    ​
A) No, because the histogram of standardized residuals is skewed. 
B) No, because the residual plot shows a curved pattern. 
C) No, because the spread around the line on the residual plot does not appear to be constant. 
D) No, because the residual plot indicates a large residual. 
E) Yes, all the conditions for a linear regression are met.

Quizplus · Accepted Answer

The assumptions of the simple linear regression model rely on several key conditions, including linearity, independence, normality, and constant variance. In this case, the residual plot shows a pattern where the spread around the line is not constant, which violates the assumption of constant variance. Answer options A, B, and D also represent violations of other assumptions, including normality and linearity. Therefore, the best choice is C.

A Manager of the Restaurant Chain Examines How Waiters' Hourly