Researchers study the relationship between x = Average salary (in thousands of dollars) and y = Percent of total income spent on recreation and culture. The x values and the corresponding standardized residuals from a simple linear regression are as follows: Construct a standardized residual plot. Based on this plot, does the simple linear regression model seems reasonable?
A) The plot suggests that the model is appropriate.
B) A potentially influential observation suggests that the model is not appropriate.
C) The outliers suggest that the model is not appropriate.
D) The curved pattern suggests that the model is not appropriate.
E) An estimated regression line is needed to make the assumptions.

Question

Researchers study the relationship between x = Average salary (in thousands of dollars) and y = Percent of total income spent on recreation and culture. The x values and the corresponding standardized residuals from a simple linear regression are as follows: ​  ​ Construct a standardized residual plot. Based on this plot, does the simple linear regression model seems reasonable? ​
A) The plot suggests that the model is appropriate. 
B) A potentially influential observation suggests that the model is not appropriate. 
C) The outliers suggest that the model is not appropriate. 
D) The curved pattern suggests that the model is not appropriate. 
E) An estimated regression line is needed to make the assumptions.

Quizplus · Accepted Answer

A standardized residual plot is used to assess the assumption of linearity in a simple linear regression model. A plot with a curved pattern suggests that the relationship between the variables may not be linear and the model may not be appropriate. In this case, the plot shows a slight curve, indicating that the linear model may not fit perfectly. Therefore, choice D is the best answer. The other options are not supported by the plot.

Researchers Study the Relationship Between X = Average Salary (In