Question

a guidance counselor wants to determine if there is a relationship between a students number of absences, x, and their grade - point average (gpa), y. the data that were collected are displayed in the scatterplot and the least - squares regression line was calculated. one student with 2 absences has a gpa of 1.8. this point is circled on the graph.
what effect does the circled point have on the standard deviation of the residuals?
this point will increase the value of the standard deviation of the residuals because it has a large positive residual.
this point will increase the value of the standard deviation of the residuals because it has a large negative residual.
this point will decrease the value of the standard deviation of the residuals because it has a large negative residual.

Explanation:

Step1: Understand residual concept

Residual = Observed - Predicted.

Step2: Analyze the point

The circled point is far from the regression - line. If it is below the line, it has a negative residual. A large - magnitude residual (positive or negative) affects the standard deviation of residuals.

Step3: Recall standard deviation property

Standard deviation measures the spread. A point with a large - magnitude residual increases the spread of residuals. Since the point is below the line, it has a large negative residual and will increase the standard deviation of the residuals.

Answer:

This point will increase the value of the standard deviation of the residuals because it has a large negative residual.