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 circled point

The circled point is well - below the regression line. So it has a large negative residual.

Step3: Recall standard deviation property

Standard deviation measures spread. A large residual (in magnitude) increases spread.

Answer:

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