What effect does the circled point have on the slope and y-intercept of the least-squares regression line?

Question

A guidance counselor wants to determine if there is a relationship between a student’s 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 slope and y-intercept of the least-squares regression line?

A.This point will increase the value of the slope and increase the value of the y-intercept.

B.This point will increase the value of the slope and decrease the value of the y-intercept.

C.This point will decrease the value of the slope and increase the value of the y-intercept.

D. This point will decrease the value of the slope and decrease the value of the y-intercept.

Answer 1

Without seeing the graph, I'm going to guess that an increase in absences leads to a lower GPA. If this is the case, the circled point is likely an outlier far below the rest of the points where x = 2 absences (feel free to show me a contradictory picture that's attached to this question and I'll modify the answer).

So a point like this would tend to "flatten" the regression line. This would make the slope less pronounced (closer to zero) and make the y-intercept smaller. So at this point it's a question of how you define "decreasing the slope": if it means "making the slope closer to zero," select choice D; if it means "subtracting some value from the slope coefficient," you'll want to select B. I tend to go towards choice D in my interpretation, but that's more up to you.