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 slope and y - intercept of the least - squares regression line? this point will increase the value of the slope and increase the value of the y - intercept. this point will increase the value of the slope and decrease the value of the y - intercept. this point will decrease the value of the slope and increase the value of the y - intercept. this point will decrease the value of the slope and decrease the value of the y - intercept.

Explanation:

The slope of a regression line represents the change in \(y\) (GPA) for a unit change in \(x\) (absences). A lower - than - expected \(y\) value (lower GPA) for a given \(x\) (number of absences) pulls the line down. This makes the line steeper in the negative direction (decreases the slope). The \(y\) - intercept is the value of \(y\) when \(x = 0\). Since the overall line is pulled down (because of the out - lying point with low \(y\) for a relatively low \(x\)), the \(y\) - intercept (value of \(y\) at \(x = 0\)) also decreases.

Answer:

This point will decrease the value of the slope and decrease the value of the \(y\) - intercept.