Question

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph.

What effect will the circled point have on the y-intercept?

The y-intercept will not change with the addition of this point.
The y-intercept will decrease because the point pulls the least-squares regression line toward it.
The y-intercept will increase because the point pulls the least-squares regression line toward it.
The y-intercept will increase because this point represents an extremely high number of pretzels grabbed with the dominant hand.

Answer 1

The circled point in the scatterplot will cause the y-intercept to increase because it pulls the least-squares regression line towards it.

The circled point in the scatterplot represents a student with a handspan of 23 cm who grabbed 38 pretzels.

This point is considered an outlier because it is significantly far away from the least-squares regression line.

An outlier can affect the slope and y-intercept of the regression line.

In this case, the y-intercept will be pulled towards the outlier, causing it to increase.

So, the correct answer is: The y-intercept will increase because the point pulls the least-squares regression line towards it.