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 y-intercept will increase because the point pulls the least-squares regression line toward it. Hence the correct option is c.

The circled point, representing a student with a handspan of 23 cm who grabbed 38 pretzels, has an influential effect on the y-intercept. In linear regression, the y-intercept is the value of the dependent variable (number of pretzels grabbed) when the independent variable (handspan) is zero.

As this particular point deviates from the overall trend, it exerts influence, causing the least-squares regression line to adjust. In this case, the y-intercept increases, reflecting the impact of the extreme data point, suggesting that, with a handspan of zero, the predicted number of pretzels grabbed is higher due to the influence of this specific observation. Hence the correct option is c.