Chapter 3.2, Problem 67E

(a)

To determine

To describe the influence that Jacob’s point has on the equation of the least squares regression line.

Explanation of Solution

We have that Jacob’s point lies at the top in the scatterplot in the question, while we note that this pint has a much higher vertical jump than all other individuals in the sample. Since this point lies above and to the right of most points in the scatterplot, the point makes the regression line steeper and thus the point increases the slope. And since the point makes the regression line steeper the intersection of the regression line with the vertical axis at x equal to zero will be lower and thus the point decreases the y -intercept.

(b)

To determine

To describe the influence that Jacob’s point has on the standard deviation of the residuals and $r^2$ .

Explanation of Solution

As we know that the Jacob’s point lies near the top right corner of the scatterplot. Since the point lies much higher than the other points and since the point lies the furthest from the regression line in the scatterplot this point has the largest residual. And since the standard deviation of the residual measures the amount of variations the amount of variations in the response variables that is explained by the least squares regression line. Since Jacob’s point deviates strongly from the least squares regression line, there appears to be less variation in the response variables explained by the regression line when the point is included and thus the point decreases the coefficient of determination.