Chapter 3.2, Problem 68E

(a)

To determine

To describe what influence the highlighted point has on the equation of the least squares regression line.

Explanation of Solution

We have that highlighted point lies at the bottom left corner in the scatterplot in the question, while we note that this point has a much lower weight and a much lower price than all other individuals in the sample. Since this point lies below the estimated regression line through the other points of 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 what influence the highlighted point has on the standard deviation of the residuals and $r^2$ .

Explanation of Solution

As we know that the highlighted point lies near the bottom left corner of the scatterplot. Since the point lies much close to the regression line in the scatterplot this point has relatively small 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 highlighted point lies very close to the least squares regression line, there appears to be more variation in the response variables explained by the regression line when the point is included and thus the point increases the coefficient of determination.