Who’s got hops? Haley, Jeff, and Nathan measured the height (in inches)

and vertical jump (in inches) of 74 students at their school.34 Here is a scatterplot of the data, along with the least-squares regression line. Jacob (highlighted in red) had a vertical jump of nearly 3 feet!

a. Describe the influence that Jacob’s point has on the equation of the least-squares regression line.

b. Describe the influence that Jacob’s point has on the standard deviation of the residuals and r2

And the player who has a batting average of $0.400$ in the first month has a batting average that is higher than the mean. Finally, we note that a player with a $0.200$ first-month batting average has a higher predicted batting average for the rest of the season, whereas a player with a $0.400$ first-month batting average has a lower predicted batting average for the rest of the season, indicating that the batting average prediction appears to be closer to the mean.

Jacob's point is near the scatterplot's top right corner, as we know. The point has the biggest residual because it is substantially higher than the other points and because it is the furthest away from the regression line in the scatterplot. The least-squares regression line explains the number of variations in the answer variables because the standard deviation of the residual measures. Because Jacob's point deviates so far from the least-squares regression line, when the point is included, there seems to be less variance in the response variables explained by the regression line, lowering the coefficient of determination.