Q 67. Who鈥檚 got hops? Haley, Jeff, a... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 3: Q 67. (page 208)

Who鈥檚 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鈥檚 point has on the equation of the least-squares regression line.
b. Describe the influence that Jacob鈥檚 point has on the standard deviation of the residuals and r2

Short Answer

Expert verified

Part (a) The point decreases the $y -$ intercept.

Part (b) The point decreases the coefficient of determination.

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

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.

Part (b) Step 1: Explanation

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.