Question

Professional basketball teams have 11 players per team. Salary is dependent upon their scoring average,

measured in points per game.
A least-squares regression line that describes the relationship between scoring average and salary for
one professional basketball team is 9 = 2,671,134.68+684,663.08x, where x is the player's scoring
average and y is the player's salary. The residuals for this regression are given in the graph below.
Residual
$20,000,000
$15,000,000
$10,000,000
$5,000,000
$0
-$5,000,000
-$10,000,000
-$15,000,000
6
10
12
14
Scoring Average (Points per Game)
16
18
a) Is a line an appropriate model to use for these data? What information tells you this?
b) What is the value of the slope of the least-squares regression line? Interpret the slope in the
context of this problem.
c)
What is the predicted salary of the basketball player with 10.9 points per game?
d) Approximate the actual salary of the basketball player with 10.9 points per game. Please HURRY THANK YOU SM

Answer 1

a) A line is an appropriate model for the data based on the scatter plot and residuals. b) The slope of the least-squares regression line is 684,663.08. c) The predicted salary for a player with 10.9 points per game is $10,687,805.02.

Step-by-step explanation:

a) To determine whether a line is an appropriate model for the data, we need to examine the scatter plot and the residuals. If the scatter plot shows a linear pattern and the residuals are randomly scattered around the line, then a line is an appropriate model. In this case, the scatter plot shows a linear pattern and the residuals are randomly scattered around the regression line, so a line is an appropriate model for these data.

b) The value of the slope of the least-squares regression line is 684,663.08 (b = 684,663.08). This means that for every point increase in the player's scoring average, the player's salary increases by approximately $684,663.08.

c) To find the predicted salary of the basketball player with 10.9 points per game, we substitute the value of x into the regression equation. Therefore, the predicted salary is 2,671,134.68 + (684,663.08 * 10.9) = $10,687,805.02.

d) Approximating the actual salary of the basketball player with 10.9 points per game is not possible without additional information.