Is there a relationship between total team salary and team
performance in a sport such as professional basketball? To answer
this question we will examine the number of wins and total team
payroll in a recent season for all the teams in the National
Basketball Association (NBA). The data are in this Excel
file.
Question 1. Let the x-variable be the team payroll and let the y-variable be the team wins. Find the intercept b0 and slope b1 of the least squares prediction line = b0 + b1*Payroll.
intercept (use 2 decimal places in your
answer)
slope (use 3 decimal places in your answer)
Question 2. If an NBA team spent an additional $9.2 million in team salary, how many more games could the team expect to win? (Use 1 decimal place in your answer).
Question 3. Suppose a basketball team spent
$111 million on salaries and won 46 games.
Part a. Based on their payroll would they have
done better or worse than predicted? (only 1 submission
allowed).
Worse than predictedBetter than predicted
Part b. What is the residual for this basketball
team? (use 2 decimal places in your answer)
Question 4. All teams have a goal to make the postseason playoffs. A basketball team thinks that it can make the playoffs next year if it wins 12 more games. How much should the basketball team increase its payroll if it wants to make the playoffs next year?
Note: Use 2 decimal places. Your answer should
be in units of $1 million; do NOT include a dollar sign in the
answer; for example, if a team should increase its payroll by
$5,250,000, then the answer is 5.25.
$
increase in team payroll (in $million) needed for basketball team to win 12 more games
Recent BASKETBALL Team Payrolls and Wins | ||
Team | Payroll | Wins |
Cleveland Cavaliers | 137.363 | 50 |
Los Angeles Lakers | 105.355 | 35 |
Boston Celtics | 115.084 | 55 |
Orlando Magic | 98.285 | 25 |
Denver Nuggets | 107.889 | 46 |
Portland Trail Blazers | 119.109 | 49 |
Houston Rockets | 119.070 | 65 |
San Antonio Spurs | 116.154 | 47 |
Dallas Mavericks | 85.904 | 24 |
New Orleans Pelicans | 119.800 | 48 |
Utah Jazz | 107.613 | 48 |
Atlanta Hawks | 100.414 | 24 |
Phoenix Suns | 94.818 | 21 |
Miami Heat | 131.223 | 44 |
Chicago Bulls | 89.425 | 27 |
Philadelphia 76ers | 100.794 | 52 |
Detroit Pistons | 100.086 | 39 |
Indiana Pacers | 94.430 | 48 |
Charlotte Hornets | 117.228 | 36 |
Milwaukee Bucks | 120.805 | 44 |
Brooklyn Nets | 96.040 | 28 |
Toronto Raptors | 116.575 | 59 |
New York Knicks | 107.855 | 29 |
Golden State Warriors | 137.495 | 58 |
Minnesota Timberwolves | 117.469 | 47 |
Memphis Grizzlies | 110.273 | 22 |
Oklahoma City Thunder | 134.294 | 48 |
Washington Wizards | 124.180 | 43 |
Los Angeles Clippers | 118.907 | 42 |
Sacramento Kings | 95.628 | 27 |
Answer to 1st question :
where x = team payroll and y is the team wins and also a = y - intercept = b0
The excel output of the following data is given below -
So, Mean of x , = 111.32 and Mean of y , = 41
Standard deviation of x , S.D. (x) = 14.02 , and , Standard Deviation of y , S.D. (y) = 12.22
Number of Observations , n = 30
b1 = 0.541 = slope and b0 = y - intercept = -19.22
The equation is -
= -19.22 + 0.541x
Answer to 2nd question :
Given , x = $ 9.2 + $ 137.363 = $146.563 (The NBA team is Cleveland
Cavaliers)
= -19.22 + (0.541 x 146.653) = 60.1 wins approximately
Originally they had 50 wins , So , the team could expect to win 10.1 extra games
Answer to 3rd question :
Given , x = $111
= -19.22 + (0.541 x 111) = 40.83
They had fared better than predicted...... (Answer a)
Originally the had won 46 games
The residual = Original - predicted = 46 - 40.83 = 5.17 (Answer b)
Answer to 4th question :
Let that basket ball team be Cleveland Cavaliers
They have originally 50 wins , If additional 12 wins are added to their tally their total wins would be 62
So , substituting these values in the prediction equation we solve for x ,
we get the value of x = $150.13
Increase in team payroll (in $million) needed for basketball team to win 12 more games = $150.13 - $137.363
= $12.77
(NOTE THAT : In Answers 2 & 4 I just took an example from the data , for other values the answer can be different)
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