Question

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 1

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)