Is there a relationship between total team salary and team performance in a sport such as professional football? 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 Football League $($NFL$).$ 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 bo and slope b$$ of the least squares prediction line Wins $=$ bo $+$ b$*$Payroll$.$

intercept $($use $3$ decimal places in your answer$)$

slope $($use $4$ decimal places in your answer$)$

Question $2.$ If an NFL team spent an additional $$89$ million in team salary, how many more games would the team be predicted to win? $($Use $3$ decimal places in your answer$).$

Question $3.$ Suppose a football team spent $$208$ million on salaries and won $9$ games.

Part a$.$ Based on their payroll would they have done better or worse than predicted? $($only $1$ submission allowed$).$

Worse than predicted

Better than predicted

Part b$.$ What is the residual for this football team? $($use $2$ decimal places in your answer$)$

Question $4.$ All teams have a goal to make the postseason playoffs. A football team thinks that it can make the playoffs next year if it wins $2$ more games. How much should the football 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 $5\mathrm{.}25.$

increase in team payroll $($in $million$)$ needed for football team to win $2$ more games