## Related questions with answers

Is it defense or offense that wins football games? Consider the following portion of data, which includes a team's winning record (Win in %), the average number of yards gained, and the average number of yards allowed during the $2009$ NFL season.

$\begin{array}{|l|c|c|c|} \hline \text { Team } & \text { Win } & \text { Yards Gained } & \text { Yards Allowed } \\ \hline \text { Arizona Cardinals } & 62.50 & 344.40 & 346.40 \\ \hline \text { Atlanta Falcons } & 56.30 & 340.40 & 348.90 \\ \hline \vdots & \vdots & \vdots & \vdots \\ \hline \text { Washington Redskins } & 25.00 & 312.50 & 319.70 \\ \hline \end{array}$

a. Compare two simple linear regression models, where Model 1 predicts the winning percentage based on Yards Gained and Model 2 uses Yards Allowed.

b. Estimate a multiple linear regression model, Model 3, that applies both Yards Gained and Yards Allowed to forecast the winning percentage. Is this model an improvement over the other two models? Explain.

Solution

VerifiedWe are given a sample of wins, yards gained and yards allowed of $32$ teams.

Our goal is to estimate two simple linear regression models: one showing the influence of yards gained on the winning percentage and the other showing the influence of yards allowed on the winning percentage.

We can write these two models as:

$\begin{aligned} (i)\quad\text{Win}&=\beta_{1,0}+\beta_{1,1} \text{Yards made}+\epsilon\\ (ii)\quad\text{Win}&=\beta_{2,0}+\beta_{2,1} \text{Yards allowed}+\epsilon \end{aligned}$

We want to compare them.

*How do we estimate these models?*

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