## 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.

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

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 a multiple linear regression model showing the influence of yards gained and yards allowed on the winning percentage.

We can write the model as:

$\begin{aligned} \text{Win}&=\beta_0+\beta_1 \text{Yards made}+\beta_2\text{Yards allowed}\quad (3)\\ \end{aligned}$

Furthermore, we want to see if this model is better than the two simple linear regression models from part a.

*How do we estimate the model?*

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