Opponent Adjusted Quarterback Rating: Explained

I recently put together a regression model to determine the factors that most drive the number of points a football team scores in any given game.  It's a work in progress, but the factors I looked at were:

• Yards per attempt (Y/A)
  
• Interception %
• Yards/Rush
• Average Y/A yielded by opponent
• Average points yielded by opponent
  

Of the variables above, Y/A was, by the far, the strongest - followed by interception percentage.  The other three were pretty close in importance.

You'll notice that a quarterback has a direct impact on 2 of the 5. With that in mind, I decided to create a quarterback rating system that looks primarily at the factors of Y/A and Int %.  Further, because a quarterback's performance is obviously affected by their opponent, I added an element that accounts for the quality of the opponent's defense.

The formula for the rating, which I'm going to call the Opposition Adjusted Quarterback Rating (OA Quarterback Rating) until I can think of a cooler or funnier name.

The formula was basically:

• Y/A minus the opponent's average Y/A yielded (times a factor of 2.8 - as determined by the regression model) PLUS
• Int % minus the opponent's average Int % yielded (times a factor of -54 - again, as determined by the model)