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Regression Analysis: National Football League

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(15.23)

For the National Football League, ratings for the alltime leading passers were as shown below. Also shown for each quarterback is the percentage of passes that were interceptions, along with the percentage of passes that were touchdowns.

Player Rating TD% Inter%
Steve Young 96.8 5.6 2.6
Kurt Warner 95.7 5.5 3.5
Daunte Culpepper 93.2 5.4 3.1
Peyton Manning 92.3 5.6 3.1
Joe Montana 92.3 5.1 2.6
Trent Green 87.9 4.7 2.9
Tom Brady 87.5 4.8 2.6

a. Determine the least-squares regression line for estimating the passer rating based on the percentage of passes that were touchdowns.
b. A quarterback says 5.0% of his passes will be touchdowns next year. Assuming this to be true, estimate his rating for the coming season.
c. Determine the standard error of estimate.
d. For the quarterback in part (b), what is the 95% prediction interval for his pass rating next year?
e. For quarterbacks similar to the one in part (b), what is the 95% confidence interval for their mean rating next year?

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The solution provides step by step method for the calculation of regression analysis, prediction interval and confidence interval. Formula for the calculation and Interpretations of the results are also included.

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