Assignment:
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
|
|
Torn 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 passer 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?
Provide complete and step by step solution for the question and show calculations and use formulas.