In American college football, Rivals.com constructs a widely followed index for rating colleges based on the high school players they recruit and Jeff Sagarin constructs a highly regarded system for rating college football teams based on their performance.

Table 8.7 shows the average 2005–2008 performance and recruiting ratings for the 20 colleges with the highest recruiting averages. Use these data to estimate a simple linear regression model with performance as the dependent variable and recruiting as the explanatory variable.

a. Draw a scatter diagram and the least squares line.

b. Is the relationship statistically significant at the 5 percent level?

c. Is the size of the estimated relationship substantial?

d. Which team overperformed the most, in that its performance was much higher than predicted by your estimated equation?

e. Which team underperformed the most, in that its performance was much lower than predicted by your estimated equation?

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Recruiting Performance Alabama 2,044.00 81.538 Auburn 1,773.00 81.918 California 1,444.00 83.048 Clemson 1,710.00 80.545 Florida 2,481.75 91.615 Florida State 2,232.50 80.308 Georgia 2,116.50 85.590 LSU 2,100.50 89.480 Miami-FL Michigan 1,920.00 76.290 1,984.75 80.435 Nebraska 1,625.75 78.618 Notre Dame 1,881.50 77.013 Ohio State 1,928.00 90.390 Oklahoma 2,186.75 88.978 Penn State 1,349.50 86.678 South Carolina 1,514.50 78.425 Southern California 2,680.50 95.073 Tennessee 1,850.25 79.040 Texas UCLA 2,043.25 92.398 1,355.75 77.525