Question

PLEASE ANSWER A-E showing for each

De Rose and Galarza (2000) used multiple linear regression to study Att = average attendance from the first few years of Major League Soccer (MLS, the professional soccer league in the U.S.).The 12 MLS teams at the time ranged in average attendance from 10,000 to 22,000 per game. De Rose and Galarza used the following predictor variables: Pop = total population of metropolitan area within 40 miles (millions) Teams = number of (male) professional sports teams in the four major sports Temp = average temperature (April-September, oF). The regression results reported in the study were: Predictor Parameter Two tail Variable estimate p-value ______________________________________ Intercept 28.721 0.001 Pop 1.350 0.001 Teams -0.972 0.037 Temp -0.238 0.012

a. Write out the estimated least squares (regression) equation for predicting Att (average attendance in thousands) from Pop, Teams, and Temp.

b. R 2 was 91.4%, suggesting that this model may be useful for predicting average attendance (for expansion teams, say). Test the global usefulness of the model using a significance level of 5%. Hint: You will need to use the second formula for the global F-statistic on page 101 to solve this part. Also, you may find the following information useful: the 95th percentile of the F-distribution with 3 numerator degrees of freedom and 8 denominator degrees of freedom is 4.07

. c. Test, at a 5% significance level, whether the regression parameter estimate for Teams suggests that increasing the number of (male) professional sports teams in the four major sports (football, baseball, basketball, hockey) in a city is associated with a decrease in average MLS attendance in that city (all else being equal). Hint: You'll need to do a lower-tail hypothesis test using the p-value method, but be careful because the p-values given in the table are twotailed.

d. According to the model results, how much does average attendance differ for two cities with the same population and average temperature when one city has one fewer (male) professional sports teams in the four major sports?Hint: Write out the equation from part (a) for predicted average attendance in thousands for one city (plug in Teams=1, say) and then do the same for the other city (plug in Teams=2). The difference between the two equations gives you the answer to the problem. You should find that as long as you plug in values for Teams that differ by 1, you'll always get the same answer.

e. One purpose for the study was to predict attendance for future expansion teams. Since the study was published, some of the included cities are no longer represented in MLS and have been replaced by others. In one case, beginning with the 2006 season, the San Jose Earthquakes MLS franchise relocated to Houston, Texas, which was one of the potential cities considered in the study. A 95% prediction interval for average attendance for a potential Houston MLS team based on the model came to (10,980, 15,340). Briefly discuss how studies like this can help to inform decisions about future expansion teams for professional leagues like MLS.

Answer 1