Chapter 13, Problem 82PS

Can you use the annual revenues generated by National Basketball Association (NBA) franchises to predict franchise values? Figure 2.17 on page 68 shows a scatter plot of revenue with franchise value, and Figure 3.10 on page 148, shows the correlation coefficient. Now, you want to develop a simple linear regression model to predict franchise values based on revenues. (Franchise values and revenues are stored in NBAValues.)

a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients $b_0$ and $b_1.$

b. Interpret the meaning of the $Y$ intercept, $b_0,$ and the slope, $b_1,$ in this problem.

c. Predict the mean value of NBA franchise that generates $\text{\$150}$ million of annual revenue.

d. Compute the coefficient of determination, $r^2,$ and interpret its meaning.

e. Perform a residual analysis on your results and evaluate the regression assumptions.

f. At the 0.05 level of significance, is there evidence of linear relationship between the annual revenues generated and the value of an NBA franchise?

g. Construct a $95\%$ confidence interval estimate of the mean value of all NBA franchises that generate $\text{\$150}$ million of annual revenue.

h. Construct a $95\%$ prediction interval of the value of an individual NBA franchise that generated $\text{\$150}$ million of annual revenue.

i. Compare the result of (a) through (h) to those of baseball franchises in Problems 13.8, 13.20, 13.30, 13.46, and 13.62 and European soccer teams in Problem 13.83.