Can you use the annual revenues generated by National Basketball Association (NBA) franchises to predict franchise values? Figure 2.15 on page 57 shows a scatter plot of revenue with franchise value, and Figure 3.10 on page 129, 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 b0 and b1.
b. Interpret the meaning of the Y intercept, b0, and the slope, b1, in this problem.
c. Predict the value of an NBA franchise that generates $150 million of annual revenue.
d. Compute the coefficient of determination, r2, 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 a 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 $150 million of annual revenue.
h. Construct a 95% prediction interval of the value of an individual NBA franchise that generates $150 million of annual revenue.
i. Compare the results 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.