In: Statistics and Probability
The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. Below is the data that represents the value (in $millions) and the annual revenue (in $millions) for 30 Major League Baseball franchises. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated.
Team |
Revenue |
Value |
Baltimore |
179 |
460 |
Boston |
310 |
1000 |
Chicago White Sox |
214 |
600 |
Cleveland |
178 |
410 |
Detroit |
217 |
478 |
Kansas City |
161 |
354 |
Los Angeles Angels |
226 |
656 |
Minnesota |
213 |
510 |
New York Yankees |
439 |
1850 |
Oakland |
160 |
321 |
Seattle |
210 |
585 |
Tampa Bay |
161 |
323 |
Texas |
233 |
674 |
Toronto |
188 |
413 |
Arizona |
186 |
447 |
Atlanta |
203 |
508 |
Chicago Cubs |
266 |
879 |
Cincinnati |
185 |
424 |
Colorado |
193 |
464 |
Houston |
196 |
549 |
Los Angeles |
230 |
1400 |
Miami |
148 |
450 |
Milwaukee |
195 |
448 |
New York Mets |
225 |
719 |
Philadelphia |
249 |
723 |
Pittsburgh |
168 |
336 |
St. Louis |
233 |
591 |
San Diego |
163 |
458 |
San Francisco |
230 |
643 |
Washington |
200 |
480 |
(a ) Use the least-squares method to determine the regression coefficients (intercept and slope).
(b) Interpret the meaning of the intercept and slope in this problem.
(c) Predict the value of a baseball franchise that generates $150 million of annual revenue.
(d) determine the coefficient of determination, r2, and interpret its meaning.
(e) determine the standard error of estimate (Syx).
(f) How useful do you think this regression model is for predicting the value of a baseball franchise?