Chapter 13 Simple Linear Regression
- The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The following data represents the value in 2014 (in $millions) and the annual revenue (in $millions) for the 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 | 245 | 1000 |
| Boston | 370 | 2100 |
| Chicago White Sox | 227 | 975 |
| Cleveland | 207 | 825 |
| Detroit | 254 | 1125 |
| Houston | 175 | 800 |
| Kansas City | 231 | 700 |
| Los Angeles Angels | 304 | 1300 |
| Minnesota | 223 | 895 |
| New York Yankees | 508 | 3200 |
| Oakland | 202 | 725 |
| Seattle | 250 | 1100 |
| Tampa Bay | 188 | 625 |
| Texas | 266 | 1220 |
| Toronto | 226 | 870 |
| Arizona | 211 | 840 |
| Atlanta | 267 | 1150 |
| Chicago Cubs | 302 | 1800 |
| Cincinnati | 227 | 885 |
| Colorado | 214 | 855 |
| Los Angeles Dodgers | 403 | 2400 |
| Miami | 188 | 650 |
| Milwaukee | 226 | 875 |
| New York Mets | 263 | 1350 |
| Philadelphia | 265 | 1250 |
| Pittsburgh | 229 | 900 |
| St. Louis | 294 | 1400 |
| San Diego | 225 | 890 |
| San Francisco | 387 | 2000 |
| Washington | 287 | 1280 |
Hint: Copy and paste the data to Excel, on the Data tab, click Data Analysis and select Regression.
- Construct a scatter plot in Excel.
- Write the simple linear regression equation and interpret the meaning of and in this problem.
- Determine the coefficient of determination, , and interpret its meaning.
- At the 0.05 level of significance, is there evidence of a linear relationship between annual revenue and franchise value?
- What is the 95% confidence interval for the mean value of a baseball franchise that generates $250 million of annual revenue?
- What is the 95% prediction interval for a baseball franchise that generates $250 million of annual revenue?
