## What is the 95% prediction interval for a baseball franchise that generates \$250 million of annual revenue?

Chapter 13 Simple Linear Regression

1. 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.

1. Construct a scatter plot in Excel.
2. Write the simple linear regression equation and interpret the meaning of and in this problem.
3. Determine the coefficient of determination, , and interpret its meaning.
4. At the 0.05 level of significance, is there evidence of a linear relationship between annual revenue and franchise value?
5. What is the 95% confidence interval for the mean value of a baseball franchise that generates \$250 million of annual revenue?
6. What is the 95% prediction interval for a baseball franchise that generates \$250 million of annual revenue?

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