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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