13.20 In Problem 13.8 you used annual revenues to predict the current value of a MLB baseball team, using the data stored in [MLB Values]. Using the results of that problem, a. determine the coefficient of determination, r2 , and interpret its meaning. b. determine the standard error of the estimate. c. How useful do you think this regression model is for predicting the value of a MLB baseball team? Baltimore 253 1175 Boston 434 2700 Chicago White Sox 269 1350 Value Cleveland 271 920 4000 Detroit 275 1200 Houston 299 1450 3500 Kansas City 246 950 Los Angeles Angels 350 1750 3000 Minnesota 249 1025 New York Yankees 526 3700 2500 Oakland 216 880 Seattle 289 2000 1400 Tampa Bay 205 825 Texas 1500 298 1550 Toronto 278 1300 Arizona 1000 253 1350 : . . . Atlanta 275 1500 500 Chicago Cubs 434 2650 Cincinnati 229 915 Colorado 248 1000 100 200 300 400 500 600 Los Angeles Dodgers 462 1750 Miami 206 940 Milwaukee 239 925 New York Mets 332 2000 Philadelphia 325 1650 Pittsburgh 265 1250 St. Louis 310 1800 San Diego 259 1125 San Francisco 428 2650 Washington 304 1600 SUMMARY OUTPUT Regression Statistics Multiple R 0.980280119 R Square 0.960949113 Adjusted R Square 0.959502783 Standard Error 16.32968189 Observations 29 ANOVA df SS MS F Significance F Regression 177169.3926 177169.3926 Residua 664.4055433 1.50417E-20 27 7199.779786 266.6585106 Total 28 184369.1724 Coefficients Standard Error t Stat Intercept P-value Lower 95% Upper 95% 128.6235726 Lower 95.0% Upper 95.0% 7.397705759 17.38695438 3.43003E-16 113.4447341 1175 143.802411 113.44473 143.80241 .111826103 0.00433837 25.77606532 .50417E-20 0.102924504 .120727703 0.1029245 0.1207277 b. BO= 186.328208205722 B1= 0.0637440333305742 c. Bo is the y-intercept and has a value of 186.33 or 186.33 million will be the revenue when a team has a current value of zero. This value does not make sense since there is no MLB team that has a current value of zero and still earn a revenue. $1 is the slope of the regression equation which has a value of 0.063744. This means that for every 1 million increase in current value the revenue will increase by 0.063744 million. d. the mean current value would be $202.26 million e. There is a positive linear relationship between revenue and current value of the MLB team. As the current value of a team increases , it's revenue also increases. This is also further supported by the slop of the regression line, which is +0.0637. The r-square value is equal to 0.6996-> 69.96% of the varience in the current value is explained by revenue. In addition, if we take the square root of the r-square value, we get the Correlation coefficient, r = 0.8364. ince this value is greater than 0.5, this indicates a strong positive linear relationship between current value and revenue