Question

You are a starting pitcher in the major leagues. It's January 2008, and you are in the process of negotiating your salary for the 2008 season. You hire a statistician to help you with your negotiations. She specifies the following simple linear regression model where y2008 salary (in millions of dollars) and x = performance during the regular 2007 season Then she selects a random sample of 50 major league starting pitchers with signed salary agreements for the 2008 season. She collects data on their 2007 performance and their 2008 salary and estimates her model several times, each time with a different performance variable. The performance variable that provides the highest r2 is innings pitched (IP). You are not surprised at this result, because in Major League Baseball, the better a starting pitcher performs, the longer he remains in the game. The sample data for 2008 salary and 2007 IP are located in the Pitchers data set. [IP data source: Canadian Business Online. Salary data source: USATODAY.com.] Your statistician obtained the following output from Minitab® Statistical Software: The regression equation is Salary = -5.312 + 0.0606 IP Predictor Coef SE Coet Constant5.312 2.610 -2.04 0.047 IP 0.0606 0.01522 3.98 0.000 S 4.51685 R-Sq 24.9% R-S4 (adj ) 23.3% = = = You pitched 226 innings during the 2007 regular season. Using the regression equation estimated previously, your statistician predicts the salary of a starting pitcher who pitched 226 innings in the 2007 season to be $8.3836 million _ Use the Distributions tool to help you answer some of the questions that follow. Use the Distributions tool to help you answer some of the questions that follow. t Distribution Degrees of Freedom-26 -3 -2 -1 0 2 Your statistician would like to obtain a 95% (predictive) confidence interval for the 2008 salary of a starting pitcher who pitched 226 innings in the 2007 season. The t critical value used in the preceding 95% (predictive) confidence interval is 2.011 Your statistician is given this information: The standard error of the estimate is Se-4.51685, the sum of the x values is Ex = 8,315, and the sum of the squared x values is Xx2- 1,470,874.74 The 95% predictive confidence interval for the 2008 salary of a starting pitcher who pitched 226 innings in the 2007 season is between and -$0.9704 million -$3.0003 million $0.0334 million Minitab-$5.7219 million gos for the company's products and services are the exclusive property of Minitab Inc. All other marks referenced remain the minitab.com for more information propertyo The 95% predictive confidence interval for the 2008 salary of a starting pitcher who pitched 226 innings in the 2007 season is between and $17.7376 milion $15.4043 million and logos%12.6719,m $15.4674 million Minitab and all other tr ademarks and logos f services are the exclusive property of Minitab Inc. All other marks referenced remain the property of their respective owners. See minitab.com ror ore mmormauion.

Answer 1

50 bo- -5.312 b1- 0.0606 MSE 20.402 4.51685 S- 88090.24 166.3 226 predcited value at X-226: 8.38 s*/(1+1/n+(xo-XYSx.) std error prediction interva- 4.65 for 95 % Cl value of t 2.0110 margin of error E-t std error 9.354 lower prediction bound-sample mean-margin of error- -0.9703 Upper prediction bound-sample mean+margin of error- 17.7375

from abvoe 95% (predictive confidence interval = -0.9704 million and 17.7376 million