Question

5. Confidence intervals for prediction 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 Sala ry = -5.312 + 0.0606 1P Predictor Coef SE Coef T P Constant 5.312 2.610 -2.04 0.047 IP 0.0606 0.01522 3.98 0.000 S= 4.51685 R-Sq 24.9% R-Sq(adj ) 23.34 = = 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 Use the Distributions tool to help you answer some of the questions that follow. t Distribution Degrees of Freedom-26 -2 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 Your statistician is given this information: The standard error ofthe estimate is Se-4.51685, the sum of the x values is Σχ and the sum of the squared x values is ΣΧ2 = 1,470,874.74. 8,315 The 95% (predictive) confidence interval for the 2008 salary of a starting pitcher who pitched 226 innings in the 2007 season is between and

Answer 1

2002 seago to be &3836 2 \,2335. tawe liit Yo=8.38 36 冫8-38 36 + 2.01063x.[4-233r a to.616