The following table lists Major League Baseball’s (MLB’s) leading pitchers, thei

Question

The following table lists Major League Baseball’s (MLB’s) leading pitchers, their earned run average (ERA), and their salary (in $1,000,000s) for 2008.

  

0.2

Use Excel to estimate the model: Salary = 0 + 1ERA + . (Negative amounts should be indicated by a minus sign. Enter your answers in millions rounded to 2 decimal places.)

Use the estimated model to predict salary for each player, given his ERA. For example, use the sample regression equation to predict the salary for J. Santana with ERA = 2.31. (Round intermediate coefficient values and final answers, in millions, to 2 decimal places.)

Derive the corresponding residuals. (Negative amounts should be indicated by a minus sign. Enter your answers, in millions, rounded to 2 decimal places.)

The following table lists Major League Baseball’s (MLB’s) leading pitchers, their earned run average (ERA), and their salary (in $1,000,000s) for 2008.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Salary
Independent Variable: ERA
Salary = 14.368003 - 2.8876278 ERA
Sample size: 10
R (correlation coefficient) = -0.1680302
R-sq = 0.028234147
Estimate of error standard deviation: 5.5085385

Parameter estimates:

Analysis of variance table for regression model:

Residuals stored in new column: Residuals

Hence,

a -1: Regression equation:

Salary = 14.37 - 2.89 (ERA)

a - 2:Option A

b) For ERA = 2.31,

Salary = 14.37 - 2.89(2.31)

Salary = 7.69 millions

c) Residuals:

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 14.368003 14.866496 0 8 0.96646867 0.3621 Slope -2.8876278 5.9894882 0 8 -0.48211596 0.6426

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