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.

  

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 = 2.49. (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

Excel steps to find regression equation is

This will give you regression analysis. Regression equation to predict salary from ERA is

a-2 Interpretation of coefficient of ERA

For one unit increase in ERA predicted salary decreases by @0.99

SUMMARY OUTPUT Regression Statistics Multiple R 0.063988 R Square 0.004094 Adjusted R Square -0.12039 Standard Error 3.754288 Observations 10 ANOVA df SS MS F Significance F Regression 1 0.463583 0.463583 0.032891 0.860597 Residual 8 112.7574 14.09468 Total 9 113.221 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 8.424263 13.58469 0.620129 0.552423 -22.9021 39.75062 -22.9021 39.75062 X Variable 1 -0.99162 5.467764 -0.18136 0.860597 -13.6003 11.61706 -13.6003 11.61706

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