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 = 2.30. (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

Sol:

data--->data analysis--->Regression

regression eq is

salary=21.25-6.32(ERA)

Y INTERCEPT=21.25

SLOPE=-6.32

solutiona2:

ccoefficient of ERA=slope=-6.32

slope=change in sal/change in era

for unit increase in ERA sal decreases by 6.32

A one-unit increase in ERA, predicted salary decreases by $6.32 million

Solutionb:

Solutionc:

SUMMARY OUTPUT Regression Statistics Multiple R 0.289008 R Square 0.083526 Adjusted R Square -0.03103 Standard Error 5.091142 Observations 10 ANOVA df SS MS F Significance F Regression 1 18.8982 18.8982 0.729105 0.418006 Residual 8 207.3578 25.91972 Total 9 226.256 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 21.25488 17.61127 1.206891 0.261947 -19.3568 61.86655 ERA -6.32385 7.406051 -0.85388 0.418006 -23.4022 10.75453

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