The following table lists Major League Baseball\'s (MLB\'s) leading pitchers, th

Question

The following table lists Major League Baseball's (MLB's) leading pitchers, their earned run average (ERA), and their salary (given in millions of dollars) for 2008. The data are also available on the text website, labeled MLB Pitchers. a-1. Use Excel to estimate the model: Salary = beta_0 + beta_1ERA + epsilon. a-2. Interpret the coefficient of ERA. A one-unit increase in ERA, predicted salary decreases by $1.871352 million. A one-unit increase in ERA, predicted salary increases by $2.861352 million. A one-unit increase in ERA, predicted salary decreases by $2.861352 million. A one-unit increase in ERA, predicted salary increases by $1.871352 million. b. 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 = 2.44. c. Derive the corresponding residuals.

Explanation / Answer

Here we are given the data of ERA and salary.

In the first part we have to find regression equation.

We can find regression equation by using EXCEL.

steps :

Enter data into EXCEL sheet --> Data --> Data Analysis --> Regression --> ok --> Input Y Range : select range of salary --> Input X Range : select range of ERA --> Output Range : select one empty cell --> ok

We get the regression equation is,

Salary = 13.88 - 2.86*ERA

Interpret the coefficient of ERA.

A one unit increase in ERA predicted salary decreases by 2.861352 million.

Now we have to find predicted salary for all the player.

This we can find by using regression equation.

In the regression equation we put ERA values of corresponding player and find predicted value.

And in the same table we find residuals as,

Residual = y - y^ (where y^ is predicted value)

ERA salary predicted salary Residual (y-y^) 2.44 17 6.9016 10.0984 2.35 4 7.159 -3.159 2.31 0.1 7.2734 -7.1734 2.57 9 6.5298 2.4702 2.36 7 7.1304 -0.1304 2.61 6 6.4154 -0.4154 2.09 7.5 7.9026 -0.4026 2.54 5.6 6.6156 -1.0156 2.72 10.8 6.1008 4.6992 3.01 0.3 5.2714 -4.9714

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