Question

13. The following table lists a portion of Major League Baseball’s (MLB’s) leading pitchers, each pitcher’s salary (In $ millions), and earned run average (ERA) for 2008.

	Salary			ERA
J. Santana		15.0			2.26
C. Lee		1.0			2.36
⋮		⋮			⋮
C. Hamels		0.4			2.70

a-1. Estimate the model: Salary = β₀ + β₁ERA + ε. (Negative values should be indicated by a minus sign. Enter your answers, in millions, rounded to 2 decimal places.)

Salaryˆ=Salary^=    +  ERA

a-2. Interpret the coefficient of ERA.

• A one-unit increase in ERA, predicted salary decreases by $2.02 million.

• A one-unit increase in ERA, predicted salary increases by $2.02 million.

• A one-unit increase in ERA, predicted salary decreases by $9.13 million.

• A one-unit increase in ERA, predicted salary increases by $9.13 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 = 2.26. (Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)

c. Derive the corresponding residuals. (Negative values should be indicated by a minus sign. Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)

	Salary	ERA
J. Santana	15.0	2.26
C. Lee	1.0	2.36
T. Lincecum	0.3	2.17
C. Sabathia	8.0	2.15
R. Halladay	8.0	2.20
J. Peavy	6.1	2.21
D. Matsuzaka	7.8	2.26
R. Dempster	7.2	2.29
B. Sheets	10.6	2.75
C. Hamels	0.4	2.70

Answer 1

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