Question

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	17.0	2.25
C. Lee	2.0	2.37
T. Lincecum	0.1	2.57
C. Sabathia	10.0	2.11
R. Halladay	7.0	2.52
J. Peavy	5.7	2.77
D. Matsuzaka	6.7	2.44
R. Dempster	6.6	2.89
B. Sheets	11.5	2.90
C. Hamels	0.3	2.91

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.)

Salary= _______+________ERA

a-2. Interpret the coefficient of ERA.

• A one-unit increase in ERA, predicted salary decreases by $6.37 million.

• A one-unit increase in ERA, predicted salary increases by $6.37 million.

• A one-unit increase in ERA, predicted salary decreases by $16.70 million.

• A one-unit increase in ERA, predicted salary increases by $16.70 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 = 2.25. (Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)

	predicted salary (in $ Money)
j. santana
c. lee
t. linecum
c. Sabathia
r. Halladay
j. peavy
d. Matsuzaka
r. Dempster
b. sheets
c. hamels

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.)

	predicted salary (in $ Money)
j. santana
c. lee
t. linecum
c. Sabathia
r. Halladay
j. peavy
d. Matsuzaka
r. Dempster
b. sheets
c. hamels

Answer 1

Appplying regression on above data"

a-1) Salary= 23.0715+(-6.3667)*x

a-2) A one-unit increase in ERA, predicted salary decreases by $6.37 million.

b)

		predicted salary
J. Santana		8.75
C. Lee		7.98
T. Lincecum		6.71
C. Sabathia		9.64
R. Halladay		7.03
J. Peavy		5.44
D. Matsuzaka		7.54
R. Dempster		4.67
B. Sheets		4.61
C. Hamels		4.54

c)

		residuals
J. Santana		8.25
C. Lee		-5.98
T. Lincecum		-6.61
C. Sabathia		0.36
R. Halladay		-0.03
J. Peavy		0.26
D. Matsuzaka		-0.84
R. Dempster		1.93
B. Sheets		6.89
C. Hamels		-4.24