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 2.28 C. Lee 3.0 2.39 ⋮ ⋮ ⋮ C. Hamels 0.2 3.00 Click here for the Excel Data File 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= + ERA a-2. Interpret the coefficient of ERA. A one-unit increase in ERA, predicted salary decreases by $3.20 million. A one-unit increase in ERA, predicted salary increases by $3.20 million. A one-unit increase in ERA, predicted salary decreases by $11.92 million. A one-unit increase in ERA, predicted salary increases by $11.92 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 = 2.28. (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.)

Answer 1

Given that

we have to Use Excel to estimate the model: Salary = β₀ + β₁ERA + ε. (Negative amounts should be indicated by a minus sign. Enter your answers in millions rounded to 2 decimal places.)

From the given inform ati on, Descriptive Statistics for ERA (X) and Salary (Y) are n = 10, ΣΧ, = 24.62;ΣΧ2 = 61.4704ΣΊτ 72.5ΣΥ2-775.43, and ΣΧΊτ|75.76 (a-1)The regression line of Y on X is YAX, 10 10 i-1 i-1 i-1 -1 . i 10(175.76)-(24.62x72. 5) where (źr)-(,x). 10(61 4704)-(24 62) IỆT)-AEX). 725-(-3.1952)(2462.15 1166-151 72.5-(-3.1952)(24.62) 15.1166 15.12 2 The regression equati on for predicting Salary (Y) corresponding to ERA (X) is 15.12-3.20x (a-2)A one-unit increase in ERA, predicted salary decreases by $3.20 million Predicted Salary ERA (in S millions) -15.12-3.20X 7.82 7.47 7.38 8.08 7.47 8.24 7.34 7.70 5.39 5.52 J. Santana2.28 2.39 Lincecum 2.42 C Sabathia 2.20 R.Halladay 2.39 J.Peavy2.15 D.Matsuzaka2.43 R Dempster 2.32 B.Sheets 3.04 CHamels 3.00 C.Lee

Resi dual J. Santana 7.82 17.0-7.82 - 9.18 CLee |7.47 | 3.0-7.47 =-4.47 TLincecum7.38 0.3-7.38-7.08 C Sabathia 8.08 10.0-8.08 -1.92 R.Halladay7.4710.0-7.47 2.53 J Peavy8.24 5.4-8.24--2.84 D.Matsuzaka | 7.34 | 7.8-7.34=0.46 R Dempster7.70 7.1-7.70 -0.6 B.Sheets 5.39 11.7-5.39 6.31 C. Hamels 5.52 0.2-5.52-5.32