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We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2.  HR – Home runs – hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI – Run batted in – number of runners who scored due to a batters’s action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. The following is a chart of baseball players’ salaries and statistics from 2016. Player Name RBI’s HR’s Salary (in millions) Adrian Beltre 104 32 18.000 Justin Smoak 34 14 3.900 Jean Segura 64 20 2.600 Justin Upton 87 31 22.125 Brandon Crawford 84 12 6.000 Curtis Granderson 59 30 16.000 Aaron Hill 38 10 12.000 Miquel Cabrera 108 38 28.050 Adrian Gonzalez 90 18 21.857 Jacoby Ellsbury 56 9 21.143 Mark Teixeira 44 15 23.125 Albert Pujols 119 31 25.000 Matt Wieters 66 17 15.800 Logan Forsythe 52 20 2.750 Matt Kemp 108 35 21.500 Joey Votto 97 29 20.000 Victor Martinez 86 27 18.000 Prince Fielder 44 8 18.000 Shin-Soo Choo 17 7 20.000 Colby Rasmus 54 15 15.800 Evan Gattis 72 32 3.300 Brian McCann 58 20 17.000 Buster Posey 80 14 20.802 Denard Span 53 11 5.000 Jason Heyward 49 7 21.667   So you don’t have to type all the data into the Reg2 sheet, you can copy the entire table and paste it into the Reg3 sheet or a new sheet. Then copy just the rows you need from the Reg3 sheet or the new sheet and paste them into the Reg2 sheet. a) Find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places.      y^=  +  x1 +  x2  b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 38 and HR of 19. Round your answer to 1 decimal place, do not convert numbers to dollars.  millions of dollars  c) Holding all other variables constant, what is the correct interpretation of the coefficient b1=0.1506 in the multiple linear regression equation? For each million dollars in salary, their RBIs should increase by 0.1506. For each RBI, a baseball player’s predicted sallary increases by 0.1506 million dollars. If the baseball player’s salary increases by 0.1506 million dollars, then the predicted RBI will increase by -0.1407. For each HR, a baseball player’s predicted sallary increases by 0.1506 million dollars.

- August 24, 2022 - Edwin Tunner

We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2. 

  • HR – Home runs – hits on which the batter successfully touched all four bases, without the contribution of a fielding error.
  • RBI – Run batted in – number of runners who scored due to a batters’s action, except when batter grounded into double play or reached on an error
  • Salary is in millions of dollars.

The following is a chart of baseball players’ salaries and statistics from 2016.

Player Name RBI’s HR’s Salary (in millions)
Adrian Beltre 104 32 18.000
Justin Smoak 34 14 3.900
Jean Segura 64 20 2.600
Justin Upton 87 31 22.125
Brandon Crawford 84 12 6.000
Curtis Granderson 59 30 16.000
Aaron Hill 38 10 12.000
Miquel Cabrera 108 38 28.050
Adrian Gonzalez 90 18 21.857
Jacoby Ellsbury 56 9 21.143
Mark Teixeira 44 15 23.125
Albert Pujols 119 31 25.000
Matt Wieters 66 17 15.800
Logan Forsythe 52 20 2.750
Matt Kemp 108 35 21.500
Joey Votto 97 29 20.000
Victor Martinez 86 27 18.000
Prince Fielder 44 8 18.000
Shin-Soo Choo 17 7 20.000
Colby Rasmus 54 15 15.800
Evan Gattis 72 32 3.300
Brian McCann 58 20 17.000
Buster Posey 80 14 20.802
Denard Span 53 11 5.000
Jason Heyward 49 7 21.667

 

So you don’t have to type all the data into the Reg2 sheet, you can copy the entire table and paste it into the Reg3 sheet or a new sheet. Then copy just the rows you need from the Reg3 sheet or the new sheet and paste them into the Reg2 sheet.

a) Find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places.
     y^=  +  x1 +  x2 

b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 38 and HR of 19. Round your answer to 1 decimal place, do not convert numbers to dollars.
 millions of dollars 

c) Holding all other variables constant, what is the correct interpretation of the coefficient b1=0.1506 in the multiple linear regression equation?

  • For each million dollars in salary, their RBIs should increase by 0.1506.
  • For each RBI, a baseball player’s predicted sallary increases by 0.1506 million dollars.
  • If the baseball player’s salary increases by 0.1506 million dollars, then the predicted RBI will increase by -0.1407.
  • For each HR, a baseball player’s predicted sallary increases by 0.1506 million dollars.

 

d) Holding all other variables constant, what is the correct interpretation of the coefficient b2=−0.1407 in the multiple linear regression equation?

  • If the baseball player’s salary increases by -0.1407 million dollars, then the predicted HR will increase by 0.1506.
  • For each HR, a baseball player’s predicted sallary increases by -0.1407 million dollars.
  • For each RBI, a baseball player’s predicted sallary increases by -0.1407 million dollars.
  • For each million dollars in salary, a baseball player’s HR will increase by -0.1407.
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