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We wish to predict the salary for baseball players (yy) using the variables RBI (x1x1) and HR (x2x2), 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) |
---|---|---|---|
Miquel Cabrera | 108 | 38 | 28.050 |
Yoenis Cespedes | 86 | 31 | 27.500 |
Ryan Howard | 59 | 25 | 25.000 |
Albert Pujols | 119 | 31 | 25.000 |
Robinson Cano | 103 | 39 | 24.050 |
Mark Teixeira | 44 | 15 | 23.125 |
Joe Mauer | 49 | 11 | 23.000 |
Hanley Ramirez | 111 | 30 | 22.750 |
Justin Upton | 87 | 31 | 22.125 |
Adrian Gonzalez | 90 | 18 | 21.857 |
Jason Heyward | 49 | 7 | 21.667 |
Jayson Werth | 70 | 21 | 21.571 |
Matt Kemp | 108 | 35 | 21.500 |
Jacoby Ellsbury | 56 | 9 | 21.143 |
Chris Davis | 84 | 38 | 21.119 |
Buster Posey | 80 | 14 | 20.802 |
Shin-Soo Choo | 17 | 7 | 20.000 |
Troy Tulowitzki | 79 | 24 | 20.000 |
Ryan Braun | 91 | 31 | 20.000 |
Joey Votto | 97 | 29 | 20.000 |
Hunter Pence | 57 | 13 | 18.500 |
Prince Fielder | 44 | 8 | 18.000 |
Adrian Beltre | 104 | 32 | 18.000 |
Victor Martinez | 86 | 27 | 18.000 |
Carlos Gonzalez | 100 | 25 | 17.454 |
Matt Holliday | 62 | 20 | 17.000 |
Brian McCann | 58 | 20 | 17.000 |
Mike Trout | 100 | 29 | 16.083 |
David Ortiz | 127 | 38 | 16.000 |
Adam Jones | 83 | 29 | 16.000 |
Curtis Granderson | 59 | 30 | 16.000 |
Colby Rasmus | 54 | 15 | 15.800 |
Matt Wieters | 66 | 17 | 15.800 |
J.D. Martinez | 68 | 22 | 6.750 |
Brandon Crawford | 84 | 12 | 6.000 |
Rajai Davis | 48 | 12 | 5.950 |
Aaron Hill | 38 | 10 | 12.000 |
Coco Crisp | 55 | 13 | 11.000 |
Ben Zobrist | 76 | 18 | 10.500 |
Justin Turner | 90 | 27 | 5.100 |
Denard Span | 53 | 11 | 5.000 |
Chris Iannetta | 24 | 7 | 4.550 |
Leonys Martin | 47 | 15 | 4.150 |
Justin Smoak | 34 | 14 | 3.900 |
Jorge Soler | 31 | 12 | 3.667 |
Evan Gattis | 72 | 32 | 3.300 |
Logan Forsythe | 52 | 20 | 2.750 |
Jean Segura | 64 | 20 | 2.600 |
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.
ˆy=y^= + x1x1 + x2x2
b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 30 and HR of 21. Round your answer to 1 decimal place, do not convert numbers to dollars.
millions of dollars
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