We wish to predict the salary for baseball players (y) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=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 a) Use software to find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places. ˆy= ? + ? x1 + ? x2 b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 88 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=0.111 in the multiple linear regression equation? For each HR, a baseball player's predicted sallary increases by 0.111 million dollars. For each RBI, a baseball player's predicted sallary increases by 0.111 million dollars. If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by one. If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by 0.0371. d) Holding all other variables constant, what is the correct interpretation of the coefficient b2=0.0371 in the multiple linear regression equation? For each RBI, a baseball player's predicted sallary increases by 0.0371 million dollars. If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by one. For each HR, a baseball player's predicted sallary increases by 0.0371 million dollars. If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by 0.111.

We wish to predict the salary for baseball players (y) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=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 a) Use software to find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places. ˆy= ? + ? x1 + ? x2 b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 88 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=0.111 in the multiple linear regression equation? For each HR, a baseball player's predicted sallary increases by 0.111 million dollars. For each RBI, a baseball player's predicted sallary increases by 0.111 million dollars. If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by one. If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by 0.0371. d) Holding all other variables constant, what is the correct interpretation of the coefficient b2=0.0371 in the multiple linear regression equation? For each RBI, a baseball player's predicted sallary increases by 0.0371 million dollars. If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by one. For each HR, a baseball player's predicted sallary increases by 0.0371 million dollars. If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by 0.111.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 5PPS

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We wish to predict the salary for baseball players (y) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=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

a) Use software to find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places.
ˆy= ? + ? x1 + ? x2

b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 88 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=0.111 in the multiple linear regression equation?

For each HR, a baseball player's predicted sallary increases by 0.111 million dollars.
For each RBI, a baseball player's predicted sallary increases by 0.111 million dollars.
If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by one.
If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by 0.0371.

d) Holding all other variables constant, what is the correct interpretation of the coefficient b2=0.0371 in the multiple linear regression equation?

For each RBI, a baseball player's predicted sallary increases by 0.0371 million dollars.
If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by one.
For each HR, a baseball player's predicted sallary increases by 0.0371 million dollars.
If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by 0.111.

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