Question

We wish to predict the salary for baseball players (y) using the variables RBI (3) and HR (22), then we use a regression equation of the form y = b + b + b 22. • 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) Victor Martinez 86 27 . 18.000 Justin Turner 90 27 5.100 Brandon Crawford 84 12 6.000 Robinson Cano 103 39 24.050 Adrian Beltre 104 32 18.000 Ben Zobrist 76 18 10.500 Logan Forsythe 52 20 2.750 Troy Tulowitzki 79 24 20.000 Leonys Martin 47 4.150 Joey Votto 97 29 20.000 Jorge Soler 31 12 3.667 Shin-Soo Choo 17 7 20.000 Brian McCann 58 20 17.000 Coco Crisp 11.000 Miquel Cabrera 108 38 28.050 Ryan Howard 59 25 25.000 Matt Wieters 15.800 Chris Davis 21.119 Justin Smoak 3.900 Denard Span 5.000 Hanley Ramirez 111 30 22.750 Raja Davis 12 5.950 Joe Mauer 4911 23.000 Jason Heyward 49 7 2 1.667 Matt Kemp 10B 35 21.500 Deals 330 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 b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 66 and HR of 27. Round your answer to 1 decimal place, do not convert numbers to dollars. millions of dollars

Answer 1

(a) y = 5462.9704 + 18.3632*x1 + 385.1406*x2

(b) 17073.7

(c) Option A

(d) Option C

RBI	HR	Salary
86	27	18000
90	27	5100
84	12	6000
103	39	24050
104	32	18000
76	18	10500
52	20	2750
79	24	20000
47	15	4150
97	29	20000
31	12	3667
17	7	20000
58	20	17000
55	13	11000
108	38	28050
59	25	25000
66	17	15800
84	38	21119
34	14	3900
53	11	5000
111	30	22750
48	12	5950
49	11	23000
49	7	21667
108	35	21500

	R²	0.279
	Adjusted R²	0.214
	R	0.528
	Std. Error	7273.886
	n	25
	k	2
	Dep. Var.	Salary
ANOVA table
Source	SS	df	MS	F	p-value
Regression	45,05,91,849.9053	2	22,52,95,924.9526	4.26	.0273
Residual	1,16,40,07,240.7347	22	5,29,09,420.0334
Total	1,61,45,99,090.6400	24
Regression output				confidence interval
variables	coefficients	std. error	t (df=22)	p-value	95% lower	95% upper
Intercept	5,462.9704
RBI	18.3632	103.9768	0.177	.8614	-197.2716	233.9979
HR	385.1406	275.5878	1.398	.1762	-186.3936	956.6747
Predicted values for: Salary
			95% Confidence Interval	95% Prediction Interval
RBI	HR	Predicted	lower	upper	lower	upper
66	27	17,073.7	12,073.183	22,074.287	1,181.401	32,966.068