Question

The following is a chart of 25 baseball players' salaries and statistics from 2016.

Player Name	RBI's	HR's	AVG	Salary (in millions)
Joe Mauer	49	11	0.261	23.000
Robinson Cano	103	39	0.298	24.050
Leonys Martin	47	15	0.245	4.150
Brandon Crawford	84	12	0.275	6.000
Colby Rasmus	54	15	0.206	15.800
Carlos Gonzalez	100	25	0.298	17.454
Matt Kemp	108	35	0.268	21.500
Prince Fielder	44	8	0.212	18.000
Mark Teixeira	44	15	0.204	23.125
Yoenis Cespedes	86	31	0.284	27.500
Chris Iannetta	24	7	0.210	4.550
Ryan Howard	59	25	0.196	25.000
Matt Wieters	66	17	0.243	15.800
Jayson Werth	70	21	0.244	21.571
Justin Smoak	34	14	0.217	3.900
Adrian Gonzalez	90	18	0.285	21.857
Coco Crisp	55	13	0.231	11.000
Ben Zobrist	76	18	0.272	10.500
J.D. Martinez	68	22	0.307	6.750
Aaron Hill	38	10	0.262	12.000
Adrian Beltre	104	32	0.300	18.000
David Ortiz	127	38	0.315	16.000
Chris Davis	84	38	0.221	21.119
Evan Gattis	72	32	0.251	3.300
Curtis Granderson	59	30	0.237	16.000

In order to have correlation with 95% significance, what is the critical r-value that we would like to have?  

(Round to three decimal places for all answers on this assignment.)

RBI vs. Salary

Complete a correlation analysis, using RBI's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=y=    

Do you have significant correlation? Select an answer Yes No

HR vs. Salary

Complete a correlation analysis, using HR's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=y=       

Do you have significant correlation? Select an answer Yes No   

AVG vs. Salary

Complete a correlation analysis, using AVG as the x-value and salary as the y-value.

Correlation coefficient:   

Regression Equation: y=y=       

Do you have significant correlation? Select an answer Yes No

Prediction

Based on your analysis, if you had to predict a player's salary, which method would be the best? Select an answer Regression equation with RBI's Regression equation with HR's Regression equation with AVG The average of the 25 salaries

Using that method, predict the salary for Ryan Braun. His stats were:

RBI: 91

HR: 31

AVG: 0.305

Based on your analysis, his predicted salary would be: $ million  

His actual salary was $20.000 million.

Answer 1

df = n-2 = 25-2 = 23

critical r for 95% confidence level =

0.413

	RBI's	HR's	AVG	Salary (in millions)
RBI's	1
HR's	0.783324	1
AVG	0.745874	0.444824	1
Salary (in millions)	0.369887	0.384432	0.05653	1

RBI vs. Salary

Complete a correlation analysis, using RBI's as the x-value and salary as the y-value.

Correlation coefficient: 0.369887

Regression Equation: y^ = 8.1429 + 0.1056 RBI

Do you have significant correlation? No

as r < critical value (0.413)

HR vs. Salary

Complete a correlation analysis, using HR's as the x-value and salary as the y-value.

Correlation coefficient: 0.783324

Regression Equation: y^ = 9.3843 + 0.2834 HR

Do you have significant correlation? yes

r > critical r

AVG vs. Salary

Complete a correlation analysis, using AVG as the x-value and salary as the y-value.

Correlation coefficient:    0.745874

Regression Equation: y^ = 12.5309 + 11.7711 AVG

Do you have significant correlation? yes

r > critical r

Prediction

Based on your analysis, if you had to predict a player's salary, which method would be the best?   Regression equation with HR's

Using that method, predict the salary for Ryan Braun. His stats were:

RBI: 91

HR: 31

AVG: 0.305

y^ = 9.3843 + 0.2834 *31 = 18.1697

Based on your analysis, his predicted salary would be: $ 18.1697 million  

His actual salary was $20.000 million.