Question

ANSWER ALL PARTS USE A TI84. All other methods give the wrong answer

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

Player Name	RBI's	HR's	AVG	Salary (in millions)
Matt Wieters	66	17	0.243	15.800
Ryan Braun	91	31	0.305	20.000
J.D. Martinez	68	22	0.307	6.750
Ryan Howard	59	25	0.196	25.000
Jayson Werth	70	21	0.244	21.571
Mark Teixeira	44	15	0.204	23.125
Adam Jones	83	29	0.265	16.000
Hanley Ramirez	111	30	0.286	22.750
Miquel Cabrera	108	38	0.316	28.050
Adrian Gonzalez	90	18	0.285	21.857
Victor Martinez	86	27	0.289	18.000
Prince Fielder	44	8	0.212	18.000
Albert Pujols	119	31	0.268	25.000
Justin Turner	90	27	0.277	5.100
Jean Segura	64	20	0.320	2.600
Coco Crisp	55	13	0.231	11.000
Rajai Davis	48	12	0.249	5.950
Chris Davis	84	38	0.221	21.119
Ben Zobrist	76	18	0.272	10.500
Curtis Granderson	59	30	0.237	16.000
Buster Posey	80	14	0.288	20.802
Evan Gattis	72	32	0.251	3.300
Matt Kemp	108	35	0.268	21.500
Colby Rasmus	54	15	0.206	15.800
Troy Tulowitzki	79	24	0.256	20.000

In order to have correlation with 95% confidence (5% 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=

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=

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=

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 Mike Trout. His stats were:

RBI: 100

HR: 29

AVG: 0.315

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

His actual salary was $16.083 million.

Answer 1

For a two tailed hypothesis at 0.05 significance level and 25 sample size, the r critical value is 0.396

RBI vs. Salary -

Correlation coefficient -

0.3954

Since, the correlation coefficient < critical r value, we do not have significant correlation

Regression equation -

y = 6.169 + 0.137 * RBI

HR vs. Salary -

Correlation coefficient -

0.274

Regression equation -

y = 11.036 + 0.237 * HR

Since, the correlation coefficient < critical r value, we do not have significant correlation

AVG vs. Salary -

Correlation coefficient -

-0.1589

Regression equation -

y = 25.068 − 32.5 * AVG

Since, the correlation coefficient < critical r value, we do not have significant correlation

Prediction -

Based on the p values, the closest to significance level is RBI.

So, we choose a model with RBI as an independent variable.

Based on the regression equation for model with RBI as an independent variable -

predicted salary = 6.169 + 0.137 * 100

= $19.869 mn

Actual salary = $16.083 mn

Percentage error = 23.54%