1. The following is a chart of 25 baseball players' salaries and statistics from 2019

Player Name	RBI's	HR's	AVG	Salary (in millions)
Freddie Freeman	121	38	0.295	21.409
Kevin Kiermaier	55	14	0.228	8.167
Bryce Harper	114	35	0.260	11.538
AJ Pollock	47	15	0.266	4.000
Brandon Crawford	59	11	0.228	15.200
Brock Holt	31	3	0.297	3.575
Lourdes Gurriel Jr	50	20	0.277	1.929
Christian Yelich	97	44	0.329	9.750
Jason Heyward	62	21	0.252	22.500
Ketel Marte	92	32	0.329	2.000
Carlos Santana	93	34	0.281	20.333
Jorge Polanco	79	22	0.295	3.583
Buster Posey	38	7	0.257	22.178
Charlie Blackmon	86	32	0.314	21.333
Chris Davis	36	12	0.179	21.119
Miguel Cabrera	59	12	0.283	30.000
Anthony Rizzo	94	27	0.293	11.286
Jose Martinez	42	10	0.270	1.125
Rougned Odor	93	30	0.205	7.833
Paul Goldschmidt	97	34	0.260	15.500
Brandon Lowe	51	17	0.270	1.000
Manny Machado	85	32	0.256	12.000
Cameron Maybin	32	11	0.285	0.555
Brian McCann	45	12	0.249	2.000
Brandon Belt	57	17	0.234	17.200

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:=

Do you have significant correlation? ? Yes No

HRvs. Salary

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

Correlation coefficient:

Regression Equation:=

Do you have significant correlation? ? Yes No

AVGvs. Salary

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

Correlation coefficient:

Regression Equation:=

Do you have significant correlation? ? 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 JD Martinez. His stats were:

RBI: 105

HR: 36

AVG: 0.304

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

His actual salary was $23.750 million.

2. Based on the data shown below, a statistician calculates a linear model =-0.94+17.70.

x	y
3	15.95
4	12.6
5	13.15
6	12.2
7	10.35
8	10.9

Use the model to estimate the -value when =7 = Round your answer to two decimal places.

3. A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were:y=ax+b a=-1.046 b=36.204 r²=0.966289 r=-0.983 n=27 Use this to predict the number of situps a person who watches 2 hours of TV can do (to one decimal place)

4. Suppose that you run a correlation and find the correlation coefficient is -0.787 and the regression equation is ^=-2.5+36.4. The mean of your x-values was 5.2. The mean of your y-values was 23.7. If the critical value is .606, use the appropriate method to predict the value when is 3.2.

5. Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
19.2	42.6
26.4	31.4
13.9	41.9
37.3	19.2
31.5	39
29.9	40.5
36.3	37.2
19.4	38.5
37	41.4
29.6	31.8
24	36.3
17.9	36

Verify that the correlation is significant at an =0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 28.8 on the response variable. What is the predicted explanatory value? x = (Report answer accurate to one decimal place.)

6. A random sample of 22 pre-school children was taken. The child was asked to draw a nickel. The diameter of that nickel was recorded. Their parent's incomes (in thousands of $) and the diameter of the nickel they drew are given below.

Income (thousands of $)	Coin size (mm)
8	21
28	21
27	31
31	20
24	25
33	19
12	25
15	21
17	21
18	29
25	19
33	22
17	28
20	19
36	19
65	23
42	17
47	23
92	26
45	17
75	22
65	19

Test the claim that there is significant correlation at the 0.01 significance level. Retain at least 3 decimals on all values. a) Identify the correct alternative hypothesis.

• 1:
• 1:=0
• 1:0
• 1:0
• 1:0

b) The test statistic value is: c) The critical value is: d) Based on this, we

• Reject 0
• Fail to reject 0

e) Which means

• There is sufficient evidence to warrant rejection of the claim
• There is not sufficient evidence to support the claim
• There is not sufficient evidence to warrant rejection of the claim
• The sample data supports the claim

f) The regression equation (in terms of income ) is: ^= g) To predict what diameter a child would draw a nickel given family income, it would be most appropriate to:

• Use the regression equation
• Use the mean coin size
• Use the P-Value
• Use the residual