10-Based on the data shown below, calculate the regression line.

Regression Equation:

Enter the equation in slope-intercept form(y=mx+b) with parameters accurate to three decimal places.

x	y
-4	-14
-2	-2
0	10
2	22
4	34
6	46
8	58
10	70

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11-You wish to determine if there is a linear correlation between the two variables at a significance level of=0.01. You have the following bivariate data set.

x	y
89.8	-3.7
65.4	42
95.5	-14.1
91.8	-20.5
66.6	50.8
88.8	-0.1
67.9	47.1
108	-55.8
50.2	94.4
53.4	61.4
49.7	73.9
53.6	31.9
83.5	-12.5
77.5	20.9
80.1	6.4
92.4	-18.8
76.3	42.8
92.5	-44
68.8	56.4

What is the correlation coefficient for this data set?

r =

What is the p-value for this correlation coefficient?

p-value =

Your final conclusion is that...

• There is insufficient sample evidence to support the claim the there is a correlation between the two variables.
• There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.

Note: Round answers to three decimal places.

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12-You run a regression analysis on a bivariate set of data (n=29). You obtain the regression equationy=3.737x+9.729with a correlation coefficient ofr=0.775 (which is significant at=0.01). You want to predict what value (on average) for the explanatory variable will give you a value of 130 on the response variable.

What is the predicted explanatory value?

x =

(Report answer accurate to one decimal place.)

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13-Run a regression analysis on the following bivariate set of data withy as the response variable.

x	y
65.5	48
76.6	37.3
57	-25.1
80.9	39.3
69.8	18.8
62.6	32.4
72.2	25.1
71	53.7
65.4	22
74.7	44.7
80.2	24.6

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 -22.1 on the response variable.

What is the predicted explanatory value?

x =

(Report answer accurate to one decimal place.)

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14- Suppose that you run a correlation and find the correlation coefficient is -0.4 and the regression equation isy=6.6x+54.82. The mean of your x-values was 4.7. The mean of your y-values was 23.7.

If the critical value is .505, use the appropriate method to predict they value whenxis 5.9.

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

Player Name	RBI's	HR's	AVG	Salary (in millions)
Gerardo Parra	48	9	0.234	0.555
Elvis Andrus	72	12	0.275	15.250
Christian Vazquez	72	23	0.276	2.850
Kevin Kiermaier	55	14	0.228	8.167
Wilson Ramos	72	14	0.288	7.250
Dee Gordon	34	3	0.275	13.300
Josh Reddick	56	14	0.275	13.000
Brandon Lowe	51	17	0.270	1.000
Brian Dozier	50	20	0.238	9.000
Kolten Wong	59	11	0.285	6.500
AJ Pollock	47	15	0.266	4.000
Eloy Jimenez	79	31	0.267	1.833
Daniel Descalso	15	2	0.173	1.500
Miguel Cabrera	59	12	0.283	30.000
Nelson Cruz	108	41	0.311	14.000
Jarrod Dyson	27	7	0.230	4.000
Brian McCann	45	12	0.249	2.000
Jason Heyward	62	21	0.252	22.500
Jean Segura	60	12	0.280	14.950
Cameron Maybin	32	11	0.285	0.555
Justin Turner	67	27	0.290	19.000
Ronald Acuna	101	41	0.280	1.000
Curtis Granderson	34	12	0.183	1.750
Martin Prado	15	2	0.233	15.000
Daniel Murphy	78	13	0.279	10.000

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? ? 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? ? 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? ? 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.

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16-The following bivariate data set contains an outlier.

x	y
19.2	33.8
24.8	-71.1
57	102.5
45.2	-4.9
62.2	241.9
33.3	17.9
43.9	90.4
52.1	140.8
51.4	115.9
53.6	214.9
42.7	173.9
57.9	83.6
48.2	90.3
21.7	98.6
191.2	-1010.1

What is the correlation coefficientwith the outlier?

r_w =

What is the correlation coefficientwithout the outlier?

r_wo =

For the next questions, I want you to consider that there is more than the existence or non-existence of correlation. You can have:

• Strong positive correlation
• Moderate positive correlation
• No correlation
• Moderate negative correlation
• Strong negative correlation

Would inclusion of the outlier change the evidence for or against a significant linear correlation at 5% significance?

• No. Including the outlier does not change the evidence regarding a linear correlation.
• Yes. Including the outlier changes the evidence regarding a linear correlation.

Would you always draw the same conclusion to the above question with the addition of any outlier?

• Yes, any outlier would result in the same conclusion.
• No, a different outlier in a different problem could lead to a different conclusion.
• Explain your answer to the second multiple-choice question.

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16-A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 83 individual that have been using their program for 9 months. For each individual person, the company records the individual's weight when they started the program 9 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (188, 162) would be for a specific person and it would indicate that the individual started the program weighing 188 pounds and currently weighs 162 pounds. In other words, they lost 26 pounds.

When the company performed a regression analysis, they found a correlation coefficient of r = 0.82. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is weight loss. Which tool would be more appropriate?

• 1-Sample Mean
• 2-Sample Mean (Independent Samples)
• 2-Sample Mean (Matched Pairs)
• 1-Sample Proportion
• 2-Sample Proportion

Explain what the correlation DOES show in this example, in terms of weights of individuals.