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# Correlation Coefficient

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X Y

90 10

86 9

94 7

70 6

86 7

90 15

94 10

66 5

98 11

86 9

1. Calculate and interpret the mean and standard deviation for variables X and Y. (5 points)

2. Calculate and interpret the Pearson's correlation coefficient between test scores (X) and
number of hours a person studied for the test (Y). (10 points)

3. Determine if the coefficient is statistically significant and tell me how you reach that
conclusion. (10 points)

4. Based on your prior answer, reject/accept null hypothesis (2-tailed) and tell me what that
means. (5 points)

https://brainmass.com/statistics/pearson-product-moment-correlation/correlation-coefficient-240891

#### Solution Preview

1. Calculate and interpret the mean and standard deviation for variables X and Y. (5 points)

I did this in Excel (see the attached file). Here are the means and standard deviations for X and Y:

mean of X: 86
std. dev. of X: 10.328

mean of Y: 8.9
std. dev. of Y: 2.885

2. Calculate and interpret the Pearson's correlation coefficient between test scores (X) and
number of hours a person studied for the test (Y). (10 points)

I also did this in Excel, by using the Excel function =PEARSON(y-values, x-values). The correlation coefficient is:

r = ...

\$2.19

## Statistics: least squares, sample correlation coefficient, coefficient of determination

Exhibit 12-1

You are given the following information about y and x.

y x
Dependent Variable Independent Variable
5 15
7 12
9 10
11 7

16. Refer to Exhibit 12-1. The least squares estimate of b1 equals

a. -0.7647

b. -0.13

c. 21.4

d. 16.412

17. Refer to Exhibit 12-1. The least squares estimate of b0
equals

a. -7.647

b. -1.3

c. 21.4

d. 16.41176

18. Refer to Exhibit 12-1. The sample correlation coefficient equals

a. -86.667

b. -0.99705

c. 0.9941

d. 0.99705

19. Refer to Exhibit 12-1. The coefficient of determination equals

a. -0.99705

b. -0.9941

c. 0.9941

d. 0.99705

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