# Correlation Coefficient & Regression Analysis

See attached file for tables.

Problem Set 1: Chapter 16, problems 2, 6c, 14; Chapter 17, problem 14

2. What information is provided by the numerical value of the Pearson correlation?

6. For the following scores,

X Y

1 5

2 9

4 3

5 1

3 2

c. Compute a Pearson Correlation

14. It is well known that similarity. Compute a Pearson correlation for these data and determine whether there is a significant correlation between attitudes for husbands and wives. Set alpha at .05, two-tailed.

Couple Wife (X) Husband (Y)

A 11 14

B 6 7

C 16 15

D 4 7

E 1 3

F 10 9

G 5 9

H 3 8

Chapter 17

14. Problem 15 in Chapter 16 described a study examining the effectiveness of a 7-minute Screen test for Alzheimer's disease: A sample of n = 9, mean scores on the 7-minute test = M = 7, SS = 92. The cognitive test scores averaged M = 17 with SS = 236. For these data, SP = 127.

a. Find the regression equation for predicting the cognitive scores from the 7-Minute Screen score.

b. What percentage of variance in the cognitive scores is accounted for by the regression equation?

c. Does the regression equation account for a significant portion of the variance in the cognitive scores? Use Ã?¯Ã??Ã?¡ = .05 to evaluate the F-ratio.

#### Solution Preview

Please see the attachments for proper format and tables.

Problem Set 1: Chapter 16, problems 2, 6c, 14; Chapter 17, problem 14

2. What information is provided by the numerical value of the Pearson correlation?

Answer

The numerical value of the Pearson correlation indicates the strength of the linear relationship between two variables.

6. For the following scores,

X Y

1 5

2 9

4 3

5 1

3 2

c. Compute a Pearson Correlation

The correlation between X, Y is given by the formula

The details are given below.

X Y X^2 Y^2 XY

1 5 1 25 5

2 9 4 81 18

4 3 16 9 12

5 1 25 1 5

3 2 9 4 6

15 20 55 120 46

Therefore, = -0.70

14. It is well known that similarity...Compute a Pearson correlation for these data and determine whether there is a significant correlation between attitudes for husbands and wives. Set alpha at .05, two-tailed.

Couple Wife (X) Husband (Y)

A 11 14

B 6 7

C 16 15

D 4 7

E 1 3

F 10 9

G 5 9

H 3 8

Answer

The correlation between X, Y is given by the formula

The details are given below.

Couple Wife, X Husband, Y X^2 Y^2 XY

A 11 14 121 196 154

B 6 7 36 49 42

C 16 15 256 225 240

D 4 7 16 49 28

E 1 3 1 9 3

F 10 9 100 81 90

G 5 9 25 81 45

H 3 8 9 64 24

Total 56 72 564 754 626

Therefore, = 0.903530203

The ...

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for significance of correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.