# Correlation Coefficient, Coefficient of Determination and ANOVA

See attached file.

There a 3 problems. Please follow instructions on document which includes showing all work.

Do not include attachments. Note below the point value of each exercise. Show all calculations for credit.

A. Use Excel or Megastat to determine the following correlations of analysis:

X 2 3 5 5 10

y 6 9 14 16 30

a. Place the Excel or Megastat results here:

b. What is the coefficient of correlation? (place in box)

c. What is the coefficient of determination? (place in box)

B. What is the relationship between the amount spent per week on food and the

size of family? Do larger families spend on more food? The following data is the amount of family size and amount spent for food.

Family Size Amount of Food Spent

3 91

5 151

4 74

4 91

3 111

3 99

6 142

6 129

6 104

5 119

c. Place the Excel or Megastat results here:

d. What is the coefficient of correlation? (place in box)

c. What is the coefficient of determination? (place in box)

C. Using the coefficient of correlation and coefficient of determination in Part B, calculate the t test for the coefficient of correlation.

Ho: p = 0

H1: p ≠ 0

a.

b.

t =

c. Considering this is a two tail test and level of significance of 0.05, what is the critical value?

Reject Ho if t is:

C. Given the following sample information, test the hypothesis that the treatment means are equal at the 0.05 significance level.

Treatment 1 Treatment 2 Treatment 3

8 3 11

11 12 20

10 11 18

8 12

4

a. Set up the null hypothesis and alternative hypothesis.

b. State the decision rule.

c. Use Excel or Megastat to complete an ANOVA table. Copy the table and paste it here, not as a separate attachment.

d. Accept or reject the null?

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#### Solution Summary

The solution provides step by step method for the calculation of correlation coefficient and coefficient of determination. This solution also gives the step by step method for ANOVA. Formula for the calculation and Interpretations of the results are also included.