# Correlation and regression analysis

1. DEFINE: Correlation

2. Students were asked the following: Imagine that you lost (X dollars) amount of money. How much (Y dollars) would you pay to get it back? Imagine that these are the answers.

Calculate the correlation coefficient for the following X - Y pairs.

X___ __Y _

10.00 4.55

6.00 7.11

14.50 7.01

9.00 5.05

11.00 4.26

16.05 8.10

4.11 9.10

21.00 11.14

3.00 10.14

14.00 6.30

4.00 9.75

12.00 5.13

7.00 6.05

5.00 8.00

16.00 8.20

16.00 9.11

17.00 9.55

19.00 10.32

a) Which type of correlation do you use? Why?

b) What do you conclude about these data? What do you conclude about correlational analysis, per se?

3. Here are some scores on two different tests taken by 11 students.

Student X Y

1 8 6.58

2 8 5.76

3 8 7.71

4 8 8.84

5 8 8.47

6 8 7.04

7 8 5.25

8 19 12.5

9 8 5.56

10 8 7.91

11 8 6.89

a.Which type of correlation do you use? Why?

b. What do you conclude about these data? What do you conclude about correlational analysis, per se?

c) Would you Prep here? Why or why not?

4. 15 students receive both their class ranks and their ranks on the ACT. A higher score indicates higher rank. Perform the appropriate analysis on the following:

Student Class Rank ACT Rank

1 13 14

2 6 6

3 1 3

4 8 11

5 4 5

6 12 15

7 11 12

8 1 4

9 9 9

10 2 2

11 3 7

12 10 13

13 2 1

14 5 8

15 7 10

a) What analysis did you perform and why?

b) What conclusions can you make concerning class rank and ACT score?

c) What is PRep for this analysis?

5. What is a good effect size statistic for r (the correlation coefficient)? Show that the effect size statistic you choose works for BOTH positive and negative correlations.

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