# Correlation, Regression & Chi-square Test

See attached file for clarity.

Study Discussion Questions for final

Problem Set 2: Chapter 16 and 17

Chapter 16

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

The numerical value of the Pearson correlation indicates how well the data points fit a straight line. And the value of 1.00 indicates a perfect linear fit and a value of zero indicates no linear trend (Gravetter, & Wallnau, 2010).

8c. For the following scores,

_____________

_X______Y___

3 12

6 7

3 9

5 7

3 10

c. Compute the Pearson correlation.

14. It is well known that similarity in attitudes, belief, and interest plays an important role interpersonal attraction (see Byrne, 1971, for example). Thus, correlations for attitudes between married couples should be strong. Suppose a researcher developed a questionnaire that measures how liberal or conservative oneâ??s attitudes are. Low scores indicate that the person has liberal attitudes, whereas high scores indicate conservatism. The following hypothetical data are scores for married couples.

_______________________________________

Couple__________Wife____________Husband___

A 11 14

B 6 7

C 16 15

D 4 7

E 1 3

F 10 9

G 5 9

H 3 8

Compute the Pearson correlation for these data, and determine whether there is a significant correlation between attitude for husband and wives. Set alpha at .05. Two tails.

Chapter 17

10. For the following scores

_______________

_X__________Y__

3 0

8 10

7 8

5 3

7 7

6 8

a. Find the regression equation for predicting Y from X.

b. Calculate the predicted Y value for each X.

Problem Set 2: Chapter 18, problems

2 .The student populations at the state college consist of 55% females and 45% males.

a. The college theater department recently staged a production of modern musical. A researcher recorded the gender of each student entering the theater and found a total of 385 females and 215 males. Is the gender distribution for theater goers significantly different from the distribution for the general college? Test at the .05 level of significance.

b. The same researcher also recorded the gender of each student watching a menâ??s basketball game in the college gym and found a total of 83 females and 97 males. Is the gender distribution for basketball fans significantly different from the distribution for the general college? Test at .05 level of significance.

12. A communication company has developed three new designs for a cell phone. To evaluate consumer response, a sample of 120 college student is selected and each student is given all three phones to use for 1 week. At the end of the week, the student must identify which of the designs they prefer. The distribution of preference is as follows:

Design 1 Design 2 Design 3

54 38 28

Do the results indicate any significant preferences among the three designs?

20. Gender difference in dream content are well documented (see Winget & Kramer, 1979). Suppose a researcher studies aggression content in the dreams of men and women. Each participant reports his or her most recent dream then each dream is judged by a panel of experts to have low, medium, or high aggression content. The observed frequencies are shown in the matrix:

Aggression Content

Low Medium High

18 4 2

4 17 15

Gender: Female Male

Is there a relationship between gender and the aggression content off dreams? Test with ? = .01.

References

Gravetter, F. J., & Wallnau, L. B. (2010). Statistics for the Behavioral Sciences (8th Ed.).

Belmont, CA: Thomson/Wadsworth.

#### Solution Summary

The solution provides step by step method for the calculation of Pearson correlation coefficient, regression analysis, test statistic for significance of correlation coefficient, chi square test for association and goodness of fit. Formula for the calculation and Interpretations of the results are also included.