Correlation and Regression
Use the following hypothetical correlation matrix to answer the first two problems:
Variable A Variable B Variable C Dep. Variable
Variable A 1.00 .62 .86 .54
Variable B 1.00 .68 .36
Variable C 1.00 .48
Dep. Variable 1.00
1. If a regression analysis is performed using Variable A, Variable B and Variable C as independent variables to predict Dep. Variable, what is the lowest possible value of R2?
2. Considering the correlations among the variables, what problem is likely to develop when a regression analysis is done using Variable A, Variable B, and Variable C to predict Dep. Variable?
3. Using Polit dataset C, analyze the correlations among the variables for depression (CESD, #35), age, physical health (sf12phys, #44), and mental health (sf12ment, #45) in this sample of low-income women. To do this, select Analyze →Correlate →Bivariate, and then find the four variables and move them into the variable list. Click "OK".
a. Summarize your findings in a table similar to the one above.
b. What variables show a significant association with depression (CEDS)?
c. How did you determine "significance"? What does this mean?
d. Which variable shows the strongest correlation with depression? What is the percentage of the variance that is "shared" between these variables?
4. Run a regression analysis to predict depression using age, physical health, and mental health as independent variables. Select Analyze →Regression →Linear. Then insert CESD into the box as the dependent variable and insert the other variables into the box for independent variables. Make sure the method is set as "enter" so that all variables will be entered simultaneously and then click "OK".
a. How large is the sample on which the analysis was run? How does this compare to the number of subjects in the sample? Why do you think there is a difference?
b. What is the value of R2 and what does this mean?
c. What is the value of adjusted R2?
d. State a hypothesis and null hypothesis for this analysis. Based on the F value and p level, do you reject the null hypothesis?
e. What are the degrees of freedom for regression?
f. Examine the beta values and significance levels for each of the independent variables, and identify the variables that are significant predictors of depression using an alpha level of .05.
g. prepare a paragraph summarizing the results of this analysis as though you were reporting these results in an article.