Regression Worksheet - Oklahoma State University–Stillwater



Simple Regression Review

1. Carl Rogers was fond of discussing the discrepancy between the “actual self” (your current view of yourself) and the “ideal self”(your self as you would truly like to be). He held that the goal of therapy was to reduce the discrepancy between the two selves. A number of methods have been used over the years to measure such discrepancies within individuals’ self-concepts, and efforts have been made to correlate self-discrepancies with measures of self-esteem. Suppose a psychologist measures self-discrepancy on a scale that ranges from 0 (no discrepancy) to 24 and self-esteem on a scale that ranges from 0 (low self-esteem) to 50, and she obtains the following data:

Discrepancy Esteem

10 40

17 30

9 39

13 30

12 28

18 16

14 25

10 29

21 18

8 34

18 17

20 12

3 19

9 25

a. Compute descriptive statistics, Pearson’s r, and the covariance in SPSS. Is the correlation significant?

b. What is the proportion of overlapping variance between discrepancies and self-esteem?

c. Treat “Esteem” as the dependent variable (outcome variable) and “Discrepancy” as the independent variable (predictor variable) in a bivariate regression. Using the results you obtained from ‘a’, compute the regression coefficient and y-intercept (show your simple computations here). Check your results in SPSS by running a bivariate regression analysis.

d. What is multiple R2 and how does it compare to the proportion of overlapping variance you computed for ‘b’ above? Is the regression weight statistically significant? What is the observed p-value for the regression weight, and how does it compare to the p-value for the correlation above?

e. Write a brief summary of the results. Is “Discrepancy” a good predictor of “Esteem?”

2. Download and open the Berkeley Guidance Study data from the website. Build and test the following model in SPSS:

soma = wt9 + ht9 + lg9 + st9

The “soma” variable is a rating variable that ranges from 1 (thin) to 7 (obese) regarding body type at age 18. Wt9, ht9, lg9, and st9 are measures of weight, height, leg circumference, and strength at age nine. The equation posits the nine-year old variables as predictors of body type at 18.

Is the overall model statistically significant? In other words, is R2 significant? What proportion of variance in soma is explained by the model; in other words, what is the value for R2?

What are the beta weights for the four predictors? Which are statistically significant at the .05 level?

Interpret the direction of any significant beta weights. For example, if the beta weight for wt9 were .54, this would indicate that higher weights at age 9 are predictive of higher soma ratings at age 18.

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