1. Multiple Regression Example
David A. Kenny

2. Previous Webinars
Introduction
Advanced Topics

3. Results
Consider the hypothetical regression equation in which Age (in years) and Gender (1 = Male and –1 = Female) predict weight (in pounds):
Weight =  (Gender) + 4(Age) + Error

4. Weight = 38 + 22(Gender) + 3(Age) + Error
Interpretation
Weight =  (Gender) + 3(Age) + Error
           intercept: the predicted weight for people who are zero years of age and half way between male and female is 38 pounds; obviously a poor extrapolation            gender: a difference between men and women on the gender variable equals 2 and so there is a 44 (2 times 22) pound difference between the two groups            age: a difference of one year in age results in a difference of 4 pounds

5. Other Output
Collinearity: Only .031 correlation between Gender and Age; multicollinearity not really an issue.
Error Variance: , sd =
R2: .912, adjusted R2 = .902

6. Weight = 186 + 22(Gender) + 4(AgeC) + Error
Centering
It is advisable to center the Age variable.  To center Age, we would subtract the mean age from Age.  Doing so, would change the intercept to the predicted score for persons of average age in the study.
The average of the sample is We subtract 37 from everyone’s age or AgeC and obtain:
Weight =  (Gender) + 4(AgeC) + Error
Note the new intercept equals 38 + (4)(37) or The slope does not change.

7. Weight = 16 + 44(Gender) + 4(Age) + Error
Rescaling Gender
Note that if we recoded gender to be
1 = Male and 0 = Female,
the new equation would be:
Weight =   (Gender) + 4(Age) + Error
       intercept: the predicted weight for women who are zero years of age and is 16 pounds        gender: men weigh on average  44 more pounds than women, controlling for age        age: a difference of one year in age results in a difference of 4 pounds

8. Change in Coefficients
Note that dummy-coded gender equals
0.5 + (0.5)Gender
where Gender is coded +1/-1. Thus, the new intercept is 38 – 22 or 16 new slope for dummy-coded gender is 22/0.5 or 44:
Weight =  (GenderDC) + 3(Age) + Error
      

9. Bilinear Effects
Create two variables Age1 (equals age if Age =< 37, 0 otherwise) and Age2 (equals age if Age > 37, 0 otherwise):
Weight = Gender
Age Age2 + E
The two slopes are not all that different.

10. Download
Data
Syntax
Output
(All for SPSS 19)

11. Using SPSS: Data

15. Thank You!