Multiple RegressionExample

David A. Kenny

January 31, 2014

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Previous Webinars

IntroductionAdvanced Topics

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ResultsConsider the hypothetical regression equation in which Age (in years) and Gender (1 = Male and –1 = Female) predict weight (in pounds):

Weight = 38 + 22(Gender) + 4(Age) + Error

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InterpretationWeight = 38 + 22(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

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Other OutputCollinearity: Only .031 correlation

between Gender and Age; multicollinearity not really an issue.

Error Variance: 134.471, sd = 11.60

R2: .912, adjusted R2 = .902

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CenteringIt 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 37.1. We subtract 37 from everyone’s age or AgeC and obtain:

Weight = 186 + 22(Gender) + 4(AgeC) + Error

Note the new intercept equals 38 + (4)(37) or 186. The slope does not change.

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Rescaling GenderNote that if we recoded gender to be

1 = Male and 0 = Female,

the new equation would be:

Weight =   16 + 44(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

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Change in CoefficientsNote 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 = 16 + 44(GenderDC) + 3(Age) + Error

      

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Bilinear EffectsCreate two variables Age1 (equals

age if Age =< 37, 0 otherwise) and Age2 (equals age if Age > 37, 0 otherwise):

Weight = 60.223 + 23.349Gender

+ 3.278Age1 + 3.540Age2 + E

The two slopes are not all that different.

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DownloadData

Syntax

Output

(All for SPSS 19)

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Using SPSS: Data

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Thank You!

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