Multiple Regression

Lab Chapter 10

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Topics

• Multiple Linear Regression• Effects• Levels of Measurement• Dummy Variables

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Multiple Linear Regression

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Output from Regressing

INCOME86 on EDUC, AGE, and

SEX

Model Summary• Multiple correlation coefficient R– Correlation of all IV’s with DV– Report strength

• Coefficient of determination Adj. R2

– % of explained variability in DV by all IV’s

ANOVA Table- Size of F and p-value (sig.) indicate significance of overall model- Large F, small p-value (< .05 or .01) is a significant model

Coefficients Table• Similar to bivariate regression– unstandardized coefficients– regression equation

Y = -8142.153 + 1650.831(X1) + 267.101(X2) - 7174.415(X3) INCOME86 = -8142.153 + 1650.831(EDUC) + 267.101(AGE) - 7174.415(SEX)

Multiple Linear Regression (cont.)

• standardized coefficients (betas)– net effects– indicate direction and strength

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Net Effects

• Interpretation– “What effect does this variable have separate

from the effects of the other independent variables?”

– a way to statistically control for other variables in the model

• A potential problem: multicollinearity (more on this in lecture)

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Levels of Measurement

Can it be used in linear regression as

Dependent variable Independent variable

Interval/ratio variable yes yes

Ordinal variable Yes (but with caution) yes

Dichotomy no yes

Nominal variable (with three or more attributes)

no Maybe (as series of dummy variables)

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Dummy Variables• a way of getting nominal variables with 3 or

more attributes into regression as independent variables

• conversion into a series of dichotomies• enter all but one of the dichotomies

Original Variable REGION Northeast = 1, Midwest = 2, South = 3, West = 4 New Variables NOREAST if REGION = 1, NOREAST = 1 otherwise NOREAST = 0 MIDWEST if REGION = 2, MIDWEST = 1 otherwise MIDWEST = 0 SOUTH if REGION = 3, SOUTH = 1, otherwise SOUTH = 0 WEST if REGION = 4, WEST = 1, otherwise WEST = 0