multiple regression lab chapter 10 1. topics multiple linear regression effects levels of...
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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