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Multiple Regression Analysis
Simple vs Multiple Regression Estimate
Example:Why are these results different? Regression of Wages on Education
Regression of Wages on Education and Experience
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Multiple Regression Analysis
Ordinary Least Squares (OLS) Estimator
ˆ ˆ ˆ ˆ To estimate β0 , β1 , β2 , ..., βk we choose β0 , β1 , β2 , ..., βk that minimize 1 n ˆ ˆ ˆ ˆ S( β0 , β1 , β2 , ..., βk ) = ∑i=1 (yi n The first order conditions are 2 n ˆ u n ∑ i=1 i 2 n ˆ ux n ∑i=1 i ij j ˆ where ui = yi ˆ β0 ˆ β1 xi1 ˆ β2 xi2 ˆ β0 ˆ β1 xi1 ˆ β2 xi2 ... ˆ βk xik )2
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Multiple Regression Analysis
Now we extend the simple linear regression model to allow for more than one independent variable(more than one regressor) to influence the dependent variables: Example 1: wages = β0 + β1 education + β2 exper + u where wages hourly wages education schooling years exper years of experience Example 2: housep = β0 + β1 size + β2 bdrms + β3 bthrms + u where housep house price size size of the house bdrms number of bedrooms bthrms number of bathrooms
