ch03 - Economics 20 - Prof. Anderson 1 Multiple Regression...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 20 - Prof. Anderson 1 Multiple Regression Analysis y = β + β 1 x 1 + β 2 x 2 + . . . β k x k + u 1. Estimation Economics 20 - Prof. Anderson 2 Parallels with Simple Regression β is still the intercept β 1 to β k all called slope parameters u is still the error term (or disturbance) Still need to make a zero conditional mean assumption, so now assume that E( u|x 1 ,x 2 , …,x k ) = 0 Still minimizing the sum of squared residuals, so have k+1 first order conditions Economics 20 - Prof. Anderson 3 Interpreting Multiple Regression tion interpreta a has each is that , ˆ ˆ that implies fixed ,..., holding so , ˆ ... ˆ ˆ ˆ so , ˆ ... ˆ ˆ ˆ ˆ 1 1 2 2 2 1 1 2 2 1 1 ribus ceteris pa x y x x x x x y x x x y k k k k k β β β β β β β β β ∆ = ∆ ∆ + + ∆ + ∆ = ∆ + + + + = Economics 20 - Prof. Anderson 4 A “Partialling Out” Interpretation ( 29 2 2 1 1 2 1 1 1 2 2 1 1 ˆ ˆ ˆ ˆ regression estimated the from residuals the are ˆ where , ˆ ˆ ˆ then , ˆ ˆ ˆ ˆ i.e. , 2 where case he Consider t x x r r y r x x y k i i i i γ γ β β β β + = = + + = = ∑ ∑ Economics 20 - Prof. Anderson 5 “Partialling Out” continued Previous equation implies that regressing y on x 1 and x 2 gives same effect of x 1 as regressing y on residuals from a regression of x 1 on x 2 This means only the part of x i1 that is uncorrelated with x i2 are being related to y i so we’re estimating the effect of x 1 on y after x 2 has been “partialled out” Economics 20 - Prof. Anderson 6 Simple vs Multiple Reg Estimate sample in the ed uncorrelat are and OR ) of effect partial no (i.e. ˆ : unless ˆ ~ Generally, ˆ ˆ ˆ ˆ regression multiple with the ~ ~ ~ regression simple the Compare 2 1 2 2 1 1 2 2 1 1 1 1 x x x x x y x y = ≠ + + = + = β β β β β β β β Economics 20 - Prof. Anderson 7 Goodness-of-Fit ( 29 ( 29 SSR SSE SST Then (SSR) squares of sum residual the is ˆ (SSE) squares of sum explained the is ˆ (SST) squares...
View Full Document

This note was uploaded on 03/03/2011 for the course ECON 422 taught by Professor Staff during the Spring '08 term at Maryland.

Page1 / 28

ch03 - Economics 20 - Prof. Anderson 1 Multiple Regression...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online