Lecture 6

Lecture 6 - Multiple Regression: Goodness of Fit We can...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Multiple Regression: Goodness of Fit We can decompose Var(Y) using a multiple regression y i = α + β x i + θ z i +u i Var(Y) = {( β e ) 2 Var(X) + 2 β e θ e Cov(X,Z) + ( θ e ) 2 Var(Z)} + Var(U e ) (Other terms such as Cov( α e , X) and Cov(X,U e are 0) As in simple regression, this decomposition can be set out in an Analysis of Variance (ANOVA) table The ANOVA table Source of variance Sum of squares Degrees of freedom Mean square Total SST N-1 SST/N-1 (Var Y) Explained SSE K-1 SSE/K-1 ( F A ) Residual SSR N-K SSR/N-K ( F B ) SST has N-1 degrees of freedom because it is the variance around Mean(Y) R 2 and ‘adjusted’ R 2 R 2 = SSE/SST = (SST - SSR)/SST The value of R 2 depends on the form of Y: never use R 2 to compare regressions with different dependent variables R 2 must increase as more regressors are added Use ‘adjusted R 2 ’ to compare two regressions with same dependent variable and number of observations adjusted R 2 = R 2 - {(K-1)/(N-K)}(1 - R 2 ) Alternatively use the estimated
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/07/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.

Page1 / 4

Lecture 6 - Multiple Regression: Goodness of Fit We can...

This preview shows document pages 1 - 2. Sign up to view the full document.

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