# ALRLec4 - 1 Chapter 2 ANOVA and Tests The simplest...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Chapter 2 ANOVA and Tests The simplest regression model is Y i = + e i min (Y i ) 2 Y = Residual Sum of Square: RSS = (Y i ) 2 = (Y i Y ) 2 =SYY For simple regression model Y i = + 1 x i + e i min (Y i 1 x i ) 2 Residual Sum of Square: RSS= (Y i 1 x i ) 2 = SYY SXY 2 SXX with df=n-2 RSS-RSS = the reduction in residual sum of squares due to enlarging regression SSreg=SYY RSS = SYY (SYY ( SXY 2 SXX ) = SXY 2 SXX df= (n 1) (n 2) = 1 2 ANOVA Table Sources DF SS MS F Regression 1 SSreg SSreg 1 = MSreg F = MSreg 2 Residual n-2 RSS RSS n 2 = 2 Total n-1 SYY F-test H : E(Y|X= X )= vs H a : E(Y|X= X )= + 1 x which is equivalent to testing H : 1 = 0 H a : 1 The p-value is the probability that a random variable having the F(1, n-2) distribution F* Recall that for the same hypotheses, we can perform the t test H : 1 =0 H a : 1...
View Full Document

## This note was uploaded on 12/12/2010 for the course STAT 425 taught by Professor Ma,p during the Fall '08 term at University of Illinois, Urbana Champaign.

### Page1 / 5

ALRLec4 - 1 Chapter 2 ANOVA and Tests The simplest...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online