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

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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...
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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.

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

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