note13 - STAT5044: Regression and Anova Inyoung Kim Outline...

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Unformatted text preview: STAT5044: Regression and Anova Inyoung Kim Outline 1 Collinearity Collinearity A near-linear relationship (high correlation coefficient) among covariates Does not reduce bias much (because it can be explained roughly by a linear combination of other covariates) Increasing the variance Standard form Original model: Y 1 = + 1 x 1 i + 2 x 2 i + i (1) Standard form: Y * i = Y i- Y S ( y ) , where S ( y ) = q 1 n- 1 i = 1 ( y i- y ) 2 Standard form = Y- 1 X 1- 2 X 2 X * 1 i = X 1 i- X 1 S ( X 1 ) X * 2 i = X 2 i- X 2 S ( X 2 ) X * 1 = X * 2 = Y * i = Standard model Y * i = 1 x * 1 i + 2 x * 2 i + Standard form y i- y S ( y ) = 1 ( x 1 i- x 1 S ( x 1 ) )+ 2 ( x 2 i- x 2 S ( x 2 ) )+ * i Y i- Y = 1 ( x 1 i- x 1 ) S ( x 1 ) S ( Y )+ 2 ( x 2 i- x 2 ) S ( X 2 ) + S ( Y ) * i Y i = { Y- 1 X 1 S ( Y ) S ( X 1 )- 2 X 2 S ( y ) S ( X 2 ) } + { 1 S ( Y ) S ( X 1 ) } X 1...
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note13 - STAT5044: Regression and Anova Inyoung Kim Outline...

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