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Lecture12

# Lecture12 - Lecture 12 Multicollinearity Heteroskedasticity...

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Lecture 12 : Multicollinearity, Heteroskedasticity Econ 444, Winter 2010 Feb 23, 2010

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How to detect Multicollinearity ? 1 High R 2 but few significant t-ratios may suggest presence of multicollinearity. 2 High pairwise correlations among explanatory variables. 3 Variance Inflation Factor (VIF) : measures how much multicollinearity has increased the variance of an estimated coefficient. For example, consider the following regression equation, Y i = β 0 + β 1 X 1 i + β 2 X 2 i + β 3 X 3 i + i (1)
Now to compute the VIF corresponding to say estimate of ˆ β 1 we follow two steps: 1 Estimate the following equation and save the R 2 1 : X 1 = α 1 + α 2 X 2 + α 3 X 3 + ν i (2) 2 Then the VIF for ˆ β 1 is given by, VIF ( ˆ β 1 ) = 1 1 - R 2 1 (3)

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Similarly to obtain VIF corresponding to ˆ β 2 , 1 Estimate the following equation and save the R 2 2 : X 2 = γ 1 + γ 2 X 1 + γ 3 X 3 + ψ i (4) 2 Then the VIF for ˆ β 1 is given by, VIF ( ˆ β 2 ) = 1 1 - R 2 2 (5)
Few things to note : There will be a VIF for every coefficient estimated in the equation. So in previous example, there will be 3 VIFs.

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Lecture12 - Lecture 12 Multicollinearity Heteroskedasticity...

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