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October 05, 2006
Multicollinearity and Irrelevant Variables
We begin with some algebra for estimation of the three-variable regression model. The formula for the parameter estimate gives us the flavor of how the regression attempts to extract the effect of one variable when there are two regressors.
Correlation between the two regressors (collinearity) causes the variance of an estimate to be larger than it would be for the two-variable regression model. If both regressors belong in the model, then that is just the way things are. If one regressor really has a coefficient of zero, we have included an irrelevant variable and our estimate of the nonzero parameter is inefficient.
The notation differs from our usual notation.
For the two-variable regression model the sample covariance between the regressor and the error term causes the estimate to deviate from the true parameter value.
We can restate our previous result on a left-out variable as:
Posted by bparke at October 5, 2006 09:31 PM