8. Matrix Algebra and Multiple Regression

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Updated notes

Estimating the residual variance for OLS

(Posted 8 March 1999)

Our discussion on page 200 of the variance-covariance matrix for the ordinary least squares (OLS) estimators (Equation 8.33b) neglicted to mention how to estimate sigma^2_e, the residual variance.

Equation 8.33b gives the variance-covariance matrix for the vector b of OLS estimators as

Var(b) = (XTX)-1 sigma^2_e

We can estimate sigma^2_e from the residual sums of squares,

RSS = (y - Xb)T(y - Xb)

If the model estimates p parameters, then the estimate of sigma^2_e is simply RSS/(N-p) where N is the number of data points. Thus,

Var(b) = (XTX)-1 (y - Xb)T(y - Xb) /(N-p)


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Created 25 February 1995, last updated 8 March 1999

Bruce Walsh. jbwalsh@u.arizona.edu . Comments welcome.