Introduction to Statistical Modeling with SAS/STAT Software

Estimating the Error Variance

The least squares principle does not provide for a parameter estimator for sigma squared. The usual approach is to use a method-of-moments estimator that is based on the sum of squared residuals. If the model is correct, then the mean square for error, defined to be normal upper S normal upper S normal upper R divided by its degrees of freedom,

StartLayout 1st Row 1st Column ModifyingAbove sigma With caret squared 2nd Column equals StartFraction 1 Over n minus normal r normal a normal n normal k left-parenthesis bold upper X right-parenthesis EndFraction left-parenthesis bold upper Y minus bold upper X ModifyingAbove bold-italic beta With caret right-parenthesis prime left-parenthesis bold upper Y minus bold upper X ModifyingAbove bold-italic beta With caret right-parenthesis 2nd Row 1st Column Blank 2nd Column equals normal upper S normal upper S normal upper R slash left-parenthesis n minus normal r normal a normal n normal k left-parenthesis bold upper X right-parenthesis right-parenthesis EndLayout

is an unbiased estimator of sigma squared.

Last updated: December 09, 2022