Weighted least squares regression is a method for dealing with observations that have nonconstant variances. If the variances are not constant, observations with:
- large variances should be given relatively small weights
- small variances should be given relatively large weights
The usual choice of weights is the inverse of pure error variance in the response.
The formula for the estimated coefficients is as follows:
This is equivalent to minimizing the weighted SS Error.
|X'||transpose of the design matrix|
|W||an n x n matrix with the weights on the diagonal|
|Y||vector of response values|
|n||number of observations|
|wi||weight for the ith observation|
|yi||response value for the ith observation|
|fitted value for the ith observation|