Weighted Multiple Linear Regression. For example if the residual variance increases with the fitted values then prediction intervals will tend to be wider than they should be at low fitted values and narrower than they should be at high fitted values. Here we use the maximum likelihood estimation MLE method to derive the weighted linear regression.
The program is intended to be used to develop a regional estima-tion equation for. Weighted linear regression is a generalization of linear regression where the covariance matrix of errors is incorporated in the model. Excessive nonconstant variance can create technical difficulties with a multiple linear regression model.
Generally WLS regression is used to perform linear regression when the homogeneous variance assumption is not met aka heteroscedasticity or heteroskedasticity.
Fit a weighted least squares WLS model using weights 1 S D 2. The way to do it is to multiply every X value every y value and the constant by w i. The WREG program can be used to develop a regional estimation equation for streamflow characteristics that can be applied at an ungaged basin or to improve the corresponding estimate at continuous-record streamflow gages with short records. 5 3 Local Linear Regression 10 4 Exercises 15 1 Weighted Least Squares Instead of minimizing the residual sum of squares RSS Xn i1 y i x i 2 1 we could minimize the weighted sum of squares WSS w Xn i1 w iy.
