10.16. Weighted least squares. Suppose that we are fitting the straight line y $ "0 % "1x % ', but the variance of the y’s now depends on the level of x; that is,

where the wi are known constants, often called weights. Show that if we choose estimates of the regression coefficients to minimize the weighted sum of squared errors given by wi(yi ! "0 ! "1xi)2, the resulting least squares normal equations are

Transcribed Image Text:

V(y|x;) = = 07 i = 1, 2,...,n W