value and 2 must be estimated from data. ^WLS=(XWX)1XWY where W is a nn diagonal matrix with ith diagonal element wii=1/Vi. The covariance matrix of this estimate is 2(XWX)1 Standard errors of the estimated parameters can then be calculated as the square roots of the diagonal elements of this covariance matrix. The quantity 2 can be estimated as ^2=np1(YX)W(YX) Your task datasets (e.g. with n as large as 106 ): you may need to think about how to store the matrix W to accommodate this