How should we calculate the R^2 statistics in weighted linear regression? Should we also weight each residual to decrease the sum of squares of the residuals? If so, isn't this a biased estimate since we first fit the model with these weights and then again use it to compute the residuals?

  • $\begingroup$ If you give all data points the same weight in a standard weighted OLS regression, my understanding is that the fitted coefficient values will be the same whether the weights are all 0.01 or all 100.0 - but that this will not be true of all fit statistics. I personally do not use weights in the calculation of fit statistics, for example if you provide someone with your data they would also need both the weights and some way to use them in the calculation of fit statistics. $\endgroup$ – James Phillips Aug 14 '19 at 21:21

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