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  "body": "\n## Summary\n\nWeighted least squares fits a regression model by minimising a sum of squared residuals in which each observation has its own positive weight.\nIt is the case of [[generalized least squares|P142WXJCF3]] in which the errors are uncorrelated but [[heteroscedastic|D8VX6XQ3TT]].\nWith weights inversely proportional to the error variances, it gives the best linear unbiased estimator.\nIt is also the inner step of iteratively reweighted least squares, used to fit [[generalized linear models|K6C48KMRKC]] and robust regressions.\n\n## Explanations\n\n### L1 human\n\nSome data points are more precise than others.\nWeighted least squares lets the precise points pull harder on the fitted line.\nEach squared residual is multiplied by a weight, and a point with weight $2$ counts as much as two copies of the same point.\nFor a model that is just a constant, weighted least squares gives the weighted average $\\sum_i w_i y_i / \\sum_i w_i$.\n",
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