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In estimating a linear relationship using ordinary least squares (OLS), the regression estimates are such that the sums of squares of the residuals are minimised. This method treats all residuals as being as important as others.

There may be reasons why the treatment of all residuals in the same way may not be appropriate. One possibility is that there is reason to believe that there is a systematic trend in the size of the error term (residual). One way to compensate for such heteroscedasticity is to give less weight to the residual when the residual is expected to be larger. So, in the regression calculations, rather than minimise the sum of squares of the residuals, what is minimised is their weighted sum of squares.

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Q: What is weighted residual method?
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