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data. When the method of least squares is used to estimate and , then the residuals , unlike the errors , cannot be independent since they satisfy the two constraints

:

and

:

(Here ?_i is the ith error, and is the ith residual.)

The residuals, unlike the errors, do not all have the same variance: the variance decreases as the corresponding x-value gets farther from the average x-value. This is not a feature of the data itself, but of the regression better

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