If ordinary least squares is used to estimate a linear function, then the sum of the e_t will always be equal to zero.

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Quizplus · Accepted Answer

In ordinary least squares regression, the method minimizes the sum of the squared residuals, and as a result, the sum of the residuals (differences between observed and predicted values) is always equal to zero. This is a property of the least squares estimation method.

If Ordinary Least Squares Is Used to Estimate a Linear