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Why not minimize the sum of the residuals, instead of the sum of the squared residuals?

A

Whichever you use, you will obtain the same estimate, so the use of the squared residuals is just convention.

B

The minimum point of the sum of the residuals will always be the sample average of $y$ -- we therefore gain nothing from using this method.

C

By squaring the residuals, large deviations make a bigger impact on the sum, forcing the fit of the OLS line to be better.

D

There is no minimum point for the sum of the residuals, so it is not possible to obtain any estimates via this method.

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