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Given a multiple linear regression model with n= 3 observations and k= 4 regressors what will be the degrees of freedom for error sum of square ?

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With fewer observations than variables you will have a perfect fit. So the error sum of squares will be zero by definition. It would be usual to state that it had zero degrees of freedom although the whole thing is a bit academic.

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  • $\begingroup$ It's worse than that. The example of trying to fit a quadratic to a pair of points shows that there are many perfect fits. A good program should just throw out a request to do this with an error message. $\endgroup$ – Nick Cox Jun 10 at 12:23

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