I am trying to prep myself for data science interview & I saw the following question on a forum

In the case of least square regression, how does the variance of the error term change with the number of predictors?

I am not sure how to answer this? Any ideas?

Any help will be appreciated

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#### Best Answer

The variance of the error term decreases (or, at worst, does not increase) when you add more regressors. The reason is that a new variable can explain some more variability in the data that wasn't explained by previous regressors. This will reduce the unexplained variations in the data, whch will cause the variance of the error term to decrease.

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