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I understand that beta-1 and beta-2 are parameters/OLS Estimators. But why is the variance of the error term a parameter?

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  • $\begingroup$ What do you assume about the variance? That will determine whether it is a parameter or not. $\endgroup$
    – whuber
    Oct 22 '18 at 16:06
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The "parameters" in the regression model are just the unknown and unobservable aspect of the model. It is usual to assume that we don't know how variable the error term in the model is, and since this variance is not directly observable (it is inferred from the data), it is a parameter.

Also, I notice that your question has a secondary confusion. The parameters $\beta_0$ and $\beta_1$ are not the same as their corresponding OLS estimators. The parameters are unknown unobservable values, whereas the estimators are functions of the data that are used to estimate the parameters. This is another aspect of the confusion between a parameter, and the estimator that is estimating that parameter.

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