If we know the population parameters ($B_0$ and $B_1$) of y = $B_0 + B_1 x + \varepsilon$, what formula can we use to estimate the standard deviation $\sigma$?

  • $\begingroup$ Assuming $\sigma^2$ is variance of $y$, if you have $n$ observations on $(x,y)$ then an unbiased estimate of the variance is $\hat\sigma^2=\frac1{n-2}\sum_{i=1}^n (y_i-\hat y_i)^2$ where $\hat y$ is the fitted model. $\endgroup$ Commented Jan 20, 2020 at 15:39
  • $\begingroup$ Thank you, I did not realize that I'm asked to find the unbiased estimator, but I guess it makes sense since the regression model shouldn't be biased and we know the parameters. $\endgroup$
    – user380572
    Commented Jan 20, 2020 at 17:14
  • $\begingroup$ In case your $\varepsilon_i$ s are i.i.d normal, then this estimator is the usual choice since it has other properties aside from unbiasedness. $\endgroup$ Commented Jan 20, 2020 at 17:26


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