Estimated variance of OLS estimators - intuition behind maths

[@ahmadghaemi2192]

I understand that a larger amount of observations make the sum in denominator bigger. But if the data points lie far from the mean, the denominator will also be larger, and thus the variance smaller. Doesn't that seem counterintuitive? Is it so that the combination of large deviations from the mean but small residuals make the best estimate?

[@kurtaykarayel8003]

Hi Ahmad, I was thinking the same thing. But I believe its not counter. If the data points lie far from the mean that means the residuals must be higher. So the denominator will be greater in that scenario but so the residual.

[@valewang8547]

Hi, Ben. Thank you for the video. It is really helpful. I have one question regarding the estimated variance. my understanding is: since the last two items do not contribute variance to the sample U, so the expected estimated variance from the sample is equal to (n-2)n*variance. if we use this expected estimated variance from the sample as the population variance of u,we will underestimate the population variance, so the estimated population variance is adjusted back to 1/(n-2)*variance. if my understanding correct? Thank you.