Question. What is the distribution that the estimated regression coefficients?Question. What is the expectation and variance of the estimated regression coefficients?

To answer the first question, we need to understand that the distribution of the estimated regression coefficients depends on the assumptions of the regression model. In linear regression, for example, if the errors are normally distributed and the assumptions of the model are met, then the estimated regression coefficients follow a t-distribution.

To answer the second question, the expectation of the estimated regression coefficients is equal to the true population regression coefficients. In other words, on average, the estimated coefficients will be equal to the true coefficients.

The variance of the estimated regression coefficients, on the other hand, depends on the variability of the data and the sample size. Generally, as the sample size increases, the variance of the estimated coefficients decreases. Additionally, if the predictors are highly correlated, the variance of the estimated coefficients can also increase.

It is important to note that these answers assume that the assumptions of the regression model are met. If the assumptions are violated, the distribution, expectation, and variance of the estimated regression coefficients may be different.