Answer to Question #261662 in Statistics and Probability for seli

Question

 State the assumption of ordinary least square and explain the Guass-Markov theorem

Answer 1

Solution:

Ordinary least squares assumptions:

1. The regression model is linear in the coefficients and the error term.
2. The error term has a population mean of zero.
3. All independent variables are uncorrelated with the error term.
4. Observations of the error term are uncorrelated with each other.

The Gauss-Markov (GM) theorem states that for an additive linear model, and under the ”standard” GM assumptions that the errors are uncorrelated and homoscedastic with expectation value zero, the Ordinary Least Squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators.