Gauss-Markov Theorem

Assumptions

1. Given $x_i,y_i$ are normally distributed
2. mean: $\mu =\alpha +\beta x$A
3. $Y_i$s are independent
4. $Var(Y_i)={\sigma }^2$

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The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

The Gauss–Markov theorem holds when we adhere to the four assumptions of OLS:

• linearity,
• no multicollinearity,
• strict exogeneity,
• and spherical errors