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Assumptions of Classical Linear Regression Models (CLRM)

The following post will give a short introduction about the underlying assumptions of the classical linear regression model (OLS assumptions), which we derived in the following post. Given the  Gauss-Markov Theorem we know that the least squares estimator b_{0} and b_{1} are unbiased and have minimum variance among all unbiased linear estimators. The Gauss-Markov Theorem is telling us that in a regression model, where the expected value of our error terms is zero, E(\epsilon_{i}) = 0 and variance of the error terms is constant and finite \sigma^{2}(\epsilon_{i}) = \sigma^{2} \textless \infty and \epsilon_{i} and \epsilon_{j} are uncorrelated for all i and j the least squares estimator b_{0} and b_{1} are unbiased and have minimum variance among all unbiased linear estimators. (A detailed proof of the Gauss-Markov Theorem can be found here)

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