State and explain the Gauss-Markov theorem. Data From Gauss-Markov Theorem:- 2.5 The Gauss-Markov Theorem What can we

State and explain the Gauss-Markov theorem.

Data From Gauss-Markov Theorem:-

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2.5 The Gauss-Markov Theorem What can we say about the least squares estimators b and b so far? The estimators are perfectly general. Formulas (2.7) and (2.8) can be used to estimate the unknown parameters B1 and B2 in the simple linear regression model, no matter what the data turn out to be. Consequently, viewed in this way, the least squares estimators b and by are random variables. The least squares estimators are linear estimators, as defined in (2.10). Both by and b can be written as weighted averages of the y, values. If assumptions SR1-SR5 hold, then the least squares estimators are conditionally unbiased. This means that E(b|x) = B and E(b|x) = B2. Given x we have expressions for the variances of b and by and their covariance. Furthermore, we have argued that for any unbiased estimator, having a smaller variance is better, as this implies we have a higher chance of obtaining an estimate close to the true parameter value.