Assumption 3 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is best.

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Assumption 3 of the Classical Linear Regression Model (CLRM), which is the assumption of zero conditional mean (E[ε|X] = 0), is necessary to ensure that the OLS estimator $\hat { \beta } _ { 1 }$ is unbiased. However, being unbiased alone does not guarantee that it is the best (in the sense of having the smallest variance among all unbiased estimators), which requires additional assumptions like homoscedasticity and no autocorrelation of errors.

Assumption 3 of the CLRM Is Necessary but Not Sufficient β^1\hat { \beta } _ { 1 }β^​1​

Assumption 3 of the CLRM Is Necessary but Not Sufficient $\hat { \beta } _ { 1 }$