Assumption 4 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

Question

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Assumption 4 of the Classical Linear Regression Model (CLRM) pertains to the zero conditional mean assumption, which states that the expected value of the error term, given any value of the independent variable, is zero. This assumption is crucial for unbiasedness of the estimators, not directly for proving linearity of $\hat { \beta } _ { 1 }$. Linearity of the estimator is a property derived from the linear specification of the model itself, not from this assumption.

Assumption 4 of the CLRM Is Necessary but Not Sufficient β^1\hat { \beta } _ { 1 }β^​1​

Assumption 4 of the CLRM Is Necessary but Not Sufficient $\hat { \beta } _ { 1 }$