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

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Assumption 3 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 OLS estimators but does not directly pertain to proving the linearity of $\hat { \beta } _ { 1 }$. Linearity of the estimator is a property ensured by the linear formulation of the model itself and the method of estimation (OLS), rather than by this specific assumption.

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 $\hat { \beta } _ { 1 }$