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

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Assumption 1 of the Classical Linear Regression Model (CLRM), which states that the relationship between the dependent and independent variables is linear, is necessary to ensure that the Ordinary Least Squares (OLS) estimator $\hat { \beta } _ { 1 }$ is unbiased and consistent. However, it is not sufficient on its own to prove that $\hat { \beta } _ { 1 }$ is the Best Linear Unbiased Estimator (BLUE); additional assumptions are required for the Gauss-Markov theorem to hold, which establishes the BLUE property.

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

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