Question

Which of the following is/are NOT the assumption(s) of Classical Linear Regression Model (CLRM)?

• A. Variance of the dependent variable (\( Y_i \)) is greater than the variance of the explanatory variable (\( X_i \))
• B. The model is linear in both parameters and variables.
• C. The \( \text{Cov}(Y_i, u_i) = 0 \), where \( u_i \) is the error term.
• D. The \( \text{Cov}(X_i, u_i) = 0 \), where \( u_i \) is the error term.

Hint:

In CLRM, the assumption regarding the relationship between the variance of the dependent and explanatory variables is not a required assumption for the validity of the regression model.

Answer 1

The Correct Option is A

Step 1: Understand the assumptions of the Classical Linear Regression Model (CLRM).
The assumptions of CLRM are crucial for the Ordinary Least Squares (OLS) estimates to be the Best Linear Unbiased Estimators (BLUE). The assumptions include:
1. Linearity in both parameters and variables.
2. No correlation between the explanatory variables and the error term (\( \text{Cov}(X_i, u_i) = 0 \)).
3. No correlation between the dependent variable and the error term (\( \text{Cov}(Y_i, u_i) = 0 \)).
4. Homoscedasticity: Constant variance of the error term.
5. The error term should have zero mean.
Step 2: Analyze the options.
- Option (A) is incorrect because the assumption of CLRM does not require the variance of the dependent variable to be greater than the variance of the explanatory variable. This is not part of the CLRM assumptions.
- Option (B) is correct because the model must be linear in both the parameters (coefficients) and variables for the assumptions to hold.
- Option (C) is correct because the error term must have zero covariance with the dependent variable, as the error should not be systematically related to the observations.
- Option (D) is correct because the explanatory variables should not be correlated with the error term, which ensures that the model provides unbiased estimates.
Final Answer: \[ \boxed{\text{Variance of the dependent variable } (Y_i) \text{ is greater than the variance of the explanatory variable } (X_i) \text{ is NOT an assumption of CLRM.}} \]