Question

Linear regression model is

• A. linear in explanatory variables but may not be linear in parameters
• B. non-linear in parameters and must be linear in variables
• C. linear in parameters and must be linear in variables
• D. linear in parameters and may be linear in variables

Hint:

In linear regression, the key requirement is linearity in parameters (coefficients). The variables themselves may be transformed, but the model must remain linear in terms of the coefficients.

Answer 1

The Correct Option is D

Topic: The Classical Linear Regression Model (CLRM)
Understanding the Question: What defines a model as "linear" in the context of econometrics?
Key Formulas and Approach: A model is $Y = \beta_1 + \beta_2 X + u$. The "linearity" refers to the power of the $\beta$ coefficients.
Detailed Solution:
Step 1: Define Linearity in Parameters. For OLS to work, the coefficients ($\beta$) must be raised to the power of 1 and not be multiplied by each other. This is a strict requirement.
Step 2: Define Linearity in Variables. We can have models like $Y = \beta_1 + \beta_2 X^2$. Here, the variable is squared (non-linear), but the model is still a "Linear Regression" because $\beta_2$ is linear.
Step 3: Synthesis. Therefore, a linear regression model must be linear in parameters ($\beta$), but it can be linear or non-linear in variables ($X$).
Conclusion: Option (D) correctly describes this flexibility.