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:

A linear regression model must be linear in its parameters, but the independent variables may not always be linear.

Answer 1

The Correct Option is D

Step 1: Understanding linear regression.
A linear regression model is one in which the dependent variable is modeled as a linear combination of the independent variables. Importantly, the model must be linear in parameters, but the variables may or may not be linear.

Step 2: Analysis of options.
- (A) linear in explanatory variables but may not be linear in parameters: This is incorrect. A linear regression model must be linear in parameters.
- (B) non-linear in parameters and must be linear in variables: This is incorrect. The model should be linear in parameters.
- (C) linear in parameters and must be linear in variables: This is incorrect. The model can be linear in parameters, but the variables do not need to be linear.
- (D) linear in parameters and may be linear in variables: This is correct. Linear regression models are linear in parameters, and the explanatory variables may or may not be linear.

Step 3: Conclusion.
The correct answer is (D), as a linear regression model must be linear in parameters.