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: Defining linear regression.
A linear regression model represents the dependent variable as a linear combination of independent variables. Crucially, the model must be linear with respect to its parameters, though the variables themselves may or may not exhibit linearity.

Step 2: Evaluating the options.
- (A) Linear in explanatory variables but not necessarily in parameters: Incorrect. Linear regression models are defined by linearity in parameters.
- (B) Non-linear in parameters and linear in variables: Incorrect. The requirement is for linearity in parameters.
- (C) Linear in parameters and necessarily in variables: Incorrect. While linearity in parameters is mandatory, linearity in variables is not a requirement.
- (D) Linear in parameters and possibly linear in variables: Correct. Linear regression models must be linear in parameters, and the variables can be either linear or non-linear.

Step 3: Final determination.
Option (D) is the correct choice because the fundamental characteristic of a linear regression model is its linearity with respect to its parameters.