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

In linear regression, the model is linear in parameters, which means that the relationship between the dependent and independent variables is linear when expressed in terms of the parameters (coefficients). This means that even if the regression involves non-linear transformations of the explanatory variables, as long as the parameters (coefficients) appear linearly, it is considered a linear model.

 - (A) Linear in explanatory variables but may not be linear in parameters: This is incorrect because the linear regression model must always be linear in parameters.
- (B) Non-linear in parameters and must be linear in variables: This is incorrect because linear regression is linear in parameters, not non-linear.
- (C) Linear in parameters and must be linear in variables: This is incorrect because while the model must be linear in parameters, it does not have to be linear in the variables themselves. Non-linear transformations of the variables can still be used in a linear regression model.
- (D) Linear in parameters and may be linear in variables: This is correct. The model must be linear in parameters, and it can be linear or non-linear in the explanatory variables.
The correct answer is (D), as the linear regression model must be linear in parameters, and the explanatory variables can be either linear or non-linear.

 Final Answer: (D) Linear in parameters and may be linear in variables.