Question

Discuss functional forms of the regression model and how do we decide to use one?

Answer 1

The need to change the functional form of the model arises if one of the following hypotheses is incorrect, the fulfillment of which is required for that the usual least-squares method (OLS) applied to the regression model

$$Y_i=X_i\beta+\epsilon_i$$

(i = 1, ..., N) gave good results:

1. Errors have zero mathematical expectation, or, what is the same, mate. the expectation of the dependent variable is a linear combination regressor:

$$E(\epsilon_i)=0$$

$$E(Y_i)=X_i\beta$$

2. Errors are homoscedastic, that is, they have the same variance for

all observations:

$$V(\epsilon^2_i)=E(\epsilon^2_i)=\sigma^2$$