Question

explain nonlinear regression. explain the cautions and pitfalls in regression analysis

Answer 1

In theory and practice mostly linear regression models are used, there are a few occasions where non linear regression models are used. Non regression is a regression process where the dependent or the criterion variables are modeled as non linear function of model parameters and of one or more independent variables. An example of intrinsically non linear regression model is the constant elasticity of substitution. The CES production function takes the following form:

Cautions and pitfalls of regression anayalis-

1. For intrinsically non linear regression models, the parameter values cannot be obtained explicitly, unlike the linear regression models. They are to be obtained by numerical process mainly by the iterative procedures.

2. The regression models can be plagued by autocorrelation, heteroscedasticity and model specification problems.

3. If legitimate variables are omitted from a model, then consequences can be severe as the model will not only be biased but also inconsistent.

4. Considering the complex conditions arising when we employ a regression analysis, it should be noted that we must make use of the simple regression models where ever it can be employed. In most of the cases, three independent variables are enough for a complex problem.

5. Employing residual plots in our regression analysis would help us in checking the problems arising in the regression models.