Describe the following functional forms of a regression model clearly explaining under
what circumstances they can be suitably used. Give examples where possible.
e) A polynomial regression models.
A polynomial regression model is a type of regression model that uses a polynomial equation to fit a nonlinear relationship between a dependent variable and one or more independent variables. It is a generalization of linear regression, where the relationship between the dependent variable and the independent variables is modeled as a polynomial of degree n.
Polynomial regression models can be used when the relationship between the dependent variable and the independent variables is nonlinear. For example, if the relationship between the dependent variable and the independent variables is quadratic, then a polynomial regression model of degree 2 can be used. Similarly, if the relationship is cubic, then a polynomial regression model of degree 3 can be used.
For example, if we are trying to predict the price of a house based on its size, then a polynomial regression model can be used to capture the nonlinear relationship between the price and the size of the house.