An overview of the technique
What Is Polynomial Regression
A polynomial is a mathematical expression that is a sum of more than one monomial (Wikipedia). A monomial can be a constant, or a variable (also called indeterminate). In a monomial, the coefficients should be involved with only the operations of addition, subtraction, multiplication, and non-negative integer exponents (Wikipedia). For example, X2+5X-7 is a polynomial, and it is a quadratic one. Polynomial regression is the regression technique that tries to figure out the polynomial that fits the relationship of one dependent variable (Y) and one or more independent variables (X1, X2…). When there is only one ...view middle of the document...
Multiple linear regression is the most fundamental, the most frequently used, and the simplest regression technique among the multiple regression family (Jia, 2011). Both solving nonlinear regression and polynomial regression problems are built on the core techniques of solving multiple linear regression problems. Basically, when we want to solve a problem by using polynomial regression, first we need to transform it into multiple linear regression model (Jia, 2011). In fact, polynomial regression is a special case of multiple linear regression from an estimation point of view, although it fits data into a nonlinear model (Wikipedia).
There are some differences between polynomial regression and nonlinear (curve) regression. After we have our data ready, the first thing we need to do is to draw a scattered plot and determine whether the relationship between x and y is nonlinear or not. Or sometimes, we have previous theories and literature review to indicate that the relationship could be nonlinear. When it is a nonlinear relationship, if it is easy to tell what exact kind of curve model that your data are going to fit, then we should use nonlinear regression. For example, we already know graphs of some curve function such as y=x2 and y=x3. If it is hard to tell which curve model that you data are going to fit, then it’s time to use polynomial regression to get the best approximation. Polynomial regression is a very powerful tool in the regression family because we can get a pretty good estimation just by adding higher order terms of x (Jia, 2011).
How to Solve A Polynomial Regression Problem
The general form of a univariate mth power polynomial regression model looks like yestimated=b0+b1x+b2x2+…+bmxm. If we treat x as x1, x2 as x2, and finally xm as xm, then the mathematical expression becomes as ye=b0+b1x1+b2x2+…+bmxm, a linear equation with m...