Polynomial Regression

Often in real-world data, the response variable and the predictor variable don't have a linear relationship, and we may need a nonlinear polynomial function to fit the data. Various scatterplot-like residual versus each predictor and residual versus fitted values reveal the violation of linearity if any, which could potentially help in identifying the need for introducing the quadratic or cubic term in the equation. The following function is a generic polynomial equation:

Where k is the degree of the polynomial. For k=2, f(X) is called quadratic and h=4 is called cubic. Note that polynomial regression is still considered linear regression since it is still linear in coefficient .

Before revisiting the Beijing PM2.5 example, let's understand how polynomial regression works using simulated data from the quadratic equation we introduced in the Linear Regression section.

Exercise 55: Performing Uniform Distribution Using the runif() Function

In this exercise, we will generate...