Turning a linear regression model into a curve – polynomial regression

In the previous sections, we assumed a linear relationship between explanatory and response variables. One way to account for the violation of linearity assumption is to use a polynomial regression model by adding polynomial terms:

Here, denotes the degree of the polynomial. Although we can use polynomial regression to model a nonlinear relationship, it is still considered a multiple linear regression model because of the linear regression coefficients .

We will now discuss how to use the PolynomialFeatures transformer class from scikit-learn to add a quadratic term () to a simple regression problem with one explanatory variable, and compare the polynomial to the linear fit. The steps are as follows:

1. Add a second degree polynomial term:

   from sklearn.preprocessing import PolynomialFeatures
   >>> X = np.array([258.0, 270.0, 294.0,
   …                          320.0, 342.0, 368.0,
   …              ...