Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an nth-degree polynomial in x. It provides the best approximation for non-linear relations between the x/y. The polynomial regression equation is as follows:

 

Polynomial regression builds upon the standard linear regression model by adding extra predictors obtained by raising each of the original predictors to a power. For example, a cubic regression uses three variables, X, X2, and X3, as predictors. It does this to increase the accuracy of the model. Below is an example of how a polynomial differs from a linear model.

Steps of Polynomial Regression:

• Data Pre-processing:
  • This step is like the other regression models with a couple of exceptions, such as there is no feature scaling, and there is no need to split the dataset into a training set and a test set. This is because normally, datasets for this model contain very little information, so if we separate it into even smaller parts, the accuracy of the results of our model is reduced.
• Building a Linear Regression model and fitting it to the dataset:
  • This is done because it is needed as a reference to build the polynomial model. Furthermore, it will be used as a comparison against the polynomial model.
• Building a Polynomial Regression model and fit it to the dataset:
  • In order to do this, a class called PolynomialFeatures from the preprocessing library needs to be used to add some extra features to the dataset.
• Visualize both models:
  • Create graphs for both models based on the pre-processing done on the datasets.
• Predict the output:
  • The final output is predicted using the polynomial regression compared to the linear model.