# Polynomial Features and Polynomial Regression

Polynomial features are higher power polynomial terms of the original features, which are added to the feature space of a model.

Let us understand this with a few examples.

Suppose we have a dataset with features x_1, x_2 and target variable y. A multivariable linear regression model for this set of data would be:

Polynomial features are higher ordered values of x_1 and x_2 which we can add to this model, for eg. x_1^2, x_1^3, x_2^2 , etc.

Our new model would look like this:

This is known as a **polynomial regression** model.

We can also combine the features to create higher ordered terms like: x_1x_2 or x_1x_2^2 .

__Important Note:__

We treat the polynomial regression model just like a linear regression model, where each of the polynomial terms are additional features. Although new polynomial terms are added as features, the model is still a linear model in terms of the model parameters w and b. Hence, each of the **new features are still linearly related to the outcome variable**.

The training method is exactly the same as a linear regression model. We can use gradient descent to find the optimal values of each of the weights in our model.