Polynomial regression can be very useful. There isn’t always a linear relationship between X and Y. Sometime the relation is exponential or Nth order.

**Related course:** Python Machine Learning Course

## Regression

### Polynomial regression

You can plot a polynomial relationship between X and Y. If there isn’t a linear relationship, you may need a polynomial. Unlike a linear relationship, a polynomial can fit the data better.

You create this polynomial line with just one line of code.

1 | poly_fit = np.poly1d(np.polyfit(X,Y, 2)) |

That would train the algorithm and use a 2nd degree polynomial.

After training, you can predict a value by calling polyfit, with a new example. It will then output a continous value.

### Example

The example below plots a polynomial line on top of the collected data. It trains the algorithm, then it makes a prediction of a continous value.

1 | import numpy as np |

### Overfitting and underfitting

It’s important to not overfit or underfit, you want to capture the relationship but not follow the points exactly. A linear relationship would underfit, overfitting would be picking the degree so high that it fits the points. Instead, you want to capture the relationship.