In **Machine Learning**, Polynomial Regression is a regression algorithm used to model nonlinear relationships between input features and output labels. So, if you are new to Machine Learning and want to know how the Polynomial Regression algorithm works, this article is for you. In this article, I will introduce how the Polynomial Regression algorithm works and how to implement it using Python.

## Here’s How Polynomial Regression Algorithm Works

In Machine Learning, polynomial regression is an algorithm that allows us to model nonlinear relationships between input features and output labels. It can be used in real-time business problems, such as sales forecasting, where the relationship between variables is not linear. Let’s understand how the Polynomial Regression algorithm works by taking an example of a real-time business problem.

Suppose you work as a Data Science professional in a company that sells a certain product. You have historical sales data from past years and want to predict next year’s sales. However, the relationship between sales and time (in months) is not linear, and you cannot use a simple linear regression model to accurately predict future sales.

This is where polynomial regression comes in. Instead of using a straight line to fit the data, it fits a polynomial curve of degree ‘n’ to the data points. The degree ‘n’ determines the complexity of the curve and can be chosen according to the degree of non-linearity of the data. For example, if the data has a quadratic relationship, we can use a degree of 2, which will fit a parabolic curve to the data points.

## Implementation of Polynomial Regression Algorithm using Python

Now let’s see how to implement the Polynomial Regression algorithm using Python. To implement it using Python, we can use the **scikit-learn** library in Python, which provides the functionality of implementing all Machine Learning algorithms and concepts using Python.

Now let’s create an example dataset and implement polynomial regression using Python. For this example, we’ll create sales data for a product over the past ten months:

import numpy as np import pandas as pd import plotly.express as px import plotly.graph_objs as go from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression # Create sample dataset months = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) sales = np.array([10, 20, 30, 50, 80, 120, 150, 180, 200, 220])

Now let’s fit a polynomial curve to the data using polynomial regression:

# Fit polynomial curve to the data poly_reg = PolynomialFeatures(degree=4) X_poly = poly_reg.fit_transform(months.reshape(-1, 1)) lin_reg = LinearRegression() lin_reg.fit(X_poly, sales)

Now let’s use the model to make predictions for the next three months:

# Make predictions for the next 3 months future_months = np.array([11, 12, 13]) future_X_poly = poly_reg.fit_transform(future_months.reshape(-1, 1)) future_sales = lin_reg.predict(future_X_poly) print(future_sales)

[219.16666667 202.04545455 162.57575758]

And here is how we can plot the fitted curve and the predicted sales values:

fig = go.Figure() fig.add_trace(go.Scatter(x=months, y=sales, name='Actual Sales')) fig.add_trace(go.Scatter(x=months, y=lin_reg.predict(X_poly), name='Fitted Curve')) fig.add_trace(go.Scatter(x=future_months, y=future_sales, name='Predicted Sales')) fig.show()

Note that the degree of the polynomial curve is chosen based on the degree of nonlinearity in the data, and the choice of degree can have a significant impact on the accuracy of predictions. In this example, we used a degree of 4, but in real-world scenarios, the optimal degree may need to be determined by experimentation.

## Advantages and Disadvantages of Polynomial Regression Algorithm

##### Advantages:

- Polynomial regression can model a wide range of nonlinear relationships between input and output variables. It can capture complex patterns that are difficult to model with linear regression.
- Polynomial regression is a simple algorithm that can be easily implemented and understood. It does not require advanced mathematical knowledge or complex algorithms.

##### Disadvantages:

- Polynomial regression can easily overfit the data if the degree of the polynomial curve is too high. It can lead to poor generalization and inaccurate predictions on new data.
- Polynomial regression can be sensitive to outliers in the data. Outliers can significantly affect the shape of the polynomial curve and lead to inaccurate predictions.

### Summary

In Machine Learning, polynomial regression is an algorithm that allows us to model nonlinear relationships between input features and output labels. It can be used in real-time business problems, such as sales forecasting, where the relationship between variables is not linear. I hope you liked this article on how the Polynomial Regression algorithm works. Feel free to ask valuable questions in the comments section below.

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