Lecture 34:- Polynomial Linear Regression Hands on

Polynomial Linear Regression is an extension of simple linear regression, where the relationship between the independent variable(s) and the dependent variable is modeled as a higher-degree polynomial. It allows us to capture more complex patterns and non-linear relationships between the variables. Let's perform Polynomial Linear Regression using scikit-learn:

pythonCopy code

import numpy as np import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures # Example data x = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)  # Reshape to a column vector y = np.array([2, 3, 4, 2, 3]) # Transform the features into polynomial features poly_transformer = PolynomialFeatures(degree=3)  # Choose the degree of the polynomial x_poly = poly_transformer.fit_transform(x) # Create and fit the polynomial regression model model = LinearRegression() model.fit(x_poly, y) # Predict using the model x_new = np.array([6, 7, 8]).reshape(-1, 1) x_new_poly = poly_transformer.transform(x_new) predictions = model.predict(x_new_poly) # Visualize the Polynomial Regression Model plt.scatter(x, y, color='blue', label='Data Points') plt.plot(x, model.predict(x_poly), color='red', label='Polynomial Model') plt.scatter(x_new, predictions, color='green', label='Predictions') plt.xlabel('Independent Variable (x)') plt.ylabel('Dependent Variable (y)') plt.title('Polynomial Linear Regression using scikit-learn') plt.legend() plt.show() print("Predictions on new data:", predictions)

In this implementation, we used scikit-learn's PolynomialFeatures class to transform the original feature x into polynomial features of a chosen degree (in this case, degree=3). We then used LinearRegression as before to create and train the polynomial regression model.

We imported the necessary libraries, including numpy, matplotlib.pyplot, LinearRegression, and PolynomialFeatures.

We defined the example data x and y.

We transformed the original features x into polynomial features of degree 3 using PolynomialFeatures. This transforms the feature x into [x, x^2, x^3].

We created an instance of LinearRegression as model and fit it with the transformed data x_poly and the target variable y.

We then made predictions on new data x_new using the model. To make predictions on polynomial features, we also transformed x_new using poly_transformer.transform(x_new).

Finally, we used matplotlib to visualize the polynomial regression model's line of best fit, data points, and predictions.

Polynomial Linear Regression allows us to capture more complex relationships between the variables, making it useful for modeling non-linear patterns in the data. The degree of the polynomial is a hyperparameter that needs to be chosen based on the data and the complexity of the relationship.