NumPy provides essential tools for implementing multiple regression models from scratch. We’ll explore the key concepts of multiple regression and demonstrate how to perform multiple regression using NumPy.
Understanding Multiple Regression
Multiple regression aims to find a linear relationship between a dependent variable (Y) and two or more independent variables (X1, X2, …, Xn). The model assumes that this relationship can be expressed as:
Y = β0 + β1X1 + β2X2 + … + βnXn + ε
- Y is the dependent variable (the variable we want to predict).
- X1, X2, …, Xn are the independent variables (features).
- β0 is the intercept (the value of Y when all X values are zero).
- β1, β2, …, βn are the coefficients (weights) of the independent variables.
- ε represents the error term (the difference between the predicted and actual values).
Performing Multiple Regression with NumPy
To perform multiple regression using NumPy, follow these steps:
- Import NumPy:
- Define your data: Prepare your dataset with the dependent variable (Y) and multiple independent variables (X1, X2, …, Xn).
- Calculate the coefficients: Use NumPy functions to calculate the coefficients β0, β1, β2, etc.
- Make predictions: Use the calculated coefficients to make predictions.
import numpy as np
X1 = np.array([1, 2, 3, 4, 5]) X2 = np.array([2, 3, 4, 5, 6]) Y = np.array([3, 5, 7, 8, 10])
X = np.column_stack((np.ones_like(X1), X1, X2)) coefficients = np.linalg.inv(X.T @ X) @ X.T @ Y beta_0 = coefficients beta_1 = coefficients beta_2 = coefficients
Y_pred = beta_0 + (beta_1 * X1) + (beta_2 * X2)