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 (*X _{1}, X_{2}, …, X_{n}*). The model assumes that this relationship can be expressed as:

*Y = β _{0} + β_{1}X_{1} + β_{2}X_{2} + … + β_{n}X_{n} + ε*

Where:

*Y*is the dependent variable (the variable we want to predict).*X*are the independent variables (features)._{1}, X_{2}, …, X_{n}*β*is the intercept (the value of_{0}*Y*when all*X*values are zero).*β*are the coefficients (weights) of the independent variables._{1}, β_{2}, …, β_{n}*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 (*X*)._{1}, X_{2}, …, X_{n}**Calculate the coefficients:**Use NumPy functions to calculate the coefficients*β*,_{0}*β*,_{1}*β*, etc._{2}**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[0] beta_1 = coefficients[1] beta_2 = coefficients[2]

Y_pred = beta_0 + (beta_1 * X1) + (beta_2 * X2)