NumPy provides essential tools for implementing exponential regression models from scratch. We’ll explore the key concepts of exponential regression and demonstrate how to perform exponential regression using NumPy.

## Understanding Exponential Regression

Exponential regression aims to find a relationship between a dependent variable (*Y*) and an independent variable (*X*) that can be expressed as an exponential equation:

*Y = β _{0} * e^{(β1 * X)} + ε*

Where:

*Y*is the dependent variable (the variable we want to predict).*X*is the independent variable (usually time).*β*is the coefficient representing the initial value of_{0}*Y*.*β*is the coefficient representing the growth or decay rate._{1}*e*is the base of the natural logarithm (approximately 2.71828).*ε*represents the error term (the difference between the predicted and actual values).

## Performing Exponential Regression with NumPy

To perform exponential regression using NumPy, follow these steps:

**Import NumPy:****Define your data:**Prepare your dataset with the dependent variable (*Y*) and independent variable (*X*).**Calculate the coefficients:**Use NumPy functions to calculate the coefficients*β*and_{0}*β*._{1}**Make predictions:**Use the calculated coefficients to make predictions.

`import numpy as np`

X = np.array([1, 2, 3, 4, 5]) Y = np.array([5, 20, 45, 80, 125])

log_Y = np.log(Y) coefficients = np.polyfit(X, log_Y, 1) beta_1 = coefficients[0] beta_0 = np.exp(coefficients[1])

Y_pred = beta_0 * np.exp(beta_1 * X)