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 = β0 * e(β1 * X) + ε
- Y is the dependent variable (the variable we want to predict).
- X is the independent variable (usually time).
- β0 is the coefficient representing the initial value of Y.
- β1 is the coefficient representing the growth or decay rate.
- 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 β0 and β1.
- 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 beta_0 = np.exp(coefficients)
Y_pred = beta_0 * np.exp(beta_1 * X)