Regression Analysis with SciPy

Last Updated : 23 Jun, 2025

Regression analysis is a statistical technique used to examine the relationship between one or more independent variables and a dependent variable. It helps in modelling and analyzing data where the focus is on the relationship between variables. In Python SciPy is a popular library for statistical analysis which offers simple and efficient tools for performing regression using its stats module.

Regression-Line-copy — Regression Analysis

Regression Analysis

Regression analysis is a statistical technique used to test the relationship between a dependent variable and one or more independent variables. It helps in understanding how the dependent variable changes when any one of the independent variables is varied while the others are held fixed. Regression analysis is commonly used for prediction, forecasting and determining causal relationships between variables.

1. Using SciPy for Linear Regression

Linear Regression models a straight line relationship between one independent and one dependent variable:

y = mx+c

This code performs Linear regression using SciPy’s linregress() on sample x and y data.
It calculates the slope, intercept and R squared value to describe the line of best fit.
Finally, it visualizes the original data points and the fitted regression line using Matplotlib.

Python

import numpy as np from scipy import stats import matplotlib.pyplot as plt  # Sample data x = np.array([1, 2, 3, 4, 5]) y = np.array([2, 4, 5, 4, 5])  # Perform linear regression slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)  print(f"Slope: {slope}") print(f"Intercept: {intercept}") print(f"R-squared: {r_value**2}")  plt.scatter(x, y, color='blue', label='Data') plt.plot(x, slope * x + intercept, color='red', label='Regression Line') plt.legend() plt.xlabel("X") plt.ylabel("Y") plt.title("Linear Regression with SciPy") plt.show()

Output:

Screenshot-2025-06-23-095651 — Output for Linear Regression

2. Using SciPy for Exponential Regression

Exponential Regression is used when data shows exponential growth or decay modelled as:

y = a \cdot e^{bx}

This code performs Exponential regression using curve_fit from SciPy.
It fits the data to the model and finds the best values for a and b. The result is plotted by showing both the original data points and the fitted exponential curve.

Python

import numpy as np from scipy.optimize import curve_fit import matplotlib.pyplot as plt  #Sample data x = np.array([0, 1, 2, 3, 4]) y = np.array([1, 2.7, 7.4, 20.1, 54.6])    # Define the exponential function def exp_func(x, a, b):     return a * np.exp(b * x)  # Fit curve params, _ = curve_fit(exp_func, x, y) a, b = params print(f"a = {a}, b = {b}")  # Plot x_line = np.linspace(min(x), max(x), 100) plt.scatter(x, y) plt.plot(x_line, exp_func(x_line, *params), color='green') plt.show()

Output:

Screenshot-2025-06-23-095544 — Output for Exponential Regression

3. Using SciPy for Logarithmic Regression

Logarithmic Regression models relationships where the dependent variable changes proportionally to the logarithm of the independent variable:

y = a + b \ln(x)

This code fits a Logarithmic regression model to the data using curve_fit. It estimates the parameters a and b that best describe the relationship between x and y.
The plot visualizes the original data points alongside the fitted logarithmic curve.

Python

import numpy as np from scipy.optimize import curve_fit import matplotlib.pyplot as plt  x = np.array([1, 2, 3, 4, 5]) y = np.array([2.3, 3.1, 3.8, 4.4, 5.0])  def log_func(x, a, b):     return a + b * np.log(x)  params, _ = curve_fit(log_func, x, y) print(f"a = {params[0]}, b = {params[1]}")  # Plot x_line = np.linspace(min(x), max(x), 100) plt.scatter(x, y) plt.plot(x_line, log_func(x_line, *params), color='purple') plt.show()

Output:

Screenshot-2025-06-23-095722 — Output for Logarithmic Regression

4. Using SciPy for Logistic Regression

Logistic Regression models S shaped curves often used for classification or growth processes:

y = \frac{L}{1 + e^{-k(x - x_0)}}

This code fits a Logistic regression curve to the data, modelling an S shaped growth using the logistic function.
It estimates parameters for curve height (L), growth rate (k) and midpoint (x0) using curve_fit. The plot shows the noisy data points and the smooth fitted logistic curve.

Python

import numpy as np from scipy.optimize import curve_fit import matplotlib.pyplot as plt  x = np.linspace(0, 10, 100) y = 1 / (1 + np.exp(-1.5*(x - 5))) + 0.05 * np.random.normal(size=len(x))   def logistic(x, L, k, x0):     return L / (1 + np.exp(-k*(x - x0)))  params, _ = curve_fit(logistic, x, y, p0=[1, 1, 1]) print(f"L = {params[0]}, k = {params[1]}, x0 = {params[2]}")  plt.scatter(x, y, s=10) plt.plot(x, logistic(x, *params), color='red') plt.title("Logistic Regression") plt.show()

Output:

Screenshot-2025-06-23-095850 — Output for Logistic Regression

Regression Analysis with SciPy

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Article Tags :

Regression Analysis with SciPy

Regression Analysis

1. Using SciPy for Linear Regression

2. Using SciPy for Exponential Regression

3. Using SciPy for Logarithmic Regression

4. Using SciPy for Logistic Regression

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