Introduction to Simple Linear Regression with Python

Linear regression is a widely used statistical technique for modeling the relationship between a dependent variable and one or more independent variables. In this article, we will introduce simple linear regression and demonstrate how to implement it using Python’s statsmodels and scikit-learn libraries.

Simple Linear Regression

Simple linear regression is a linear model that assumes a linear relationship between a single independent variable and a dependent variable. The model can be represented by the equation:

Y = β0 + β1X + ε

Where Y is the dependent variable, X is the independent variable, β0 is the intercept, β1 is the slope, and ε is the error term.

Using statsmodels

Statsmodels is a popular Python library for estimating and interpreting statistical models. To perform simple linear regression with statsmodels, we can use the OLS (ordinary least squares) method, which minimizes the sum of squared errors to estimate the regression coefficients.

“`python
import statsmodels.api as sm
import numpy as np
import pandas as pd

# Generate some random data
np.random.seed(0)
X = np.random.rand(100, 1)
y = 2 + 3 * X + np.random.rand(100, 1)

# Add a constant to the independent variable matrix
X = sm.add_constant(X)

# Fit the regression model
model = sm.OLS(y, X).fit()

# Print the model summary
print(model.summary())
“`

Using scikit-learn

Scikit-learn is a powerful machine learning library that provides a wide range of tools for building predictive models. To perform simple linear regression with scikit-learn, we can use the LinearRegression class, which fits a linear model to the data using the least squares method.

“`python
from sklearn.linear_model import LinearRegression

# Create a linear regression model
model = LinearRegression()

# Fit the model to the data
model.fit(X, y)

# Print the model coefficients
print(“Intercept:”, model.intercept_)
print(“Slope:”, model.coef_)
“`

Conclusion

Simple linear regression is a fundamental technique for modeling the relationship between a single independent variable and a dependent variable. In this article, we have demonstrated how to implement simple linear regression using Python’s statsmodels and scikit-learn libraries. Both libraries provide easy-to-use tools for fitting and interpreting regression models, making them valuable resources for data analysis and predictive modeling.