Linear regression is one of the most fundamental and widely used machine learning algorithms. It is used to predict a continuous target variable based on one or more input variables. In this tutorial, we will learn the basics of linear regression, including its mathematical formulation, implementation, and interpretation.
Basic Concept
Linear regression assumes a linear relationship between the input variables (X) and the output variable (Y). The goal is to find the best-fitting line that minimizes the distance between the line and the actual data points.
Mathematical Formulation
The linear regression equation is given by:
Y = β_0 + β_1 * X + ε
Where:
- Y is the output variable.
- X is the input variable.
- β_0 is the intercept.
- β_1 is the slope.
- ε is the error term.
Implementation
To implement linear regression, we can use libraries such as scikit-learn in Python. Here's a simple example:
from sklearn.linear_model import LinearRegression
# Create a linear regression model
model = LinearRegression()
# Fit the model to the data
model.fit(X_train, y_train)
# Predict the output for new data
y_pred = model.predict(X_test)
Interpretation
The slope (β_1) of the linear regression line indicates the change in the output variable for a one-unit change in the input variable. The intercept (β_0) represents the value of the output variable when the input variable is zero.
Further Reading
For more information on linear regression, you can read the following tutorials: