Linear Regression
Understanding the fundamentals of linear regression and its implementation
What is Linear Regression?
A fundamental supervised learning algorithm for predicting continuous values
Linear regression is one of the simplest and most widely used statistical models for predictive analysis. It attempts to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.
The Linear Equation
y = mx + b
- y: The dependent variable (what we're trying to predict)
- x: The independent variable (our input feature)
- m: The slope (how much y changes when x changes)
- b: The y-intercept (the value of y when x = 0)
How Linear Regression Works
- Collect data: Gather pairs of input (x) and output (y) values.
- Find the best-fitting line: Use a method called "Ordinary Least Squares" to find the line that minimizes the sum of squared differences between observed and predicted values.
- Evaluate the model: Assess how well the line fits the data using metrics like R-squared or Mean Squared Error.
- Make predictions: Use the fitted line to predict y values for new x inputs.
Cost Function: Mean Squared Error
Linear regression finds the best line by minimizing the Mean Squared Error (MSE):
MSE = (1/n) * Σ(y_actual - y_predicted)²
This measures the average squared difference between the actual values and the predicted values.
Applications of Linear Regression
Linear regression is used in various fields for prediction and analysis:
- Economics: Predicting sales, pricing, and economic trends
- Finance: Risk assessment, stock price prediction
- Healthcare: Predicting patient outcomes based on treatment variables
- Real Estate: Estimating property values based on features
- Marketing: Analyzing the relationship between advertising spend and sales