Linear Regression Intuition

Linear regression is often the first ML algorithm you learn - and for good reason. It's simple, interpretable, and surprisingly powerful. Understanding linear regression gives you the foundation for understanding more complex models.

The Core Idea

Linear regression finds a straight line that best describes the relationship between inputs and outputs.

The Linear Equation

Linear regression finds values for the equation:

y = mx + b

Where:

• y = prediction (dependent variable)
• x = input feature (independent variable)
• m = slope (how much y changes when x increases by 1)
• b = intercept (value of y when x = 0)

What Makes a "Good" Line?

The best line minimizes the distance between predictions and actual values.

Residuals: The Errors

The difference between actual and predicted values is called a residual.

Multiple Features

Real-world predictions often use multiple inputs.

When to Use Linear Regression

Key Takeaways

• Linear regression finds the best straight line through your data
• The equation is y = mx + b (slope and intercept)
• Residuals are the errors between predictions and actual values
• The best line minimizes squared residuals
• Can use multiple features for more complex predictions
• It's simple, interpretable, and a great starting point

Next, we'll learn how linear regression finds that best line using cost functions and gradient descent!