Understanding Linear Regression

We use a powerful mathematical tool called linear regression to make predictions in machine learning. For example, imagine you have data points showing how many hours students studied and their test scores. Linear regression helps you find the line best describes the relationship between study time and test performance. This line can help predict how well someone might do based on their study hours. Think of linear regression as drawing the "best fit" line through many points on a graph. The goal is to draw one smooth line that passes as close as possible to all the points.

A Bit of History

Linear regression may sound modern, but it's been around for over 200 years! It was first used by mathematical giants like Carl Friedrich Gauss (1795). Gauss, also known as the "Prince of Mathematics," used this method to study something incredibly ambitious - the movement of planets and stars. Imagine using math to understand the universe - precisely what he did!

What's fascinating is that this same mathematical tool is still used today for things like:

• Predicting housing prices
• Forecasting sales for businesses
• Understanding climate patterns
• Analyzing social media trends

Even though it was invented centuries ago, linear regression remains one of the most practical and widely-used tool in artificial intelligence and machine learning.

Recall Supervised Learning

Recall that in machine learning, we typically deal with two main types of prediction problems:

Classification: When we're trying to predict a category

Example: Predicting if an email is spam or not spam In math terms, we use a label as $y \in \{-1, +1\}$ for two categories The function making these predictions is called a "classifier."

Regression: When we're trying to predict a number

Example: Predicting someone's height (5'8", 6'2", etc.) In math terms, we use a label $y \in \mathbb{R}$ (meaning $y$ can be any real number). The function that makes these predictions is called a "regressor."