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Outline

In this week we will study regression, a supervised learning problem, and a simple yet powerful ML technique called linear regression that tries to solve the problem. Specifically, we will try to answer the following questions:

  • What is a linear regression model?
  • How do we solve for \(\theta\) in the equation \(X\theta = 0\)?
  • How do we solve for \(\theta\) in the equation \(X\theta = y\)?
  • How do we solve for \(\theta\) in \(X\theta \approx y\)?
  • What does a linear model look like?
  • Geometrically, what is the relationship between the approximation \(X \hat{\theta}\) and the vector \(y\)?

We will be working with a labeled dataset of the form \((X, y)\).