Content from Introducing Regression Models

Last updated on 2024-03-12 | Edit this page

Overview

Questions

  • What is a Regression Model?

Objectives

  • Explain what a Regression Model is.
  • Recognize a Simple Linear Regression Model.
  • Understand its usages and interpret it in real life context.

What is a “Regression”?

Regression analysis is a core concept in machine learning, specifically supervised learning where our dataset has both input features and output labels. The goal is to determine a relationship amongst variables by analyzing how one affects the others.

The example that we’ll work with in this lesson is related to movies. Imagine if you are a producer who wants to know the success of a movie before it is released. You have a dataset of around 5000 films, containing information on their ratings, popularity, etc… How can we predict the revenue based on the ratings or popularity of a certain film? Understanding regression models may allow you to answer such questions.

Key Points

Definition: Regression models are mathematical methods that predicts a continuous outcome (usually called y) based on the value of one or more predictor variables (x).

Motivation: Determine the nature of the relationship between the two numerical variables and quantify it

What is an SLR?

The most basic regression model and well-known algorithm is the Simple Linear Regression Model (SLR), which we will focus on in this introductory modual.

A linear regression line has an equation of the form \(Y = \beta_1x + \beta_0 + \epsilon\)

\(\beta_1\): slope of line

\(\beta_0\): intercept

\(X\): explanatory variable

\(Y\): dependent variable

\(\epsilon\): difference between our predicted value from the regression line and the actual value

SLR in Action?

Think about a problem in your academic field or everyday life where an SLR model could help you solve?

  • Predict film revenue based on their ratings
  • Predict wine price by its date

How does it apply to a real life scenario?

Now that you know about the components of a simple linear regression model, take some time to think about how it may apply to our movies dataset.

Challenge

Consider 1) ratings and 2) revenues related to movies. How might these two variables fit into an SLR?

Ratings might be seen as \(X\), our explanatory variable, and revenue as \(Y\), the dependent variable. We could construct a linear relationships where ratings are used to predict revenue in the form of \(\hat{Revenue} = \beta_1 ratings + \beta_0 + \epsilon\).

Summary

Key Points

In this episode, we learned what a regression Model, and now can identify a Simple Linear Regression Model in context. In future episodes, we will examine how to actually construct the relationships, by finding \(\beta_1\), \(\beta_0\).