Simple linear regression – part 1

08/31/2020

Instructions:

Use the left and right arrow keys to navigate the presentation forward and backward respectively. You can also use the arrows at the bottom right of the screen to navigate with a mouse.

FAIR USE ACT DISCLAIMER:
This site is for educational purposes only. This website may contain copyrighted material, the use of which has not been specifically authorized by the copyright holders. The material is made available on this website as a way to advance teaching, and copyright-protected materials are used to the extent necessary to make this class function in a distance learning environment. The Fair Use Copyright Disclaimer is under section 107 of the Copyright Act of 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research.

Outline

  • The following topics will be covered in this lecture:

    • Linear models
    • Simple linear regression
    • Basic regression assumptions
    • The process of creating a regression model

Introducing linear models

Image of 2-dimensional plot with one data point.
  • In past mathematics courses, we have seen many examples of linear models.
  • Suppose that we wish to model a relationship between two variables, \( x \) and \( y \) to the left.
  • We will call \( y \) a dependent variable, or the response variable.
  • On the other hand, we will call \( x \) an independent variable, an explanatory variable or a predictor variable for the response.
  • Q: can you propose a valid linear model for the relationship between the response and the predictor?

Introducing linear models – continued

Image of 2-dimensional plot with one data point.
  • A: actually, any line that passes through the point is a valid linear model.
  • Particularly, this relationship is underconstrained and there exists infinitely many choices of linear models;
    • given the current data, any choice is as valid as any other.

Introducing linear models – continued

Image of 2-dimensional plot with two data points.
  • Q: given the data on the left, can you propose a valid linear model for the relationship between \( x \) and \( y \)?

Introducing linear models – continued