“Theory Behind Linear Regression”
Theory Behind Linear Regression
Aug 8, 2012
- This online applet demonstrates visually the theory behind finding the least squares regression line from generated data and how that compares to a hypothetical “true line” from which the data was generated.
- Type of Material:
- Recommended Uses:
- This can be used either as a demonstration tool in class or as a “prelecture” for students to listen to before class on this topic. There is a short 6 minute lecture associated with the applet, so that students can explore the applet on their own.
- Technical Requirements:
- Browser required for the website. Works in Firefox, Safari, and Chrome. If using Internet Explorer, you must have Java installed. Speakers are also necessary since there are audio files on the site.
- Identify Major Learning Goals:
- The applet provides a comparison between a hypothetical “true line” from which the data was generated and the least squares regression line that is derived from the data that is actually generated. The applet also visually presents the concepts of residuals, random errors, sum of squares, and minimizing the sum of squares.
- Target Student Population:
- Introductory level statistics students could use this to understand the basics of regression, but it appears this would be best suited for more advanced students who are just beginning to study regression.
- Prerequisite Knowledge or Skills:
- Students should be able to read a scatterplot.
- Like the other applets by this author, this is a straightforward and easy to use applet that clearly and simply demonstrates the concept presented. The audio file is a very nice supplement in that it explains what the student should do and describes what they are seeing on the screen.
- Although it is understood that the point is to have students focus on theory here, there is no context for the data and points that are being simulated. The idea of a “true line” from which the points are coming from is an unusual approach to this reviewer and the author does not provide general linear equation anywhere on the page to represent the true line. This would provide an introduction to the concept of least-squares, but the student would need other instruction to actually create the least-squares regression line and interpretation of the information.
- This applet allows students to explore the connection between random errors, residuals and the least squares regression line, which makes it more likely they will remember the concept well past the assignment and/or the course. It also connects the idea of the sum of squares to the least squares regression again (as in a previous applet by this author), and reinforces this concept with the repetition. The study of linear regression is common in introductory statistics courses and the site provides background information on what least-squares means.
- As a demonstration tool, this would be a useful tool. However, in terms of writing assignments and easily assessing students' understanding of the concept presented, that would be more difficult. There is not a way to enter student data so it would be difficult to use for an assignment. As designed, students clik on buttons as requested in the accompanying audio. The assignment link on the page gives the message "Oops! This link appears to be broken."
- The design of website is very clean and simple.
- The buttons on the page work, but are not completely displayed to the user. This problem occurs in all browsers. Resizing the window does not fix this problem. Also, the "new" button provides a new set of data points, but there does not appear to be a way to allow the user to move points to see changes in the least-squares line.
- Other Issues and Comments:
- Does not work on iPad
- Creative Commons: