This simulation illustrates least squares regression and how the least squares solution minimizes the sum of the squared residuals. The applet demonstrates, in a visual manner, various concepts related to least squares regression. These include residuals, sum of squares, the mean line, how the line of best fit is determined, and how the line of least squares solution minimizes the sum of the squared residuals.
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Technical Requirements:
Java enabled Internet browser
Content Quality Concerns:
For each use of the applet, the user can generate a unique set of points that are plotted on the scatterplot and a LS line is fit to those points. I ran through 20+ sets of these points and every set had a very distinct positive slope. It would be helpful to see examples with negative slopes, non-linear relationships, etc. It would also be helpful to incorporate the notation version of the formulas as well as the written-out versions.
Content Quality Strengths:
This applet is a great in-class or out-of-class tool for reviewing the concepts behind least squares regression. There is audio and written explanation for understanding the use of the applet.
Ease of Use Concerns:
The engagement could be enhanced with an animation showing a good fit vs. a bad fit to the points. It is left up to the students to find the line, while an animation might give them a better idea about where to start.
Ease of Use Strengths:
Easy to use and the concepts are clearly demonstrated by the applet. The design of the website is very clean and simple.
Potential Effectiveness Concerns:
There could be more detailed steps for the students to follow to elicit "discovery" learning. The audio guides the student through the applet and definitions are written out on the website. However, there could be more detailed "questions" provided that the student needs to investigate.
Potential Effectiveness Strengths:
This allows students to discover why least squares regression is called least squares regression. Students can make and test their own conjectures about which line best fits the data, 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, which often isn't linked for students in a visual manner.
Potential Effectiveness Rating:
4
Source Code Available:
Source Code Available
Intended User Role:
Learner
Teacher
Material Type:
Resource Type:
Statistical Topic:
Cost:
Free for All
Format:
Math Level: