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# Peer Review

## Least Squares Applet

by Dwight Lahr , Don Kreider

## Ratings

### Overall Rating:

Content Quality:
Effectiveness:
Ease of Use:
 Reviewed: Jun 29, 2008 by Mathematics Overview: Quoted from the site: This applet explores fitting a polynomial p(x) of degree n to a given set of data points. It computes the best least squares approximation to the data, "best" in the sense that SUM (p(xi) - yi)^2 is minimized. The applet provides controls for choosing the degree n, setting the precision of all displayed numbers, selecting and deselecting data points, and editing the data list. It also allows for entry of your own custom polynomial and computing its least squares error. Learning Goals: Using experimentation and visualization to facilitate an understanding of fitting a polynomial to a set of data. Target Student Population: Students taking a first-year course in Calculus. Prerequisite Knowledge or Skills: Students should be familiar with the method of least squares. Type of Material: Simulation. Recommended Uses: classroom demonstration or guided exercises. Technical Requirements: A Java-enabled Web browser.

### Content Quality

Rating:
 Strengths: This applet is part of an excellent mother site called Principles of Calculus Modeling: An Interactive Approach (http://www.merlot.org/merlot/viewMaterial.htm?id=297526). However, the applet can easily stand alone for the purpose of classroom demonstration or tutorial. The applet allows the user to specify the data points and the maximal degree of the fitting polynomial. The user can even experiment by choosing his own polynomial and testing the accuracy of its fit. The graph has a very useful zoom feature, the data points are prominently displayed, and both the best fitting polynomial and the user-defined polynomial are displayed graphically. The least squares error is calculated for both polynomials. All of this is contained in a colorful and well-designed user interface. Concerns: None.

### Potential Effectiveness as a Teaching Tool

Rating:
 Strengths: This applet should be quite useful for purposes of classroom demonstration of the concept of fitting a polynomial to a set of data. Also, the instructor could easily design some guided exercises for this applet or assign it as a tool for a take-home project. One such exercise is provided in the applet. Concerns: None.

### Ease of Use for Both Students and Faculty

Rating:
 Strengths: The applet is quite intuitive. Use of the applet is thoroughly explained. Also, some of the theory behind the least squares method is presented. Concerns: The site could use a title and a hyperlinked navigation structure but this is rather a design suggestion.
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