This apLet is designed to show visually the process of finding the gradient of the tangent to a curve by finding the limiting gradient of a series of chords.
The user can nominate the left and right ends of the chord and then choose to have the chords drawn either automatically (fast or slow) or with a wait for a key press in between chords. The interval and the gradient are quoted at the top of the screen. 
Three ready made functions are supplied but the user can nominate their own also.


Linear Fit
We all know that the line of regression is chosen so as to minimize the residuals but this is often overlooked in the explanations given to students. This apLet is designed to allow the student to propose a line and then to adjust their line until the quoted sum of squares of residuals is as small as possible.
The arrow keys can be used to move the line up and down and to twist it clockwise or anti-clockwise. The amount of movement is adjustable using the numeric keys. The residuals are shown as vertical lines from the points to the proposed line.
The apLet is a little slow, due to the need to reload the PLOT screen and then to redraw the lines after each key press but gives a very effective illustration of the role of the residual in finding the regression line. This is particularly so when the student choses the "Show true line" option at the end and finds that their line is the same as the true one.

Last modified: 19 Dec 2007                                             Sitemap        Home        Contact Me