HP 48G Linear Regression Best Fit Line

[ttw]

The least-squares fit is fairly easy. As one is fitting a quadratic, one can use linear algebra on the derivatives.

Minimizing the sum of absolute values of the vertical distances is non-linear and quite difficult. (Finding the maximum distance isn't easy either.)

One must decide why to use one type of fitting or the other. In many cases, there is little or no error in X values, so the regression of Y on X is reasonable. If the errors of both the X and Y values are similar (as in the already mentioned surveying problems), then minimizing the vertical distances is useful.

http://www.optimization-online.org/DB_FI...6/6065.pdf

This paper gives a method of solving the problem. One of my students chose this as a computer project and he did find a set of third-degree simultaneous equations and used Newton's method on them.