A straight line y = mx is to be fitted (by least squares)
to a data set that happens to lie uniformly on a circle
of radius 1 centred at (1,1).
This picture shows the data and the lines for m=1 and m=2/3.
Find the value of m that minimizes the average square distance between the data y value and the y-coordinate of the curve.
Is m=1 optimal?
Solution using maple:
| postscript | maple session file | gif |
Solution using Maxima(aka Macsyma):
| text file
The optimal m is 2/3. Bear this in mind whenever someone uses least squares fitting!