If you finish all the above and are interested in
the direct numerical solution discussed in the last part,
you are encouraged to tackle one of the following tasks
for a maximum of 10% extra marks:
- For the simple first-order polynomial fit, see if you can find
an analytical expression for the "1 sigma" (one standard deviation,
as defined above) uncertainties in each of the two fit parameters.
Implement this in python and see if it reproduces the uncertainties
quoted by the other fitting applications. OR,
- try to extend the closed-form solution from a first-order polynomial
theory function to a second order (quadratic) function. OR,
- if you're very ambitious, try to generalize this approach
to arbitrary order. [Only for Mathematicians!]
Jess H. Brewer
2010-10-11