Physics 114: Lecture 16 Linear and Non-Linear Fitting. Dale E. Gary NJIT Physics Department. Reminder of Previous Results. Last time we showed that it is possible to fit a straight line of the form to any data by minimizing chi-square:
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Dale E. Gary
NJIT Physics Department
to any data by minimizing chi-square:
Note, if errors si are all the same, they cancel, so can be ignored.
p =2.0661 2.8803 % in this case, fit equation is y = 2.8803 + 2.0661x
points have a scatter of
s = 0.3 around the fit,
as we specified above.
include ‘normal’ distribution type
% circshift() has the effect of swapping the order of p elements
n = N – 2 = 24 in this case. Since si is a constant 0.3, we can bring it out of the summation, and calculate
ans = 24.9594
which is about unity for a good fit. In this case, cn2 = 24.9594/24 = 1.04. If we look this value up in table C.4 of the text, we find that P ~ 0.4 which means if we repeated the experiment multiple times, about 40% would be expected to have a larger chi-square.
after some algebra (see text page 109), we have