A weighted straight-line fit to data points gives a minimised for degrees of freedom

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Data analysis and model fitting in the laboratory

Mathematical Methods for Physics, Ch Estimation, fitting and hypothesis testing

Problem

A weighted straight-line fit to

N=20

data points gives a minimised

\chi^2=6

for

\nu=20-2=18

degrees of freedom, and an intercept

a=3.20\pm0.05

(one sigma). Someone argues: “(i) Since

\chi^2=6

is much smaller than the number of points, this is an excellent fit, better than one could normally expect. (ii) The interval

3.20\pm0.05

means there is a

68

per cent probability that the true intercept lies between

3.15

and

3.25

.” (a) Find the error in claim (i), using the expected value and standard deviation of

\chi^2

for this

\nu

. (b) Find the error in claim (ii), and state what the quoted interval actually asserts.

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