A fit of two parameters (in cm) and (in ms) produces a contour map of

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory

Computational Physics, Ch Finding the best parameters: minimisation and fitting

Problem

A fit of two parameters

p

(in cm) and

q

(in ms) produces a contour map of

\chi^2

. The

\chi^2_{\min}+1

contour is an ellipse whose projection onto the

p

-axis runs from

3.05\,\mathrm{cm}

3.35\,\mathrm{cm}

, and whose projection onto the

q

-axis runs from

0.61\,\mathrm{ms}

1.03\,\mathrm{ms}

. The ellipse is tilted so that, moving along it, an increase in

p

is always accompanied by a decrease in

q

. ((a)) Read off the standard uncertainty

\sigma_p

from the width of the ellipse's projection onto the

p

-axis. ((b)) Read off

\sigma_q

in the same way. ((c)) State whether the correlation coefficient between

p

and

q

is positive or negative, and give that sign as

+1

-1

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