Estimate the value of chi square for this fit to within a few tenths. Do this "by eye". No need for a calculator or program. State the number of degrees of freedom. Explain how you arrived at this estimate.
x y sigma ------------ 4 3 1 5 5 2 6 8 1
Find the best slope \(m<\) and intercept \(b\) from Eqs (15) and (16).
Put your answer in the answer file.
Write the equation for the chisquare surface as a function of the deviation of the parameters from the best fit values. That is, insert the numerical values of the coefficients of Eq (19). Keep it in terms of \(u = \Delta m\) and \(v = \Delta b \).
Please put your answer in the answer file.
For gnuplot, use splot to do it. We want to plot the contours as a function of the deviations \(u = \Delta m \) and \(v = \Delta b\). The following gnuplot commands may also help with splot:
set view 0,0 set contour set cntrparam levels discrete 1,2For Pyplot, see the course notes linked above.
Find the standard deviations in \(m\) and \(b\) by using the maximum and minimum values on the \( \chi^2 - \chi^2_0 = 1 \) contour.
Please give your answer in the answer file.