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 isosamples 50,50 set contour set cntrparam levels discrete 1,2For Pyplot, see the course notes linked above. You might want to use a smaller value of delta there for better resolution.
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.