Uncertainties and variances

[m-wells]

I believe there is a typo in

DataAnalysisRecipes/straightline/straightline.tex

Line 370 in 710a6c9

When the uncertainties are Gaussian and their variances $\sigma_{yi}$

which should be

    When the uncertainties are Gaussian and their variances $\sigma_{yi}^2$

I also found this problem to be poorly worded

DataAnalysisRecipes/straightline/straightline.tex

Lines 1767 to 1774 in 710a6c9

	\begin{problem}\label{prob:chi2}
	Re-do the fit of \problemname~\ref{prob:easy} but setting all
	$\sigma_{yi}^2=S$, that is, ignoring the uncertainties and replacing
	them all with the same value $S$. What uncertainty variance $S$ would
	make $\chi^2 = N-2$? Relevant plots are shown in
	\figurename~\ref{fig:chi2}. How does it compare to the mean and
	median of the uncertainty variances $\allsigmay$?
	\end{problem}

The statement

setting all $\sigma_{yi}^2=S$, that is, ignoring the uncertainties and replacing them all with the same value $S$

is not self-consistent.
I believe it should read as

\begin{problem}\label{prob:chi2} 
 Re-do the fit of \problemname~\ref{prob:easy} but setting all 
 $\sigma_{yi}=S$, that is, ignoring the uncertainties and replacing 
 them all with the same value $\sqrt(S)$.  What uncertainty variance $S$ would 
 make $\chi^2 = N-2$?  Relevant plots are shown in 
 \figurename~\ref{fig:chi2}.  How does it compare to the mean and 
 median variance of the uncertainty $\allsigmay$? 
 \end{problem} 

[jobovy]

I don't think this is correct that we set sigma_y equal to S in this exercise (exercise 11 in the arXiv version). The code that produces these figures is here (we re-numbered the exercises after writing the code) and you can see that we set the data covariance to S x identity matrix as stated in the problem.

[m-wells]

@jobovy You are correct and I was in mid edit correction as I was looking my work. I still think the wording is a bit unclear though.

[m-wells]

@jobovy I have edited my initial comment.

[m-wells]

My confusion essentially boils down to two typos which I have fixed in the PR.