Choosing response and predictors 
Information on the Girth (), Height () and Volume () for 31 cherry trees
yielded the following correlations : $r_{12}$ = 0.519,  $r_{23}$= 0.598 and  $r_{13}$= 0.967. If you were asked to setup a regression choosing a certain characteristic as the response
and the other two as predictors, which characteristic will you choose as the
response? Give your comments.

I think we choose Girth and Height as predictors for the response Volume because the correlation between Girth and Height is the least, so we're looking at how these individually affect the Volume (i.e. the factor with which their correlation is more than that between them).
Is my reasoning correct?
This question was asked in the final examinations of the course on Multivariate Data & Linear Models and it had 10 marks. What more should I write?

The data alone does not suggest a model, just a correlation matrix.  What is the purpose of the model, and in what conditions will it be applied?  For example, if the trees are still standing in a grove or forest, it might be useful to estimate their height, based on girth (usually measured at 48" above ground).  Of course, this is an opportunistic dataset collected from a plot of felled cherry trees, so the lumber mill model, volume ~ girth + height may be the one you want.
