I think I made the formulation too wordy in previous
post.  

Let me try this simple question:

When one wishes to do a (multi)linear regression on a set of 
observed data, and one is in the (unusual) position of possessing
a set of sample standard deviations (of varying degrees of f.) 
at each value of the "explanatory" variable, how does one
determine whether one ought or ought not to solve the weighted
least squares problem using those sample standard deviations?

What is the usual decision test for "heterscedasticity" *before* one
solves the regression system?  What do people do in practise?

Thank you,
Ron


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