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st: Regressions with dependent continuous variable with bounded range


From   Suryadipta Roy <sroy2138@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Regressions with dependent continuous variable with bounded range
Date   Sat, 17 Dec 2011 12:15:14 -0500

Dear Statalisters,

I have (more of a statistical) question relating to a query that came
up in the list before:
http://stata.com/statalist/archive/2008-04/msg00603.html

I would very much appreciate some help as to how to interpret the sign
of the coefficient associated with the squared term of an explanatory
variable in such a model. Thus, if the model is of the form: Dependent
continuous variable with bounded range [-3,3] = f(x, x-squared,
controls), and if the sign of the coefficient associated with x is
positive while that with x-squared is negative, is it OK to conclude
that there are diminishing returns associated with x, since it seems
like that this is supposed to happen because of the mode of
measurement of the dependent variable. Any
thought/suggestion/reference to the appropriate literature on this
will be greatly appreciated.

Sincerely,
Suryadipta.
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