st: Estimating peak points from regressions

["Pavlos C. Symeou" <p.symeou@jbs.cam.ac.uk>]

Dear Statalisters,

First allow me to wish you a Happy New Year.

I am estimating a regression model where the dependent variable is the 
number of fixed telephony lines (fixed) regressed on (among others) the 
number of mobile subscribers (mobile), the square of this variable 
(mobile_sq), a variable that measures economy size (size), and its 
square (size_sq). Inclusion of the squares of mobile and size intends to 
examine whether the relationships between mobile and fixed and/or size 
and fixed are non-linear. Running the model gives me positive 
coefficients for mobile and size and negative coefficients for mobile_sq 
and size_sq. This would imply that the positive effects of the former 
reach a peak  and thereafter the relationship becomes negative specified 
by their respective squares. I would like to know how I can estimate the 
peaks for mobile and size. Namely, a) up to which level does mobile 
telephony go in tandem with fixed telephony; b) what is the economy size 
that is more conducive to increases in fixed telephony? All variables 
are continuous.

If the estimation of these two peak points is possible algebraically, is 
there a way to illustrate this graphically?

Best wishes,

Pavlos

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