Among other interesting queries, Pavlos wrote:
"I would like to know how I can estimate the
peaks for mobile and size"
I suppose you are searching for the turning point equation.
As you are surely alrady aware of, a quadratic function (y=ax^2 + bx) has a
maximum or minimum at x=-b/2a. Then, my poor maths stops.
Some days ago Richard Williams pointed out on the list is (beneath reported)
link on some very interesting stuff on Nonlinear relationships.
http://www.nd.edu/~rwilliam/stats2/l61.pdf
I am sure that his teaching-notes will be more useful that my scant advice!
Kind Regards and All the Best for the New Year,
Carlo
-----Messaggio originale-----
Da: [email protected]
[mailto:[email protected]] Per conto di Pavlos C. Symeou
Inviato: venerdì 2 gennaio 2009 10.29
A: [email protected]
Oggetto: st: Estimating peak points from regressions
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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