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May 2nd, 2014, 06:58 AM   #1
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Is there an analytical solution for a regression of this form?

Hi guys,

I know I can run a quadratic regression and get an analytical solution if my function looks like this:

$\displaystyle y = f(x) = a*x^2 + b*x + c$


However, the problem I'm working on involves following functional relationship:

$\displaystyle y = f(x) = (a*x^2+b*x)/(c*x+d)$

Is it still possible to get an analytical solution out of this? Possibly also with quatratic/polynomial regression?
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May 2nd, 2014, 01:03 PM   #2
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Your main problem would be if cx+d = 0 for some x in the domain.
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May 8th, 2014, 01:15 AM   #3
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The fitting of this pattern of function is possible if you consider the equation :
a*x²+b*x-c*y*x-d*y = 0
Of course, one of the four parameters must be arbitrary fixed and the regression will be carried out for three parameters only (because proportionality). This is a kind of problem of "equation fitting" or of "implicit function" fitting. For example, see Section 5 in the paper :
Régressions coniques, quadriques, circulaire, sphérique
(written in French, but the equations are undertandable in any language)
JJacquelin is offline  
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