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May 2nd, 2014, 07:58 AM  #1 
Newbie Joined: May 2014 From: Manhatten Posts: 1 Thanks: 0  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? 
May 2nd, 2014, 02:03 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,436 Thanks: 562 
Your main problem would be if cx+d = 0 for some x in the domain.

May 8th, 2014, 02:15 AM  #3 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8 
The fitting of this pattern of function is possible if you consider the equation : a*x²+b*xc*y*xd*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) 

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analytical, form, regression, solution 
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