
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 2nd, 2014, 06:58 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, 01:03 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,528 Thanks: 589 
Your main problem would be if cx+d = 0 for some x in the domain.

May 8th, 2014, 01:15 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) 

Tags 
analytical, form, regression, solution 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
analytical solution to BVP with fu'n and 2nd dr'tve of fu'n  munkifisht  Calculus  2  June 13th, 2012 12:02 PM 
is there an analytical solution to (x+a)^g(xa)^g=p*a*x  sciacallojo2  Economics  7  August 9th, 2011 11:37 AM 
poisson pde analytical solution  jangolobow  Calculus  1  April 2nd, 2010 08:51 AM 
Drag force, analytical solution  ask2  Calculus  2  November 13th, 2009 02:08 AM 
OLS Linear Regression Matrix form question  handy11  Algebra  0  December 31st, 1969 04:00 PM 