Re: Simultaneous nonlinear Regression of two data sets

*To*: mathgroup at smc.vnet.net*Subject*: [mg19469] Re: [mg19440] Simultaneous nonlinear Regression of two data sets*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Sat, 28 Aug 1999 15:53:01 -0400*References*: <199908250525.BAA24759@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Christopher Mack wrote: > > Hello, > > I want to fit two (if it works, I also want to fit threee and four) > mathematical functions to two (in future perhaps three and four) data > sets (gaussian > profiles); each function has eight parameters to fit, but four of them > are the same for all functions. > > I first thought of using the Mathematica-Function "NonlinearRegress"; > but after reading the Online-help I assumed that it only can fit > one function to one data set. > > Is there a functino implemented into Mathematica, which can solve the > described problem ? > > Thanks, > > Christopher Mack, > > Department of Chemical Process Engineering, > Darmstadt University of Technology You might set it up as one large sum-of-squares to minimize in terms of parameters. For a simple example, say you have a model function of the form Exp[a*x] + b*x with data points {x11,y11}, {x12,y12}, ... {x1m, y1m} and another of the form x^a + Log[c+x] with data points {x21,y21}, {x22,y22}, ... {x2n, y1n} (note that we are insisting one parameter be the same for both functions). Then as a reasonable approach you might minimize over {a,b,c} the sum (Exp[a*x11] + b*x11 - y11)^2 + ... + (Exp[a*x1m] + b*x1m - y1m)^2 + (x21^a + Log[c+x21] - y21)^2 + ... + (x2n^a + Log[c+x2n] - y2n)^2 Also, if you can recast as a linear least-squares problem (say, by taking logarithms) then all the better. Daniel Lichtblau Wolfram Research

**References**:**Simultaneous nonlinear Regression of two data sets***From:*Christopher Mack <mack@tvt.tu-darmstadt.de>