In sci.math Rod <[EMAIL PROTECTED]> wrote: : "Michael Hochster" <[EMAIL PROTECTED]> wrote in message : news:[EMAIL PROTECTED] :> In sci.math Phil Sherrod <[EMAIL PROTECTED]> wrote: :> :> : On 27-Apr-2004, Michael Hochster <[EMAIL PROTECTED]> wrote: :> :> :> : This isn't a "simple linear regression" problem. It is a nonlinear :> :> : regression problem. There are a number of nonlinear regression : programs :> :> : that can solve your problem for a and b. Here is such a program that : I :> :> ran :> :> : through my NLREG program (http://www.nlreg.com) :> :> :> :> Yes, it is a simple linear regression problem: ordinary regression :> :> of y on e^-x. As the author of regression software, you should know :> :> better. :> :> : I agree, by transforming the input variables this function is easily :> : converted to a linear regression. But it can be handled more easily and :> : properly as a nonlienar regression where no transformations are : required. :> : Remember that fitting a function to a transformed independent variable : does :> : not always yield the same fitting parameter results as fitting the : function :> : to the non-transformed input -- minimizing the sum of squared deviations : for :> : X is not the same as log(X) or sin(X). The difference can be : significant. :> :> There is a closed form for the a and b minimizing sum[y - a - b*e^(-x)]^2, :> provided by the usual linear regression formulas. Are you saying it is : easier :> and/or more proper to do a numerical search for a and b? :> :> Mike
: It is not the method of solving the equations but that is being debated, but : the procedure used to estimate the parameters. Since the parameter estimates provided by Phil Sherrod are exactly what you get from the ordinary regression of y on e^(-x), I don't think you are correct in this. : One method is linear regression which as you point out has a closed form : solution. There are alternatives, many of which make different assumptions : about the form the error takes. Agreed. But no one has stated any assumptions about error structure. And it is the least squares part of ordinary regression, not the linearity of the functional form, that is associated with the assumption of normal errors. Mike . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
