"Clint Cummins" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > Phil Sherrod <[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) > > >On 27-Apr-2004, Michael Hochster <[EMAIL PROTECTED]> wrote: > >> 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. > > Phil Sherrod <[EMAIL PROTECTED]> wrote: > >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. > ?? A linear regression is easier than a nonlinear regression, > in general. For example, sometimes nonlinear regressions have multiple > local optima. A linear regression has a single answer (except when > there is perfect collinearity, which should be detected automatically). > > >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. > What you are saying here only makes sense if you believe there is > some type of measurement error in X. If X is measured without error, > then all you minimize is the sum of squared deviations in *Y*, not *X*. > If X is measured with error, you will need additional information to > identify the model. Namely, some information on the variance or relative > variance of the errors in X. I didn't see any such suggestion or > information in the original post. > > Clint Cummins > (TSP International)
I haven't looked at the data for this particular model but in general I would expect the errors in Y to be proportional to Y rather than independent. If this is the case linear regression is not your best estimator irrespective of errors in X. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
