On Tue, 27 Apr 2004, Michael Hochster wrote: > In sci.math Phil Sherrod <[EMAIL PROTECTED]> wrote: > > : On 27-Apr-2004, Michael Hochster <[EMAIL PROTECTED]> wrote: > PS1> This isn't a "simple linear regression" problem. It is a nonlinear PS1> regression problem. There are a number of nonlinear regression PS1> programs that can solve your problem for a and b. Here is such a PS1> program that I ran through my NLREG program (http://www.nlreg.com)
MH> Yes, it is a simple linear regression problem: ordinary regression MH> of y on e^-x. As the author of regression software, you should know MH> better. PS> I agree, by transforming the input variables this function is easily PS> converted to a linear regression. But it can be handled more easily PS> and properly as a nonlinear regression where no transformations are PS> required. Remember that fitting a function to a transformed PS> independent variable does not always yield the same fitting PS> parameter results as fitting the function to the non-transformed PS> input -- minimizing the sum of squared deviations for X is not the PS> same as log(X) or sin(X). The difference can be significant. MH> There is a closed form for the a and b minimizing MH> sum[y - a - b*e^(-x)]^2, provided by the usual linear regression MH> formulas. Are you saying it is easier and/or more proper to do a MH> numerical search for a and b? No; he's saying that minimizing sum[y - a - b*e^(-x)]^2 is to minimize the sum of squared deviations from e^(-x), which is not the same thing as minimizing the sum of squared deviations from x. The minima in these two cases do not in general occur at the same value of x, nor do the sums of squared deviations have the same value (nor even the same units). -- Don. ------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
