# [R] Non-Linear Regression Problem

Spencer Graves spencer.graves at pdf.com
Wed Apr 14 18:26:51 CEST 2004

```1.  For the equation you mentioned, have you considered the following:

DF <- data.frame(t.=c(1, 4, 16), Y=c(.8, .45, .04))
# I do NOT use "t" as a name, as it
# may conflict with the matrix transpose function.
fit0 <- lm(log(Y)~t.-1, DF)
fit0
Call:
lm(formula = log(Y) ~ t. - 1, data = DF)

Coefficients:
t.
-0.2012
################

If this is the problem you really wanted to solve AND you honestly
need NONLINEAR least squares, I would expect that (-0.2) should provide
a reasonable starting value for nls:

> fit1 <- nls(Y~exp(-THETA*t.), data=DF, start=c(THETA=-0.2))
> fit1
Nonlinear regression model
model:  Y ~ exp(-THETA * t.)
data:  DF
THETA
0.2034489
residual sum-of-squares:  0.0003018337
>

2.  Alternatively, you could compute the sum of squares for all
values of THETA = seq(0, .01, 100) in a loop, then find the minimum by
eye.

3.  If this is just a toy example, and your real problem has
several parameters, "expand.grid" will produce a grid, and you can
compute the value of your function and the sum of squares of residuals
at every point in the grid in a single loop, etc.

hope this helps.  spencer graves

WilDscOp wrote:

> Dear all,
>
>     I was wondering if there is any way i could do a "Grid Search" on
> a parameter space using R (as SAS 6.12 and higher can do it) to start
> the Newton-Gauss Linearization least squares method when i have NO
> prior information about the parameter.
> W. N. Venables and B. D. Ripley (2002) "Modern Applied Statistics with
> S", 4 th ed., page 216-7  has a topic "Self-starting non-linear
> regressions" using negexp.SSival - but i can not solve my hypothetical
> problem using that - my problem is :
>
> Y = EXP(-(THETA * t)) with data below for estimating THETA:
>
> t        Y
> 1    0.80
> 4     0.45
> 16     0.04
>
> Whatever i could do, is in
> http://www.angelfire.com/ab5/get5/nonlinear.PDF
>
> Any response / help / comment / suggestion / idea / web-link / replies
> will be greatly appreciated.
>
>
> _______________________
>
> Mohammad Ehsanul Karim <wildscop at yahoo.com>
> Institute of Statistical Research and Training
> University of Dhaka, Dhaka- 1000, Bangladesh
>
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