# [R] fit data to y~A+B*sin(C*x)

Berend Hasselman bhh at xs4all.nl
Tue Feb 14 16:24:11 CET 2012

```On 13-02-2012, at 23:54, Jonas Stein wrote:

> I want to fit discrete data that was measured on a wavegenerator.
> In this minimal example i generate some artificial data:
>
> testsin <- 2+ 5 * sin(1:100) #generate sin data
> testsin <-  testsin+ rnorm(length(testsin), sd = 0.01) #add noise
>
> mydata <- list(X=1:100, Y=testsin) # generate mydata object
>
> nlmod <- nls(X ~ A+B*sin(C* Y), data=mydata, start=list(A=2, B=4, C=1), trace=TRUE)
>
> # this nls fit fails.

What do you mean by "fail"
> nlmod
Nonlinear regression model
model:  X ~ A + B * sin(C * Y)
data:  mydata
A       B       C
50.7553  0.6308  0.8007
residual sum-of-squares: 83308

Number of iterations to convergence: 24
Achieved convergence tolerance: 7.186e-06

Results don't seem to look ok.
But I think you made a small mistake in the formula.
The argument to sin in testsin is 1:100 but that's not what you are giving nls.

Try this

> nlmod <- nls(Y ~ A+B*sin(C* X), data=mydata, start=list(A=2, B=4, C=1), trace=TRUE)
50.30593 :  2 4 1
0.01014092 :  2.0003732 5.0002681 0.9999979
0.01014016 :  2.0003732 5.0002681 0.9999983
> nlmod
Nonlinear regression model
model:  Y ~ A + B * sin(C * X)
data:  mydata
A B C
2 5 1
residual sum-of-squares: 0.01014

Number of iterations to convergence: 2
Achieved convergence tolerance: 1.201e-07

Looks better?

Berend

```