# [R] fitting cosine curve

Jim Lemon drjimlemon at gmail.com
Wed Jun 21 02:52:10 CEST 2017

```What I did was to plot your initial values, then plot the smoothed
values and guess the constants. That is, I got an "eyeball" fit to the
smoothed values. As I have described this as "gross cheating" in the
past, you should either split your data, estimate on one subset and
then test on another, or estimate on your data and test on a
replication. If you get pretty much the same values, you can be
reasonably confident that they are reliable.

Jim

On Wed, Jun 21, 2017 at 9:52 AM, lily li <chocold12 at gmail.com> wrote:
> For example, how do you know the value 0.6, and the frequency within cos?
>
> On Tue, Jun 20, 2017 at 5:49 PM, lily li <chocold12 at gmail.com> wrote:
>>
>> Thanks, that is cool. But would there be a way that can approximate the
>> curve by trying more starting values automatically?
>>
>> On Tue, Jun 20, 2017 at 5:45 PM, Jim Lemon <drjimlemon at gmail.com> wrote:
>>>
>>> Hi lily,
>>> You can get fairly good starting values just by eyeballing the curves:
>>>
>>> plot(y)
>>> lines(supsmu(1:20,y))
>>> lines(0.6*cos((1:20)/3+0.6*pi)+17.2)
>>>
>>> Jim
>>>
>>>
>>> On Wed, Jun 21, 2017 at 9:17 AM, lily li <chocold12 at gmail.com> wrote:
>>> > Hi R users,
>>> >
>>> > I have a question about fitting a cosine curve. I don't know how to set
>>> > the
>>> > approximate starting values. Besides, does the method work for sine
>>> > curve
>>> > as well? Thanks.
>>> >
>>> > Part of the dataset is in the following:
>>> > y=c(16.82, 16.72, 16.63, 16.47, 16.84, 16.25, 16.15, 16.83, 17.41,
>>> > 17.67,
>>> > 17.62, 17.81, 17.91, 17.85, 17.70, 17.67, 17.45, 17.58, 16.99, 17.10)
>>> > t=c(7,  37,  58,  79,  96, 110, 114, 127, 146, 156, 161, 169, 176, 182,
>>> > 190, 197, 209, 218, 232, 240)
>>> >
>>> > I use the method to fit a curve, but it is different from the real
>>> > curve,
>>> > which can be seen in the figure.
>>> > linFit  <- lm(y ~ cos(t))
>>> > fullFit <- nls(y ~ A*cos(omega*t+C) + B,
>>> > start=list(A=coef(linFit)[1],B=coef(linFit)[2],C=0,omega=.4)) #omega
>>> > cannot
>>> > be set to 1, don't know why.
>>> > co <- coef(fullFit)
>>> > fit <- function(x, a, b, c, d) {a*cos(b*x+c)+d}
>>> > plot(x=t, y=y)
>>> > curve(fit(x, a=co['A'], b=co['omega'], c=co['C'],d=co['B']), add=TRUE
>>> > ,lwd=2, col="steelblue")
>>> >
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