[R] Fit a sine to data

[apjaworski at mmm.com]

Milan,

This is a fairly standard trick.  Let us generalize your equation slightly:

y ~ a + c*sin(x+b)

so the amplitude of the sine wave is adjustable (otherwise, you assume (or
know) that the amplitude is 1).  Then

y ~ a + c*sin(b)*cos(x) + c*cos(b)*sin(x)

or

y ~ b0 + b1*x1 + b2*x2

which is a linear regression form that you can do using the lm function.
After you get b0, b1 and b2 you do

a = b0
b1^2 + b2^2 = c^2*(sin^2(b) + cos^2(b)) = c^2  ====> c = sqrt(b1^2 + b2^2)
b1/b2 = tan(b)  ====>  b = arctan(b1/b2)

Hope this helps,

Andy


__________________________________
Andy Jaworski
518-1-01
Process Laboratory
3M Corporate Research Laboratory
-----
E-mail: apjaworski at mmm.com
Tel:  (651) 733-6092
Fax:  (651) 736-3122


                                                                           
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                                       [R] Fit a sine to data              
             05/23/2008 08:49                                              
             AM                                                            
                                                                           
                                                                           
                                                                           
                                                                           




Dear R-users,

I'd like to fit a sine function to my data. The result should have a format
(and thus the formula, too)

y ~ a + sin(x+b)

where y and x are vectors, and a and b are (yet) unknown values.

The data sets (vectors x and y) are OK, and I can do a simple lm fitting
lm(y~x), or lm(y~I(sin(2*pi*x/360))), succesfully  My issue is that I'm not
able to do the optional linear shift in x (e.g. x+b). What other
possibilities should I use instead of lm? I looked searched the R-seek for
terms: fit, sine, lm, and combinations, but I could not find anything
useful. Anybody would be so kind and point me to the right direction where
I
can find other fitting possibilities?

Thank you for listening and kind answers upfront.

Regards,
Milan

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