[R] regression with a*cos(angle+phi)+b

[Peter Dalgaard]

Jorge Ivan Velez wrote:
> Good morning Markus,
> 
> Perhaps ?nls might be useful in this case.


Or consult a compendium and realize that both formulas actually fit the
same class of shifted sinusoidals...  It holds that

cos(v+phi) = cos phi cos v - sin phi sin v

so you can fairly easily find A and phi from the coefficients in
lm(a~cos+sin). The only reason to use nls is that it is a nonlinear
transformation, so a profile-based confidence interval might be more
accurate than one based on the delta method.

> 
> HTH,
> Jorge
> 
> 
> On Mon, Nov 30, 2009 at 7:19 AM, Markus H�ge <> wrote:
> 
>> Hello,
>>
>> the only thing I found to fit a sin/cos is s.th like lm(a~cos+sin) But
>> this is not what I want.
>> I have a magnitude which is sinusoidal with offset and it doesn't start
>> at phi=0.
>>
>> The data is:
>>
>> angle<-c(0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180)
>>
>> Voltage<-c(-45.07, -45.24, -43.61, -40.78, -36.48, -30.92, -23.83,
>> -15.95,  -7.53,   1.06,  11.24,19.85,  27.00,  35.00,  42.90,  49.41,
>> 54.62,  58.54,  60.90)
>>
>> I need an regression with Voltage=A*cos(angle+phi)+B.
>> How does this work? With lm or shall I use twice Fourier?
>>
>> thanks
>>
>> Markus
>>
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> 
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> 
> 
> 
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