Dear 'R' Users,

I have CO2 timeseries which I want to fit with fourth harmonic function and
then would like to compute residuals.
I tried with two option but not sure which one is correct, kindly any one
can help correcting me:

#
#I would like to fit a model with Fourth harmonic function as:

#m(t)=a+bt+ct^2+c1sin(omega1*t)+d1cos(omega1.t)+c2sin(omega2.t)+d2cos(omega2.t)+c3sin(omega3.t)+d3cos(omega3.t)+c4sin(omega4.t)+d4cos(omega4.t)
# In my data 'file' I have two variable 'co2obs' and 'time'
# SO above function in R will look like EITHER as:

testfit<-lm(co2obs~1+time+(time^2)+sin(2*pi*time)+cos(2*pi*time)+sin(4*pi*time)+cos(4*pi*time)+sin(6*pi*time)+cos(6*pi*time)+sin(8*pi*time)+cos(8*pi*time),data=file)
#RESIDUALS COMPUTING for above data fit
testfit$residuals

OR as:

testfit<-lm(co2obs~1+time+I(time^2)+sin(2*pi*time)+cos(2*pi*time)+sin(4*pi*time)+cos(4*pi*time)+sin(6*pi*time)+cos(6*pi*time)+sin(8*pi*time)+cos(8*pi*time),data=file)
 #RESIDUALS COMPUTING for above data fit
testfit$residuals

NOTE: The 'third' term (ct^2) in both above is wrriten differently, rest
terms are same.

Kindly advise which one in above is correct, OR both are wrong ?

Great Thanks,

Regards,
Yogesh

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