title: Gnuplot Curve Fitting With Time-Offset
body: <p>I have an issue with curve fitting process using Gnuplot. I have data with the time starting at 0.5024. I want to use a linear sin/cos combo to fit a value M over time (M=<em>a+bsin(wt)+ccos(wt)</em>). For further processing I only need the c value.
  My code is</p>
  
  <pre><code>f(x)=a+b*sin(w*x)+c*cos(w*x)
  fit f(x) "data.dat" using 1:2 via a,b,c,w
  </code></pre>
  
  <p>the asymptotic standard error ist 66% for parameter c which seems quite high. I suspect that it has to do with the fact, that the time starts at 0.5024 instead of 0. What I could do of course is</p>
  
  <pre><code>fit f(x) "data.dat" using ($1-0.5024):2 via a,b,c,w
  </code></pre>
  
  <p>with an asymptotic error of about 10% which is way lower. The question is: Can I do that? Does my new plot with the time offset still represent the original curve? Any other ideas?</p>
  
  <p>Thanks in advance for your help :-)</p>