Least-square fitting to data (sine function) : what is the error of the derived fit parameters? I have a set of data. I want to fit it to a sine function of the form :
\begin{equation}
f(x)=A sin(\omega x+B)+C
\end{equation}
I use the least-square method to find the appropriate fit-parameters which are $A$, $B$ and $C$. In this method, each term of the cost-function has a weight calculated from the error-bar of each point in my dataset.
Now I want to calculate the visibility $V$ for the fitting curve. The visibility is defined by :
\begin{equation}
V=\frac{A}{C}
\end{equation}
I obtain a good value of $V=0.95$, but now I want to know how to calculate $\Delta V$, the error of the visibility. To get it, I need to know $\Delta A$ and $\Delta C$.
Do you know how to do it ?
EDIT : Some people suggested to post the data, so here is the figure on the link below.
Figure representing the data
Basically, each point has a poissonnian error bar $\Delta Y= \sqrt{Y}$. I did the weighted least-square method to obtain my fit-function which is the solid line you can see on this plot (there is two data-set actually, red and blue). The area in red/blue represent standard deviation of the distance in errorbar unit from the datapoints to the fit, multiplied by the poissonian error $\sqrt{Y}$ [I don't know if this is okay, maybe it's false to do like that].
 A: This fitting problem can be equivalently rewritten as fitting function of form:
$$ f(x) = K \sin(\omega x) + L \cos(\omega x) + C $$
And your original $A$ is just $A =\sqrt{K^2+L^2}$
This reduces it to just ordinary least squares problem. We get least squares estimators for $K,L$ from the equation 
$$\begin{bmatrix}
           K \\
           L \\
           C
         \end{bmatrix} = (X^TX)^{-1}X^{T}y$$
Where $X$ is matrix formed by values of $\sin(\omega x),\cos(\omega x), 1$ evaluated at consecutive values of $x$ coordinate of your observations and $y$ are values of said observations.
This way you can see that $K,L$ are some linear functions of $y_i$. I'm not sure what Poissonian error bar is but in general finding variance of sum of variables can be done if we know variance of individual variables.
Assuming $y_i$ uncorrelated we get:
$$ {Var}(K) = (1,0,0) . (X^TX)^{-1}X^{T} . Var(y_i)$$
and analog for $L$.
And $C$ is even simpler as it is just the mean value of the observations.
This way we have found $Var(K),Var(L),Var(C)$ assuming these are small enough you can just propagate error in the formula
$$ V = \frac{\sqrt{K^2+L^2}}{C} $$ 
either by direct computation or using this helpful lookup.
