Error in estimation with continuous data Is there a way to correlate error in a fit (MSD - mean squared displacement) to the error of the a calculation performed with the parameters associated with the fit?  
My specific problem is dealing with spectroscopic data. I know that many people use spectroscopic techniques to estimate concentrations of different materials, but I would like to know how accurate these measurements can be  (i.e. I would like to get an output something like "species A is $20\% \pm 1\%$ of the sample given").  Further, I would like to know how to deal with very extreme cases, where several different types of materials are present, and may have observables which fall directly on top of each other.  
A simple example may be the following:

You can see there are two species being fit to the data. If the areas are then transformed by calculation into percentages, (i.e. the sample taken is 48% B, 52% A) how can we be sure of this and how accurate is the fit?   I know this will be dependent on the accuracy of the estimate of the positions of these peaks that are (perhaps) given by the user, so I am interested in a method that takes a known error in the parameters (say $\pm 15$ on the x axis for error in the peak center position, +-10 error in the width of the peak, etc.). 
I suspect that the errors will become large when the observables overlap (i.e. the peak centers for two fitting functions are the same).  
In addition, it is possible that these spectra have a large background, which may also have error, affecting all of the other species and their errors.  I am not certain if this background would be treated differently than all of the other species, or if it could be treated within the same algorithm as all of the other species.
To illustrate my point further, here is an image of a spectroscopic measurement of several different materials:

On the top in red is the raw data given by optical absorption (the measured data), while the black is a calculated background, and the blue is a calculated sum of all of the species including the background.
On the bottom, the calculated background is subtracted (blue and red lines now DO NOT include the calculated background), while the several different colored lines below are each individual species being summed up to create the blue line.
These are the calculated measurements I am interested in estimating the error in.
As you can see, the error is enormously large in this example for most of the calculated measurements. Each species may or may not have several 'peaks' associated with it, which can be illustrated by the bolded yellow calculated line.  In addition, you can see that several of the calculated peak centers fall around the same place, so this will likely reduce the certainty that the measurements are correct even if the calculated line falls directly upon the raw data.  
I have calculated the mean squared displacement as a quick estimate of how good the fit is, but I know that this doesn't do anything to address any larger concerns of the actual calculated measurement uncertainty. The most I have really done in statistics is standard deviation and calculations dealing with several measurements, but this is quite different, since it deals with how sure you can be with only one measurement, not seeing differences in multiple measurements. Is this problem solved using confidence intervals and confidence levels?  (Again, I am very new to statistics and have never taken a course on it, so I apologize if this is elementary or trivial)
 A: The following steps will help you calculate an estimated error term in continuous data. Although I deal mainly with psychology research, I think you are looking to calculate an error term and confidence interval. Here is an example I adapted from somewhere else but shows the step by step calculation of a 95% confidence interval.
Let’s assume a sample of 30 (n=30), and that their average score is x̄=118.3, with a standard deviation of 11.4 (SD=11.4). So let’s find the 95% confidence interval for the population mean.
Definition of terms:
a) α = 1 - degree of confidence (you could choose .95, .99, etc.) , so  1 - .95 = .05.
b) Let t(α/2) be the t-value for a two-tailed distribution.
c) x̄ is the sample mean.
So,
Step 1: The maximum error is:
Error = t(α/2) * SD/sqrt(n)
We know that SD = 11.4 and n = 30, but we need t(α/2).
Step 2: To find t(α /2), we look in a Student t distribution table (if your sample (n) is greater than 30 you could use the standard t distribution table) with .05 in two tails and with 29 (that's n-1 or 30-1) degrees of freedom. We get 2.045. You could find this table in online or in the back of most stats text books.
3) Now back to our formula in step 2.
E = 2.045 *11.4/Sqrt(30) =4.256
4) Finally, the interval is:
x̄ + or - E = 118.3 + 4.256 and E = 118.3 - 4.256
You could now say 95 out of 100 times the mean score would fall somewhere between 114.044 to 122.556 of the mean score. 
