# Error from calculation of X from Y response in linear regression

#### pom134

##### New Member
Hello, I have what I am pretty sure is a simple problem that I can't get a hold on and could use some help!

I am sampling air and using a gas chromatograph (GC) quantify my results. I want to calculate a total combined error for my final number, but I am stuck on the standard error of the mass that I get back from my GC's calibration's linear regression.

Here's the whole story: I have an instrument that I have calibrated with known concentrations, x, to get instrument responses, y. I perform a linear regression to get an equation, y = mx + b. I take a sample for a measured time at a measured flow rate to get my total volume of air collected. This number has simple errors associated with them that I have not problem combining to get my volume and associated error. I then run the sample on my calibrated GC, get an instrument response, y, then use the equation for the line I got from my linear regression to calculate the mass in the sample, x = (y-b)/m.

So how do I calculate the error associated with that calculated x! The closest I have come is the equation at the bottom of the table in this link:

http://chemlab.truman.edu/DataAnalysis/Propagation of Error/PropagationofError.htm

When I use that, I get reasonable numbers, I was just hoping for a better reference to use. Any ideas?