What Are Confidence Intervals in Curve Fitting Analysis?

[pergradus]

Hello, I'm having trouble understanding the concept of confidence intervals...

I have written a program using MatLab which takes set of data points and using nonlinear least squares it produces a curve to fit these data points, and in the process calculates three parameters that determine the shape of the curve.

In trying to compute the error or uncertainty in these parameter values, I'm using one of the values the curve fitting function returns, which is a confidence interval. The problem is, I don't actually understand what this value means...

Is it a percent? Is it a difference? How does it relate to the physical measurement in my data? Would greatly appreciate if someone could explain, thanks.

 

[Stephen Tashi]

Only the documentation of the program can tell you what the program means by a confidence interval. The definition of "confidence interval" in traditional statistics will give you no confidence! Do you understand that definition?

One commonly used method is to assume the differences in the y coordinate of the data and the y coordinate of the curve are independent samples from the same normal distribution. The standard deviation of the distribution can be estimated by using the "errors" between the data and the curve. Plus or minus a given distance in y ( not percentage distance) will correspond to plus or minus a certain number of standard deviations. The program may pick a certain multiple (like two or four standard deviations) and tell you the distance corresponding to that multiple.