# Fitted curve to measured data - statistical properties of the fit error

1. Feb 4, 2012

### cmunikat

Dear all,

I have a set of measurements {xm(Ti,mi)=x(Ti)+e(Ti,mi)}, where:

_xm is the measured value
_x is the actual value
_e is a random measurement error for the measurement mi
_Ti is a parameter

I need to fit a curve to this data by some method. For example, if I use least squares best fit, the following value D is minimized:

D=Ʃ Di2

Where:
_Di=X(T=Ti)-xm(Ti)
_X is the continuous curve

Now, I define the error between the curve X(T) and the actual data x(Ti):

ef(Ti) = X(T) - x(Ti)

And here is the problem:

I need to know, for any parameter Tj, the mean and variance of this error ef(Tj), in terms of the mean and variance of the measurement errors "e(Ti,mi)" defined at the beggining.

Cmunikat