Standard deviations and Confidence intervals with respect to errors
- To: mathgroup at smc.vnet.net
- Subject: [mg101766] Standard deviations and Confidence intervals with respect to errors
- From: Alexey <lehin.p at gmail.com>
- Date: Thu, 16 Jul 2009 08:20:48 -0400 (EDT)
Hello,
I have a set of independent observations of two values (Y,X) with
known (and different) standard errors in both values for each
observation. These valueses are linearly dependent:
Yi=a*Xi+b
I need to calculate the unknown parameters {a,b} and confidence
intervals with respect to known standard errors of observations. As I
understand, the standard Mathematica's function LinearModelFit is
designed only for the case when all observations have equal standard
deviation and are normally distributed. In my case it is known only
that all observations have the same distribution that is supposed to
be nearly-normal. But standard deviations for observations are
significantly different and known.
And another question: how in this case the term "standard deviation"
may be defined and calculated?
Can anybody help me?