Re: OLS question

On 4/14/2006 10:21 PM, DAVID A MCCUTCHAN wrote:
Embarassed to ask this, but.. .
Let the data points for a regression each have different uncertainties, and
even different pdfs.
I believe OLS fits the means of the data points. But in principle
shouldn't the fit for a point involve squaring differences from the fitted
line
to a collection of y values constituting the pdf distribution for that
point?


Dave



There are many ways to fit a line through data. OLS is just one of them. It depends on the assumptions you want to make.

You can use OLS with any data set, regardless of the distribution of the errors (not the distribution of the original data points); however if you do so the fit may not be optimal. OLS is an optimal fit when the errors are iid normal. There is a weighted version of OLS which accounts for errors with differing distributions, but the errors must still be normally distributed for the fit to be optimal.

Regarding your comment that a "fit for a point involve squaring differences from the fitted line to a collection of y values consituting the pdf distribution for that point" -- in the OLS case, regression is implicitly doing that assuming a normal pdf. If you have a different pdf, there are other ways to accomplish a fit (maximum likelihood comes to mind)

--
Paige Miller
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If you get the choice to sit it out or dance,
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