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Topic: Lin. regression, probability that a sample belongs to the data set?
Replies: 6   Last Post: Aug 14, 2014 9:13 PM

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 John D'Errico Posts: 9,127 Registered: 12/7/04
Re: Lin. regression, probability that a sample belongs to the data set?
Posted: Aug 12, 2014 9:03 AM

"Aino" <aino.tietavainen@removeThis.helsinki.fi> wrote in message <lscp64\$nqi\$1@newscl01ah.mathworks.com>...
> Hi all.
>
> I have a simple linear regression with x and y data. Now, if I take a sample, say (x1, y1), how do I get some probability that the sample belongs to the regressed data at hand?
>
> In another words, it is possible (somehow..) to get for example 95% prediction bounds/intervals to the regressed data, but how do I do the opposite, how do I get the "percentage" for a certain (x1, y1)?
>
> The bigger picture (for those who are interested): I have two sets of data and two regression lines, and I have to decide to which data set the sample belongs to. Linear discriminant analysis is not an option here, but anything "ANCOVA with unequal slopes" would be interesting.
>

So given a linear regression, you can compute an uncertainty
around the line at any point x. This would be in the form of a
normal distribution, with mean at the predicted value of the line,
and a variance around that point in y. The variance will be largest
near the ends of the line of course.

So given that (x,y) pair, you will have a normal distribution. Use
the normal CDF to convert that to a probability score. You will
get different probabilities for each line of course, so the line
with the better score "wins".

A quick search online shows at least a few sites site with sufficient
information provided to do the computations, here:

http://science.widener.edu/svb/stats/regress.html

or here:

http://www.mpia-hd.mpg.de/~calj/statistical_methods_ss2013/lectures/05_regression.pdf

Should be easy enough.

John

Date Subject Author
8/12/14 Tikkuhirvi Tietavainen
8/12/14 John D'Errico
8/12/14 Jeff Miller
8/13/14 Tikkuhirvi Tietavainen
8/13/14 Jeff Miller
8/14/14 Tikkuhirvi Tietavainen
8/14/14 Jeff Miller