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From: Elad Steinberg on 5 Apr 2010 13:03
Hi all,
I'm fitting a very basic function 'x+a' to my data set which has some scatter to it. I'm interested in knowing for what range of 'a' does 95% of my data point fall into (meaning what is the minimum and maximum 'a' for which I encompass 95%).
When I click the option of show prediction bounds it appears to show me them correctly but they do not correspond to the 95% confidence of my coefficient given by the fit. How can I find out the coefficients that were used in drawing the prediction bounds?

I'm attaching a link to a print screen of my problem in order to clarify things.
http://img186.imageshack.us/img186/2057/matlabv.jpg

Thank you very much for the help,

Elad
From: Tom Lane on 5 Apr 2010 16:04
> I'm fitting a very basic function 'x+a' to my data set which has some
> scatter to it. I'm interested in knowing for what range of 'a' does 95% of
> my data point fall into (meaning what is the minimum and maximum 'a' for
> which I encompass 95%). When I click the option of show prediction bounds
> it appears to show me them correctly but they do not correspond to the 95%
> confidence of my coefficient given by the fit. How can I find out the
> coefficients that were used in drawing the prediction bounds?
>
> I'm attaching a link to a print screen of my problem in order to clarify
> things.
> http://img186.imageshack.us/img186/2057/matlabv.jpg

Elad, the default output from the PREDINT method, which is what it appears
you have drawn on your figure, is a set of "prediction" bounds for new
observations. The 95% confidence bounds for the coefficients are just that.
In the simple model that you have, these correspond to 95% "prediction"
bounds for the function. Try this for a cfit object in the variable f and
some value x:

A = predint(f,x,.95,'function') % bounds for function
B = predint(f,x,.95,'observation') % bounds for new observation

We would have 95% confidence that the true but unknown function evaluated at
x lies between the limits in A. We would have 95% confidence, loosely
speaking, that a new observation taken at the value x would lie between the
limits in B.

I hope that answers your question. If you are looking for more details on
these calculations, you can edit predint.m or ask a follow-up question.

-- Tom


From: Elad Steinberg on 5 Apr 2010 16:48
"Tom Lane" <tlane(a)mathworks.com> wrote in message <hpdfnl$ig8$1(a)fred.mathworks.com>...
> > I'm fitting a very basic function 'x+a' to my data set which has some
> > scatter to it. I'm interested in knowing for what range of 'a' does 95% of
> > my data point fall into (meaning what is the minimum and maximum 'a' for
> > which I encompass 95%). When I click the option of show prediction bounds
> > it appears to show me them correctly but they do not correspond to the 95%
> > confidence of my coefficient given by the fit. How can I find out the
> > coefficients that were used in drawing the prediction bounds?
> >
> > I'm attaching a link to a print screen of my problem in order to clarify
> > things.
> > http://img186.imageshack.us/img186/2057/matlabv.jpg
>
> Elad, the default output from the PREDINT method, which is what it appears
> you have drawn on your figure, is a set of "prediction" bounds for new
> observations. The 95% confidence bounds for the coefficients are just that.
> In the simple model that you have, these correspond to 95% "prediction"
> bounds for the function. Try this for a cfit object in the variable f and
> some value x:
>
> A = predint(f,x,.95,'function') % bounds for function
> B = predint(f,x,.95,'observation') % bounds for new observation
>
> We would have 95% confidence that the true but unknown function evaluated at
> x lies between the limits in A. We would have 95% confidence, loosely
> speaking, that a new observation taken at the value x would lie between the
> limits in B.
>
> I hope that answers your question. If you are looking for more details on
> these calculations, you can edit predint.m or ask a follow-up question.
>
> -- Tom
>
That is exactly what I needed, Thank you very much Tom!
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