Re: Simple error analysis on slopes?

From: Bruce Weaver (bweaver_at_lakeheadu.ca)
Date: 03/16/05 

Date: Wed, 16 Mar 2005 16:33:51 -0500

Paige Miller wrote:

> Bruce Weaver wrote:
>
>> PiMaster wrote:
>>
>>> Paige Miller wrote:
>>>
>>>> Linear regression (see almost any stat text book) will compute the
>>>> errors around a fitted slope determined by a set of data points.
>>>
>>>
>>> So the R and R^2 values are the only method of determining the "fit" of
>>> a slope? What if the original values had a degree of error in them,
>>> and I would like to find out the possible range of values of the slope,
>>> is there a way of determining that range given the original error?
>>>
>>> i.e. The slope has a value of 0.45, but the original data is +/- 0.1
>>> absolute in the x direction and +/- 10% in the y direction, could the
>>> slope be 0.25 or 0.75? And does this change by using log values?
>>
>>
>> Google on "orthogonal regression". This minimizes the squared
>> perpendicular distances from the fitted line rather than the squared
>> vertical distances. In the case of simple regression (one X and one
>> Y), I believe the 1st principal comonent of X and Y gives you the
>> orthogonal regression line.
>
>
> I'm not sure how this applies to the original question, or that it even
> answers the question that the user posed. Could you explain further why
> you think orthogonal regression is appropriate here?

When the OP wrote, "What if the original values had a degree of error in
them?", I took that to mean there are errors in both X and Y. I think
that orthogonal regression (or PCA) is sometimes used in that situation,
  is it not? Or have I got the wrong end of the stick? 

-- 
Bruce Weaver
bweaver@lakeheadu.ca
www.angelfire.com/wv/bwhomedir

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