Regression with different results.

["Lanzafame, Frank" <flanzafame@monroecc.edu>]

Dr. Donald E. Simanek  Internet: dsimanek@eagle.lhup.edu  writes:

> A colleague from chemistry brought to my attention an interesting difference
> in the performance of Microsoft Excel in its Mac and DOS versions. Her
> students were doing a chemistry problem requiring a data set of about 8
> points on which a linear regression was to be done. Our students use both
> Mac and DOS platforms, and our student labs have both. Excel is on both.
> Students got the same answer for the slope of the line, a, but vastly
> different results for the intercept, b. (y = ax + b). 
....
> the two versions seem to be using
> different algorithms for the calculation, and one is faulty.
> My Mathcad manual not only documents the algorithms used, but gives
> references to the literature for each.
....
> My hunch is that the difference is in the software and has nothing to do
> with the relative merits of the hardware. One can, of course, simply wave
> it away, saying that the difference is insignificant, and the intercept is
> practically zero (as theory would predict in this case). And another pet
> peeve. In a case such as this, where there's overpowering reason to say
> that the fit must pass exactly through zero, there's no graceful way to
> tell the commercial software this, forcing a fit through zero. Or maybe I
> just don't know the trick to do it, since I never use Excel, Quattro, or
> any of the other spreadsheet clones. 

I'd like to make a couple of points:

First my pet peeve is software (spreadsheets, HP calculators, etc.) which 
perform a regression and then do not provide the error in the coefficients.  I
would like to know how the experimental errors affect the slope and intercept 
which are calculated.

I've modified my HP 28S and Quattro Pro spreadsheets to provide these numbers.
When dealing with experimental data with an interest in slope and intercept, I 
want to know how good these values are.  Agreement to 15 digits may be 
comforting, but if the results are only good to 3 or 4 digits, it appears to me 
that arguing over the last 4 digits becomes more philosophical than real.

Second, I am not a fan of forcing the intercept through zero.  In chemistry we 
frequently have the occasion to use Beer's law to determine concentrations in 
solution.  Beer's law predicts Absorbance = constant X concentration.  This is
reasonable since when there is no concentration, there should be no Absorbance.
Still, I think it is wrong to force the line through zero and teach students 
NOT to do it.  Often there are non-linearities that occur in different 
concentration regions due to the chemistry of the system.  I think it is better 
to let the line fall where it will and use the small intercept to more 
faithfully represent the calibration line.

This latter point becomes academic IF the error in the intercept is larger than 
the intercept.  That is the reason I force my tools to tell me the standard 
deviation in both slope and intercept.  I then worry less about differences in 
later digits due to algorithm used.  I also use Mathcad and appreciate the 
documentation they provide to their algorithms.

Ciao,














> I also tried a polynomial fitting routine, which gave the same results.
> Try it yourself with your favorite software:
>
> x      y
>
> 0.002  0.000
> 0.117  0.025
> 0.238  0.050
> 0.356  0.075
> 0.472  0.100
> 0.597  0.125
>
> IBM Excel gives a = 4.751429,  b = 0.0050502
> MAC Excel gives a = 4.7514  ,  b = -0.0002
>
> The students obviously had different precision settings. Unfortunately
> this software doesn't (so far as I know) readily compute the uncertainties
> in a and b, which, in this case, will be quite large for b.
>
>
> 	-- Donald
>
> .....................................................................
> Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
> Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
> .....................................................................

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  :-)                                                         :-) 
  :-)   Frank M. Lanzafame           Department of Chemistry  :-) 
  :-)   Monroe Community College     1000 East Henrietta Rd.  :-) 
  :-)   Rochester, NY   14623        (716)  292-2396          :-) 
  :-)   Internet:  flanzafame@monroecc.edu                    :-) 
  :-)                                                         :-) 
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