question about r^2 values

[nolteboy]

Hello all

I've been playing around with different ways of weighting calibration plots (equal, 1/x, and 1/x^2 for linear and quadratic fits). I recently got a r^2 value of >1.0 (was actually 1.012) for a 1/x^2 weighting of a 8-point plot for 2,4-dinitrotoluene via GC/MS.

Although not a real mathematician/statistician, I am generally familiar with the whole least-squares "minimization of the residuals" process, and it has always been my understanding that a r^2 value of 1.0 indicated a 'perfect fit', and that "it don't git no better than that!"

So this is the first occasion where I've seen this number actually greater than 1.0. Can anyone shed some light on what's going on here? I am using GCMS Chemstation G1701BA.

thanks.

[tom jupille]

I can't shed any light beyond your observation that something is obviously wrong somewhere. Figuring out where is likely to be a nightmare.

Are you using pre-packaged routines for the various fits?

[bartjoosen]

Could you give us the data used for the calculations?
Maybe we get some insight in how it turned out as we can calculate by our own.

Also slope and intercept for the 1/x^2 weighted calibration line would be handy.

Bart

[nolteboy]

Thanx for the replies. Here are the #'s from the initial multi-point calibration:

2,4-dnt area / 2,4 dnt conc. / internal std area / IS conc.
22337 / 5 / 694860 / 40
49387 / 10 / 663971 / 40
102236 / 20 / 633675 / 40
227653 / 40 / 656044 / 40
358234 / 60 / 608272 / 40
515217 / 80 / 619892 / 40
659841 / 100 / 636778 / 40
796342 / 120 / 647537 / 40

Since this is an internal standard method I am of course plotting area RATIOs (2,4-dnt / IS) to amount RATIOs...

the equation generated by my software (for the 1/x^2 weighting) is:
y=0.0313x^2 + 0.338x - 0.011

and once again I get a r^2 value of 1.012

muchas gracias!

[Bruce Hamilton]

I'm not big into maths, but just plugged the data into Excel, and got R^2 values <1 for default trendline when using the IS-corrected data. I'm sure some integration experts will provide more detailed responses.

I'd suggest taking your software serial number, and logging onto the Agilent WWW site, and looking at the SSB ( software status bulletin ) for your product to ascertain if this is a known, undocumented "feature" of their software.

Please keep having fun,

Bruce Hamilton

[bartjoosen]

This seems strange, if I use your data, and do a regression of (2,4-dnt/(internal standard area*IS conc ) versus area 2,4 dnt, I get following coefficients:
0.0000195838x^2 + 0.0084457853x - -0.0110304707
with weights 1/x^2, and R^2 0.9984.

Also if I use the equation from your software, I'm not able to predict the areas as they are miles away from the experimental area's.

Looks like a software problem.

Bart

[nolteboy]

thanks, both of you. I am suspicious of my software in this case...
nolteboy