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Jeff,
Thanks for the shared reference:
Thank you for introducing such a worthwhile topic.
http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/
ErrRegr.html
I like it, except for one detail. The predicting variable y (what is
measured is fluorescence) was plotted vertically while the inferred
variable (concentration) is plotted horizontally. Their formula to
calculate standard deviation of the inferred variable contains the
slope of the line, b.
My predicting (independent) variable, r, is plotted horizontally while
the inferred (dependent) variable is plotted vertically. That seems to
be more logical.
In creating the calibration curve, it makes more sense to me to plot p
horizontally and r vertically. One prepares six samples of an alloy,
each with a fixed value of p. The resistivity of a sample depends on
the percentage p of zinc in the sample. Having prepared each sample,
one then measures the resistivity. You can tell by the regular spacings
of the values of p that it was the values of p that were chosen
independently by the experimenter. The experimenter did not, for each
data point, decide on a value of resistivity and then add zinc to the
copper until the sample had that resistivity.
It would seem that this
is an important point in that the actual value of p, not just its
standard deviation, depends on which variable is treated as the
independent variable and which variable is treated as the dependent
variable.
although the original samples may have been made with specific
compositions, the operation of the meter will take a known
resistivity and predict the composition. Hence resistivity really is
the independent variable, and composition is the dependent variable.