How could you use graphing to help you identify the composition of an
unknown sample of a substance?

Dear gazo,

Given a sample of an unknown homogeneous substance, you would want to
subdivide it into pieces and take several measurements of mass and
volume, say twenty or thirty for the sake of statistical significance.
Next, you would plot these data on a Cartesian graph, with volume
along the horizontal axis and mass on the vertical axis.

The data points will naturally tend to fall near a line, but because
the measurements are only approximations of the true values, you must
find the line that fits best with these measurements. One way to find
the line of best fit is called linear regression. The goal of linear
regression is to minimize a quantity known as R squared, which is an
aggregrate measure of the distances between the data points and a line
drawn near them. The best fit is defined as the line such that no
other line has a smaller R squared.

For more information on linear regression, consult these pages.

David M. Lane: Regression Line
http://davidmlane.com/hyperstat/A115370.html

Stefan Waner: Regression: Fitting Functions to Data
http://people.hofstra.edu/faculty/Stefan_Waner/calctopic1/regression.html

Once you have found the line of best fit by linear regression, you are
in a position to calculate the experimentally observed density of the
mystery solid, since the density in such a graph is the slope of the
line. Subsequently, a comparison of the experimentally observed
density with a table of known substance densities should allow for an
identification or at least a narrowing down of the unknown substance.

If you feel that my answer is incomplete or inaccurate in any way, please
post a clarification request so that I have a chance to meet your needs
before you assign a rating.

Regards,

leapinglizard


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