best-fit line purpose

[Robert Zellmer]

I've had a few people come ask me about the graph and calculating
the slope for the pre-lab for BAR.  It seems there seems to be a
misunderstanding of the purpose of a best-fit line and how to do the
slope.   Several people took data points for the slope instead of points
from the line.

So I guess the question is "what is the purpose of a best-fit line and
how do you use it"?

A best-fit line is used to average out the random error in your data
points.  It's like taking a graphical average of your data.  This line
may not even go through a single data point, unless you force it
through a point.  We do this for the Beer's Law graph for BAR
because we know when the concentration of your reactant is zero
the absorbance should be zero so this should be a very good data
point, plus you're taking this point several times when you calibrate.

Since the line averages out the random error in your experimental
data, the points on the line are considered better than your actual
data.  When you calculate the slope you should use points from the
line and not the actual data points, unless the line goes through one
of them.  This will give you a better slope than using your data points.

This is what you should have done for the BAR pre-lab.  Graphing
and other numerical treatments are in Appendix D (Treatment of
Numerical Data).

For the report you can use Excel.  You should include the (0,0) point
with your data and plot it with the ones for the solutions you created in
Part C.  This should give you a total of 5 points for your Beer's Law
graph.  Have Excel do a linear best-fit. It allows you to force the line
through a point (chose the origin, the (0,0) point).  Have it print the
equation and R^2 value.  Your eqn should not have an intercept.  If
it does it means you didn't force it through the origin.  You will use
the slope from this eqn as your Beer's Law slope (constant).

Dr. Zellmer