best-fit line purpose - BAR exp

[robert zellmer]

I've had a few people ask about the graph and calculating the slope
for the pre-lab for BAR, after the fact.  There seems to be a
misunderstanding of the purpose of a best-fit line and how to get
the slope.   People often take data points for the slope instead of
points from the line.   Lets get this cleared up for the report.

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.  You will force it through the origin for the Beer's
Law graph for BAR because we know when the concentration of
the 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 before taking readings for each solution.

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.
Excel essentially uses the points on the line for the slope and not your
actual data points (unless the line goes through one of them).

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 should use Excel.  For the Beer's Law graph, 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 a nonzero intercept (it should look like
y = m*x).   If it does (looks like y = m*x + #) 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) for calculating the conc. of Allura Red
from the absorbance at each time.

For the first and second-order plots do NOT force the lines through
the origin or any other point.

Dr. Zellmer
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.osu.edu/pipermail/cbc-chem1220/attachments/20190623/c0f365c4/attachment.html>