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Topic: One last question on transformation?
Replies: 0

 MR JAMES F BOHAN Posts: 4 Registered: 12/6/04
One last question on transformation?
Posted: Oct 31, 1996 11:52 AM

Thanks to all of the guidance on the use of transformations and the
care that should be exercised when using the technology that is
available. I would like some advice regarding an activity that I did
with my AP Stat class. We were working based on one of Rossman's
activities dealing with exploring the effect of relating x with y, x
with sqrt(y) and x with log y.

I instructed the students to perform each of the transformations and
to use the linear regression capability of the TI-83 not to produce
"the" line of best fit, but rather to ascertain the level of
linearity between the quantities that were related. Viewing the
scatter and residual plots of the transformed data and interpreting
the values of r^2 and r that were generated, I asked the students to
write the equation which related the quantities of interest.

With some discussion, the students agreed that we could use the
outcome of the linear regression of the transformed data that the
calculator provided with the following changes:
When we related x and y, we could use y = mx + b as displayed;
when we related x and sqrt(y), we adjusted the equation to be sqrt(y)
= mx + b;
when we related x and log y, we adjusted the equations to be log y =
mx + b.

We then solved the square root and the log forms for y and compared
the results to the quadratic and exponential regression equations
provided by the TI-83. This provided a nice review of some
elementary algebra. We found, of course, that the quadratic
regression gave a better fit than our derived quadratic but that the
exponential function matched our derived exponential exactly. The
students confirmed their suspicions by analyzing the transformation
of relating ln x and y and found that it motivated the logarithmic
regression of the calculator.

We concluded the activity with a discussion regarding a process of
determining the best regression model for a given set of bivariate
data.

I think the activity went very well. My questions to the experts out
there: Is this approach to transformations and the use of least
squares "linear" regression for nonlinear sets of bivariate data
appropriate and productive for the development of sound statistical
conceptualization of the issue? I would appreciate any insight.
Thanks.
Jim Bohan
K-12 Mathematics Program Coordinator
Manheim Township School District
Lancaster, PA