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