A Modeling Approach to Regression Analysis and Exponential Regression

Abstract

Students rely on technology and according to students if the computer or calculator provides an answer then that answer is correct.
Too often students rely only on the computer’s results and the common diagnostics such as R2, residual plots, hypothesis test on
coefficients, and percent relative errors from regression analysis to decide on the adequacy of the models developed. Additionally,
modeling with data to fit an exponential regression equation requires a good starting point or the technology yields a poorly fitted
model. We present a “real-world” data set and examples of regression models to show both the importance of a good starting point
as well as how to obtain that starting point. We apply the modeling approach to adding a reasonable and useful model that we call
the “common sense” to the diagnostics. The use of the common-sense model is a very helpful diagnostic that should be used in the
overall analysis of the models as well as the use of a good starting point to obtain the best fit exponential model for our example.