Memo Problem: DataCon Contract

11.4 Memo Problem: DataCon Contract

To:	Analysis Staff
From:	Project Management Director
Date:	May 28, 2008
Re:	DataCon Contract

We have received a contract from DataCon, a large data analysis provider that does general data analysis and management contracting for a wide variety of manufacturing and service sector businesses. They have subcontracted some of their business to us. They want us to fit some predictive models for four sets of data they have sent along. They want to see a best-fit nonlinear trendline for each data set, as well as the best model that we come up with, superimposed on both the scatterplot of the data and the best-fit trendline. DataCon management wants not only simnple trendlines but also good fitting models constructed from shifting and scaling the basic functions because models built from basic functions are more transparent and easier to analyze than typical trendline models.

As usual, direct your memo to me. Include the following:

A brief introduction
Complete information about each model, including what shifting and scaling you included, how you found optimal values for these, what the final parameter values for the best fit were, and the final equation of the model
Graphical representation of the typical trendline and the best model on the same graph
Correctly computed values for R² for the best models and a description of how well they seem fit as compared to the automatic trendlines
A few summary comments, including any special considerations your want to pass along about what you found.

Attachment: Data file C11 DataCon Data.xls [.rda]

Here are some suggestions for dealing with this assignment:

Start by fitting the best built-in trendline for your software (don’t forget to record its equation and its R²) to a scatterplot of the data set. The table below (or one like it) will help organize the information.
Now try fitting your own shifted and scaled basic function on top of the scatterplot and the best-fit trendline, comparing your computed R² to the R² of the trendline.
You might not be able to construct a better model in every case, but get as close as you reasonably can. That’s all DataCon really wants or needs.
Here are a couple of tips:
1. Don’t even try to do your own fit for a polynomial function (used when the scatter plot has a turn(s), etc) because built-in routines for a polynomial fit are already clear and understandable. Your job, in this case, is to find that polynomial.
2. If you are fitting your own exponential function, don’t bother with horizontal shifts because mathematically such shifts can be absorbed by the scaling parameter.
3. If the best trendline is a power function with a fractional power, for example, x^0.42, you might suggest using x^0.5 for your own power function because x^0.5 = x^1∕2 = , which is much easier to understand (remember, this is what DataCon wants).


DATA SET 1		EQUATION	R²

	My Best Fit

	Best Trendline Fit

DATA SET 2

	My Best Fit

	Best Trendline Fit

DATA SET 3

	My Best Fit

	Best Trendline Fit

DATA SET 4

	My Best Fit

	Best Trendline Fit

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