
Data defines the model by dint of genetic programming, producing the best decile table.


Tukey's Bulging Rule for Straightening Data Bruce Ratner, Ph.D. 

"A very effective and simple technique for straightening data is reexpressing the variables, which uses Tukey’s Ladder of Powers and the Bulging Rule. Before presenting the details of the technique, it is worth discussing the importance of straightline relationships or straight data."  Ratner, B., Statistical Modeling and Analysis for Database Marketing: Effective Techniques for Mining Big Data, CRC Press, Boca Raton, 2006. The following is an excerpt from Chapter 3, pages 39 41.
3.5.2 Bulging Rule
The Bulging Rule states the following:
 If the data have a shape similar to that shown in the first quadrant, then the data analyst tries reexpressing by going upladder for X, Y or both.
 If the data have a shape similar to that shown in the second quadrant, then the data analyst tries reexpressing by going the downladder for X, and/or upladder for Y.
 If the data have a shape similar to that shown in the third quadrant, then the data analyst tries reexpressing by going downladder for X, Y or both.
 If the data have a shape similar to that shown in the fourth quadrant, then the data analyst tries reexpressing by going the upladder for X, and/or downladder for Y.
Reexpressing is an important, yet fallible part of EDA detective work. While it will typically result in straightening the data, it might result in a deterioration of information. Here is why: reexpression (going down too far) has the potential to squeeze the data so much that its values become indistinguishable, resulting in a loss of information. Expansion (going up too far) can potentially pull apart the data so much that the new farapart values lie within an artificial range, resulting in a spurious gain of information. ... An excellent realcase illustration follows (pages 41 50 in the book).

For more information about this article, call Bruce Ratner at 516.791.3544 or 1 800 DM STAT1; or email at br@dmstat1.com. 
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