The Angle: A Goodness of Fit Metric for Cost Analysis
Dean, E.
Consultant

This paper had its origin back about 1985. We invited a well know statistician to sit in on our weekly cost analysis meeting. He attended several meetings and then failed to show up for several meetings. I went to see him and asked why he no longer showed up at our meetings. His answer was that we did not have enough data for statistics to be of any value to us.

This began a quest for an interpretation of regression that would be valid for very small data sets. In the late 1990s I discovered a geometric efficiency metric which had no connection to probability and hence could be applied to arbitrarily small data sets and began using it for stock market analysis. In the early 2000s I proved that, for regression, the geometric efficiency metric was a transformation of the angle between the data vector to be predicted and the projection of that vector on the regression manifold.

This paper will discuss the geometric efficiency metric and will prove the transformational equivalence of the "angle" and the geometric efficiency metric for regression. It will also demonstrate that the use of the "angle" leads to a form of stepwise regression useful for arbitrarily small data sets. It will also demonstrate that the "angle" is a valid goodness of fit metric for application to test data sets and with other forms of data fitting such as neural networks.