Regression Without Calculus

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It is possible that the overuse of optimization techniques brought on by Calculus has prevented a general development of statistics. Correlation Coefficients induce an "orthogonality" that can be used to develop statistical methods. This talk will show how the use of correlation allows a general definition of regression estimation in simple linear regression. The three correlation coefficients Pearson, Kendall, and Greatest Deviation will be used to illustrate an example of the general framework of the method without Calculus.

If two vectors of bivariate data (x,y) of size n are looked at in n-space, it becomes easy to define "natural" correlation coefficients. An n-dimensional interpretation of Pearson's r as the difference in the standardized L2 norms of x+y and x-y leads to correlation coefficients based on other measures of distance such as L1. This "natural" definition has been missing in statistics at least since 1906 when Charles Spearman published an incomplete attempt at an absolute value rank correlation coefficient. However, this "natural" definition has been available in analysis since the time of Hilbert.

Additional Details

Thursday, December 11, 1997
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

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