### The algorithm for determining differences in cognitive abilities and personality characteristics between track and field athletes and basketball players

#### Abstract

The resulting solution is very easy to convert into a form obtained under the canonical model of discriminant analysis. The matrix of discriminant coefficients can be defined as a matrix of partial regression coefficients that is obtained by solving the problem **ZW **= **K **+ **E **| trag(**E**t**E**) = minimum. As **K **= **ZR**-1/2**X**, it is clear that **E **= **0 **and **W **= **R**-1/2**X**. Therefore, vectors **w**k from **W **are proportional to the coordinates of the vectors of discriminant functions in the tilted coordinate system formed by vectors from **Z **with cosines of the angles between the coordinate axes equal to the elements of correlation matrix **R**. Since discriminant analysis can also be interpreted as a special case of component analysis with principal components transformed by a permissive singular transformation so as to maximize distances between centroids of subsets Ep , or canonical correlations ρk (Cooley & Lohnes, 1971), the custom is to identify the content of discriminant functions on the basis of structural vectors **f**k from the matrix **F **= **Z**t**K **= **RW **= **R**1/2**X **= (**f**k) = (**Rw**k), which is analogous to the identification of the content of canonical variables obtained by Hotelling`s method of biorthogonal canonical correlation analysis because it is possible to show by easy calculation that **F **is a factor matrix of matrix **R **In this metric, the cross structure of discriminant functions will be **U **= **Z**t**Lρ**-1 = **Z**t**PZWρ**-1 = **Wρ **as, of course, **W**t**Z**t**PZW **= ρ2, and it is clear that **U **is a factor matrix of the matrix **Z**t**PZ**, or intergroup covariance matrix defined in the space with standard metric.

**Keywords: **/canonical/discriminant analysis/coefficients /model/regression

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