Cartesian Statistics: Data Analysis by Linear Algebra and Analytic Geometry - Whitney, Sthepen (CIENCIA ergo-sum, 2017)
A linearar algebraic approach can be helpful in the computation, interpretation, teaching and understanding of statistic at all levels. Although the reference space has a dimension equal to the sample size, it is not necessay to consider more than 2 or 3 dimensions at a time, for most explications. A sample becomes a vector which has an orthogonal decomposition into mean and standard deviation projections. The correlation between two samples is essentially measured by the angle between the vectors. Even linear regression has an interpretation "dual" to the usual scatter diagram: the regression coefficients are scalar projections between the sample vectors. Orthogonal regression, somewhat neglected in the literatura, is easily treated here. This «cartesian» approach can be extended to other branches of statistics, separating, in true object-oriented fashion, he basic deterministic notions from the probabilistic and computational aspects. However, a brief examination of some references indicates only sporadic use of the cartesian approach in the leaming and use of statistics.