Perpendicular Projections and Elementary Statistics

Abstract

Abstract Beginning statistics at the undergraduate level can be taught by using a few geometric principles of linear vector space theory. Even formulas for simple sample means and variances can be derived with these principles by assuming a univariate linear statistical model. The least squares estimator of the sample mean is found by a perpendicular projection. The analogy of the bivariate model to the univariate model is indicated, and an analogous perpendicular projection solution for it is shown. Vector geometric diagrams illustrate the basic concepts. Once the basic technique is understood, the appropriate application or perpendicular projections can be used to illustrate the problems of multicollinearity and tests of hypotheses in regression models. The translation of the geometric concepts into concrete algebraic equations is shown. The emphasis is on geometric thinking as a means of visualizing and thereby improving an understanding of methods of data analysis.