On the History of the use of Geometry in the General Linear Model

Abstract

Abstract The question of why a geometric or coordinate-free approach to linear models has been subordinated to an algebraic approach is considered by reviewing selected papers having a geometric slant. These begin with R.A. Fisher's 1915 paper on the distribution of the correlation coefficient and continue through William Kruskal's elegant 1975 paper on the geometry of generalized inverses. The thesis is put forward that the relative unpopularity of the geometric approach is not due to an inherent inferiority but rather to a combination of inertia, poor exposition, and a resistance to abstraction.