This paper, a derivation of the multiple correlation formula for unstandardized (raw) scores, is the fourth in a series of publications. The purpose of these papers is to provide supplementary reading for students of applied statistics. The intended audience is social science graduate and advanced undergraduate students familiar with applied…

This paper presents in detail a proof of the limits of the sample bivariate correlation coefficient which requires only knowledge of algebra. Notation and basic formulas of standard (z) scores, bivariate correlation formulas in unstandardized and standardized form, and algebraic inequalities are reviewed first, since they are necessary for…

This document proves that the F statistic can be obtained by squaring t-test values, or that equivalent t-test values may be obtained by extracting the positive square roots of F values. Proof to varying degrees of completeness and accessibility has been given by other scholars, but generally these prior statements, particularly those available to…