Simple proofs of relations between the communality problem and multiple correlation

Solutions of the communality problem and of the problem ofmeaning of common and unique factors have been shown previously to depend intimately on certain relations with ordinary multiple correlation. To make these basic propositions more accessible, simple proofs of some of them are provided here, avoiding any matrix algebra. New results are also obtained, with no extra work, that extend the previously known propositions to a more general class of coefficients than that of communalities.Revised from a paper written while on leave at the Center for Advanced Study in the Behavioral Sciences.