The Multiple-Partial Correlation Coefficient

Abstract A partial correlation coefficient which is also a multiple correlation coefficient is discussed. Its relationship with other well-known coefficients is explained. Computational methods for computing the estimating equation and the correlation coefficient are suggested. * The writer wishes to thank Professors Harold Hotelling, George E. Nicholson, and John H. Smith for critically reading the manuscript and offering valuable comments. Professor Hotelling indicated the method of computation which he had suggested in an unpublished paper (see note 5). Professor Smith called the writer's attention to some of the earlier references to the subject in the literature. Since the first draft of this paper was written (June, 1951), it has been learned that Professor C. Horace Hamilton, of the North Carolina State College of Agriculture and Engineering, has written an article entitled “Population Pressure and Other Factors Affecting Net Rural-Urban Migration,” in which the coefficient of multiple-partial corr...