Some Deficiencies of Using Moment Generating Functions

Dissatisfaction is expressed with the well-known definitions of partial and multiple correlation. Partial correlation is defined here as the ordinary correlation between two random variables after their linear dependence on the partialed-out variables has been subtracted. This leads to familiar results; it also clarifies the auto-regressivelike assumptions required for the partial autocorrelations to have a cut-off property. Multiple correlation is similarly considered.