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Abstract
This report is concerned with estimates that are somewhat different in nature from those that are made from sample data, by raising it to the universe, and the nature of such estimates has been indicated in the discussions on correlation and regression. For example, the fundamental principle underlying the calculation of numerical expressions of cause and effect relationships is that from the determination of the extent to which independent and dependent variables are associated, or have been associated in the past, logical deductions sometimes can be made as regards future relationships. When we have measured the degree of apparent cause and effect relationships between certain variables it is often possible to estimate or predict future occurrences. This is a principle underlying many correlation analyses, for it is only on the basis of past occurrences that we can arrive at conclusions as to what is most likely to happen in the future. Simple regression lines enable us to show the relationship between a series of independent variables and a series of dependent variables, thus making it possible to make some deduction as regards most probable values of a dependent variable that are likely to be associated with given values of the independent variable. In like manner, the multiple regression equation provides a means of estimating the most probable values of a dependent variable that are likely to be associated with given values of 2 or more independents.