Multiple Correlation

By the term, ‘Multiple Correlation’ we mean the relationship between a dependent variables taken together. In such a correlation the combined effect of two or more independent variables on a single dependent variable is studied. Thus, if we study the combined effect of Demand, Money in Circulation, Export, and Import on Price at the same time, or that of Age, and Height on Weight at the same time, it would amount to a multiple correlation analysis.

The coefficient of a multiple correlation is represented by R, and the different variables denoted by 1,2,3,4 etc. respectively are subscripted to it along with a dot between therms. The only number denoting the dependent variable is placed to the left of the dot and all other numbers denoting the independent variables are placed to the right of the said dot.

Thus,

R 1.23 represents the coefficient of multiple correlation between the dependent variable X1 and the independent variables, X₂ and X₃;

R2.13 represents the coefficient of multiple correlation between the dependent variable X₂, and the independent variables, X₁ and X₃

R3.12 represents the coefficient of multiple correlation multiple correlation between the dependent variable X₃, and the independent variable X₁ and X₂ and :

R1.234 represents the coefficients of multiple correlation between the dependent variable, X1 and the independent variable, X₂X₃ and X_4.