Chart to Facilitate the Calculation of Partial Coefficients of Correlation And Regression Equations

Cover Chart to Facilitate the Calculation of Partial Coefficients of Correlation And Regression Equations
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„ , (6) in which *i2 may be read, "the coefficient of alienation between 1 and 2." •^1-2 ^^ "l ''12 Accordingly k,^^ is a measure of variability, or freedom of variable 1 from variable 2 which is independent of the standard deviations of the variables.
If 1 is the dependent variable and 2 the independent it will be convenient, in place of k^^ , to use the notation fej.j , which may be read, "the freedom of 1 from 2." Similarly ^1.23 is the freedom of 1 from 2 and 3, or "the variability in 1 una
...ccounted for by 2 and 3.'' With this explanation the meaning of such symbols as k^^s , ^1-23 • ■ • « . ^3-124 ■ • • n , etc., will be obvious.
Further, if we write, ^l23 + r\.^3 = 1 (in general : k\.^s ...n + r\.^^ . . . „ = 1) (8) ri.33 is the correlation between 1, and 2 and 3 when combined by the re- gression equation. The symbol here given, r^^.^s , is an extension of the notation introduced by Yule ^ in the symbol ai.23 . The relationship is fi ^1-23 = Oi VI— »"' The standard error of estimate, O1.23 .


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