Compte rendu des travaux de la Chambre Syndicale pendant lʹannée 1926

An Introduction to the theory of statistics

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Monograph

Identifikator:: 885356659

URN:: urn:nbn:de:zbw-retromon-5912

Document type:: Monograph

Author:: Gaebel, Käthe http://d-nb.info/gnd/1023047020; Schulz, Max von http://d-nb.info/gnd/1033198951

Title:: Die Heimarbeit im Kriege

Place of publication:: Berlin

Publisher:: Verlag von Franz Vahlen

Year of publication:: 1917

Scope:: 1 Online-Ressource (210 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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wk THEORY OF STATISTICS. values be assigned to x,,, and all the following deviations, the correlation between x, and x, on expanding x, is, as we have seen, normal correlation. Similarly, if any fixed values be assigned to aj, to #1, and all the following deviations, on reducing x, ,, to the second order we shall find that the correla- tion between x,; and x, is normal correlation, the correlation coefficient being r,,,, and so on. That is to say, using % to denote any group of secondary suffixes, (1) the correlation between any two deviations x, and x, ts normal correlation ; (2) the correla- tion between the said deviations 1S Tp, whatever the particular fixed values assigned to the remaining deviations. The latter conclusion, it will be seen, renders the meaning of partial correlation coefficients much more definite in the case of normal correlation than in the general case. In the general case 7. represents merely the average correlation, so to speak, between Zn; and z,,: in the normal case 7,,; 1s constant for all the sub- groups corresponding to particular assigned values of the other variables. Thus in the case of three variables which are normally correlated, if we assign any given value to x; the correlation between the associated values of #; and w, is ry, : in the general case rq if actually worked out for the various sub-groups corresponding, say, to increasing values of x; would probably exhibit some continuous change, increasing or decreasing as the case might be. Finally, we have to note that if, in the expression (15) for ¢, we assign fixed values, say A, ks ete., to all the deviations except a;, and then throw ¢ into the form of a perfect square (as in § 4 for the case of two variables), we obtain a normal distribution for #; in which the mean is displaced by a hi Gy.95. in F193... T1234... — ht Piosh.. ng. rn ce Ting... lg TT fen, But this is a linear function of A, As, etc., therefore in the case of normal correlation the regression of any one variable on any or all of the others ts strictly linear. The expressions Tig ....n» Gros. ...nf023....m etc. are of course the partial regressions bios... . mw ©LC. REFERENCES. General. (1) Bravars, A., “Analyse mathématique sur les probabilités des erreurs de situation d’un point,” Acad. des Sciences : Mémoires presentés par divers sawants, 11° série, ix., 1846, p. 255. (2) GavrroN, Francis, ¢“ Family Likeness in Stature,” Proc. Roy. Soc., vol. xl. . 42. (3) ha natices, Natural Inheritance ; Macmillan & Co., 1889. 296

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