An Introduction to the theory of statistics

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Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

243 THEORY OF STATISTICS. For we have (xy. e103... n) = 22) (2) — Ty 45 Sci n)=N(oF — 034 nin) and also (ef . . . n) = 22) — Fy 95 Joti n)?=N(a}- on... .n whence the correlation between Zande... . ,is 04 ! v.e. the value of By, n given by (13). The value of RB is accordingly a useful datum as indicating how closely x, can be expressed in terms of a linear function of Fo Fini oi so « &py ANA the values of the regressions may be regarded as determined by the condition that & shall be a maximum. Its value is essentially positive as the product-sum 2(xy.e95 . . . . 5) Is positive. £ may be termed a coefficient of (n—1)-fold (or double, triple, etc.) correlation; for n variables there are » such correlations, but in the limiting case of two variables the two are identical. The value may be readily calculated, either from Tio, .. 800 o, or directly from the equation 1 - Bios... w= (1 =18)1 - 7352) ~ 72s). . . (1 = Puss... (ney). (15) It is obvious from this equation that since every bracket on the right is not greater than unity, LB... Pl =7% Hence Ry; , . . . , cannot be numerically less than r,,. For the same reason, rewriting (15) in every possible form, Ba cannot be numerically less than ry, Tig + «+ « Tip 2.6. ANY ONE of the possible constituent coefficients of order zero. Further, for similar reasons, Ryn; » cannot be numerically less than any possible constituent coeflicient of any higher order. That is to say, Ry... , is not numerically less than the greatest of all the possible constituent coefficients, and is usually, though not always, markedly greater. Thus in Example i, Buy (the coeflicient of double correlation between pauperism on the one hand, out-relief and labourers’ earnings on the other) is 0-839, and the numerically greatest of the possible constituent coeflicients is 1,,= —0'73. Again, in Example iji., By, is 0:626, and the numerically greatest of the possible constituent coefficients is ry, , = + 0-573. The student should notice that R is necessarily positive. Further, even if all the variables Xp Xp... . X, were strictly uncorrelated in the original universe as a whole, we should expect "120 "13.90 "14.93 €tc., to exhibit values (whether positive or negative) By

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