An Introduction to the theory of statistics

Bibliographic data

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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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

2 THEORY OF STATISTICS. with the subscripts 34 . . . . (n—1) added throughout. The coefficient by, , may therefore be regarded as determined from a regression-equation of the form Trap le in=1)= IRE oh Diniz. m—=1) + Tn34... (n—1) Z.e. it is the ‘partial regression of #,,, .. OD gy .... mp Tn3 ....m-y Deing given. As any other secondary suffix might have been eliminated in lieu of », we might also regard it as the partial regression of 145, .. OD %ay5. .. ny %sa5....n DEINE given, and so on. 13. From equation (11) we may readily obtain a corresponding equation for correlations. For (11) may be written Brits i Trot... 0-1)” Toe ceo tn=) Tse... (0-1) TL... (n-1). Sli i 0234. ... (1) Hence, writing down the corresponding expression for bys...» and taking the square root Test....n=1) —Tmnss.... 0-1) Ton3s....(n-1) Ios ein ei te Rt sR L2 ia EEE DT az This is, similarly, the expression for three variables rama Tan Lyn Tl 2 EY -n) with the secondary subscripts added throughout, and ry, can be assigned interpretations corresponding to those of 6,53, above. Evidently equation (12) permits of an absolute check or the arithmetic in the calculation of all partial coefficients of an order higher than the first, for any one of the secondary suffixes of 7153... . » can be eliminated so as to obtain another equation of the same form as (12), and the value obtained for 7,5 .. , by inserting the values of the coefficients of lower order in the expression on the right must be the same in each case. 14. The equations now obtained provide all that is necessary for the arithmetical solution of problems in multiple correlation. The best mode of procedure on the whole, having calculated all the correlations and standard-deviations of order zero, is (1) to calculate the correlations of higher order by successive applications of equation (12); (2) to calculate any required standard-deviations by equation (10); (3) to calculate any required regressions by equation (8): the use of equation (11) for calculating the regressions of successive orders directly from each other is com- paratively clumsy. We will give two illustrations, the first for 38

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