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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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

244 THEORY OF STATISTICS. correlations of the first order (Table IL. col. 4) are obtained. The first-order coefficients are then regrouped in sets of three, with the same secondary suffix (Table IIL. col. 1), and these are treated precisely in the same way as the coefficients of order zero. In this way, it will be seen, the value of each coefficient of the second order is arrived at in two ways independently, and so the arithmetic is checked: 7, ,, occurs in the first and fourth lines, for instance, 7,,, in the second and seventh, and so on. Of course slight differences may occur in the last digit if a sufficient number of digits is not retained, and for this reason the intermediate work should be carried to a greater degree of accuracy than is necessary in the final result; thus four places of decimals were retained throughout in the intermediate work of this example, and three in the final result. If he carries out an independent calculation, the student may differ slightly from the logarithms given in this and the following work, if more or fewer figures are retained. Having obtained the correlations, the regressions can be calcu- lated from the third-order standard-deviations by equations of the form (as in the last example), a b1g.34="T1234 —y 2.134 80 the standard-deviations of lower orders need not be evaluated. Using equations of the form ores = (1 — r})}(1 - 7159) (1 — 78425)! =oy(1 = ri)1 — ri)(1 - Th)! we find log 0.45, =135740 Gon =228 log a, .:,=1:50597 i] log 03415, =0'65773 Os120=105 log 0,,3=132914 Oo pon=21'3 . All the twelve regressions of the second order can be readily calculated, given these standard deviations and the correlations, but we may confine ourselves to the equation giving the changes in pauperism (X,) in terms of other variables as the most impor- tant. It will be found to be x, =0325x, + 1:383x, — 0-383, or, transferring the origins and expressing the equation in terms of percentage-ratios, X,=-31'14+0'325X, + 1-383.X, - 0383X,,

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