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

Z THEORY OF STATISTICS of the denominators from those of the numerators we have the logarithms of the correlations of the first-order. It is also as well to calculate at once, for reference in the calculation of standard- deviations of the second-order, the values of log 1-72 for the first-order coefficients (col. 9). Having obtained the correlations we can now proceed to the regressions. If we wish to find all the regression-equations, we shall have six regressions to calculate from equations of the form b123="195" T1.3/023. These will involve all the six standard-deviations of the first order og Og Og Ogg etc. But the standard-deviations of the first-order are not in themselves of much interest, and the standard-deviations of the second-order are so, as being the standard-errors or root-mean-square errors of estimate made in using the regression-equations of the second-order. We may save needless arithmetic, therefore, by replacing the standard- deviations of the first-order by those of the second, omitting the former entirely, and transforming the above equation for &,4 to the form b193= "193" T103/Taus. This transformation is a useful one and should be noted by the student. The values of each o may be calculated twice inde- pendently by the formule of the form Tr95=0y(L = 7h)! (1 —17s,)} == oy(1 od 72:4 (1 i 72.5) so as to check the arithmetic; the work is rapidly done if the values of log /1 —72 have been tabulated: The values found are log 0.53 =0'06146 O93=1'15 log 0y,5=184584 0p15="070 log 05,,=0'34571 Ogq9= 222 From these and the logarithms of the »’s we have log 6,55 =008116,d,,,= — 1:21 : log bia =1'36174, b,,,= +023 log by, = 164993, by 5= — 045 : log by; =1'33917, bpp; = +022 log by, ,= 193024, by; ,= +085 : log bgp; = 033891, gy; = + 2°18 That is, the regression-equations are (1) z,=-1212,+023 z, (2) wg=—045 2, +022 z, (3) 2g= +085 x, +218 «, 240

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