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

IX. —CORRELATION. 123 +034 x 645/298 = 0-74, and the regression equation accordingly z=0'74y, or X=139+0747Y, the standard error made in using the equation for estimating X from Y being 0, o/T = 72= 6-07. This is the equation of greatest practical interest, telling us that, as we pass from one district to another, a rise of 1 in the ratio of the numbers relieved in their own homes to the numbers relieved in the workhouse corresponds on an average to a rise of 0-74 in the percentage in receipt of relief. The result is such as to create a presumption in favour of the view that the giving of out-relief tends to increase the numbers relieved, and this can be taken as a working hypothesis for further investigation. The student should work out the second regression equation, and check both by calculating the means of the principal rows and columns, and drawing a diagram like figs. 36, 37, and 38. Example iii., Table IX.—(Unpublished data ; measurements by G. U. Yule.) The two variables are (1) X, the length of a mother- frond of duckweed (Lemna minor); (2) Y, the length of the daughter-frond. The motherfrond was measured when the daughter-frond separated from it, and the daughter-frond when its first daughter-frond separated. Measures were taken from camera drawings made with the Zeiss-Abbé camera under a low power, the actual magnification being 24 : 1. The units of length in the tabulated measurements are millimetres on the drawings. The arbitrary origin for both X and ¥ was taken at 105 mm. The following are the values found for the constants of the single distributions :— §= -1'058 intervals= — 63 mm. M,= 98'7 mm. on drawing. = 4°11 mm. actual. oz= 2°'828 intervals= 17'0 mm. on drawing= 0°707 mm. actual. #=-0208 , =- 12mm. My=103"8 mm. on drawing. = 4°32 mm. actual. oy= 3°08¢ , = 185mm. ondrawing= 0771 mm. actual, The values of & are entered in every compartment. of the table as before, and the frequencies then collected, according to the magnitude and sign of &n, in columns 2 and 3 of Table IXa. The entries in these two columns are next checked by adding to the totals the frequency in the row and column for which &, is zero, and seeing that it gives the total number of observations (266). The numbers in column 4 are given by deducting the entries in column 3 from those in column 2. The totals so obtained are multiplied by & (column 1) and the products entered RF

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