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

XIL—PARTIAL CORRELATION. _ three and the second for four variables. The introduction of more variables does not involve any difference in the form of the arithmetic, but rapidly increases the amount. Example i.—The first illustration we shall take will be a continuation of example i. of Chapter IX. in which the correla- tion was worked out between (1) the average earnings of agri- cultural labourers and (2) the percentage of the population in receipt of Poor-law relief in a group of 38 rural districts. In Question 2 of the same chapter are given (3) the ratios of the numbers in receipt of outdoor relief to the numbers relieved in the workhouse, in the same districts. Required to work out the partial correlations, regressions, etc., for these three variables. Using as our notation X, = average earnings, X, = percentage of population in receiptof relief, X,; = out-relief ratio, the first constants determined are— M, = 15-9 shillings oy = 171 shillings ro=- 066 4',= 3°67 per cent. ¢,=1-29 per cent. r= -013 M, = 519 oy =3'09 ros = + 0°60 To obtain the partial correlations, equation (12) is used direct in its simplest form— on TT == (T= (=r) The work is best done systematically and the results collected in tabular form, especially if logarithms are used, as many of the logarithms occur repeatedly. First it will be noted that the logarithms of (1-72)! occur in all the denominators ; these had, accordingly, better be worked out at once and tabulated (col. 2 of the table below). In col. 3 the product term of the numerator of Z. Lo, 6. 7 8. o —— Product |N Nl 1 ain rp log LIFE Font Bima hl log I-72) log. | Value. rig=-066 T87580 -0:0780 -0'5820 I76492 1'89938 186554 rye5-073 I-83216 nz=-013 I'99620 -0'3960 +0-2660 142483 I77589 164599 riat0'4d T0567 23=+060 190309 +0°0858 +05142 T71113 187209 I'83904 rop.+0:69 I-85046 each partial coefficient is entered, 7.e. the product of the two other coefficients on the remaining lines in col. 1 ; subtracting this from the coefficient on the same line in col. 1 we have the numerator(col. 4) and can enter its logarithm. The logarithm of the denominator (col. 6) is obtained at once by adding the two logarithms of (1 & #2)t on the remaining lines of the table, and subtracting the logarithms 239

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