Gesamtstaat, Dualismus und Pragmatische Sanktion

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1031909583

URN:: urn:nbn:de:zbw-retromon-67385

Document type:: Monograph

Author:: Zehntbauer, Richard http://d-nb.info/gnd/1055162402

Title:: Gesamtstaat, Dualismus und Pragmatische Sanktion

Edition:: Erweiterter Sonderabdruck

Place of publication:: Freiburg (Schweiz)

Publisher:: Universitäts-Buchhandlung (Otto Gschwend)

Year of publication:: 1914

Scope:: 1 Online-Ressource (73 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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XII.—PARTIAL CORRELATION. ar, again, in terms of percentage-changes (ratio — 100): — Percentage change in pauperism = + 1°4 per cent. +0325 times the change in out-relief ratio. +1-383 3s ,, proportion of old. - 0-383 . ,» population. These results render the interpretation of the total coefficients, which might be equally consistent with several hypotheses, more clear and definite. The questions would arise, for instance, whether the correlation of changes in pauperism with changes in out-relief might not be due to correlation of the latter with the other factors introduced, and whether the negative correlation with changes in population might not be due solely to the correlation of the latter with changes in the proportion of old. As a matter of fact, the partial correlations of changes in pauperism with changes in out-relief and in proportion of old are slightly less than the total correlations, but the partial correlation with changes in population is numerically greater, the figures being r= +052 T1034 = +046 13 = TL T1394 = +028 ry, = —-Uld Tigo = — 0°36 So far, then, as we have taken the factors of the case into account, there appears to be a true correlation between changes in pauperism and changes in out-relief, proportion of old, and population—the latter serving, of course, as some index to changes in general prosperity. The relative influences of the three factors are indicated by the regression-equation above. [For the full discussion of the case cf. Jour. Roy. Stat. Soc. vol. Ixii., 1899.] 15. The correlation between pauperism and labourers’ earnings exhibited by the figures of Example i. was illustrated by a diagram (fig. 40, p. 180), in which scales of “pauperism” and “earnings ” were taken along two axes at right angles, and every observed pair of values was entered by marking the corresponding point with a small circle: the diagram was completed by drawing in the lines of regression. In precisely the same way the correlation between three variables may be represented by a model showing the distribution of points in space ; for any set of observed values Xp X,, X,; may be regarded as determining a point in space, just as any pair of values X, and X, may be regarded as determining a point in a plane. Fig. 45 is drawn from such a model, constructed from the data of Example i. Four pieces of wood are fixed together 245

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