Die neuere Entwicklung des Petroleumhandels in Deutschland

An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 883967979

URN:: urn:nbn:de:zbw-retromon-3049

Document type:: Monograph

Author:: Gehrke, Franz

Title:: Die neuere Entwicklung des Petroleumhandels in Deutschland

Place of publication:: Tübingen

Publisher:: Verlag der H. Laupp'schen Buchhandlung

Year of publication:: 1906

Scope:: 1 Online-Ressource (VII, 121 Seiten)

Digitisation:: 2017

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: I. Fundstätten

Collection:: Economics Books

out THEORY OF STATISTICS. and possesses all the properties of, a correlation-coefficient ; the name may, however, be applied to it, pending the proof. A correlation-coefficient with » secondary subscripts will be termed a correlation of order p. Evidently, in the case of a correlation- coefficient, the order in which both primary and secondary subscripts is written is indifferent, for the right-hand side of equation (2) is unaltered by writing 2 for 1 and 1 for 2. The correlations 7, 74, etc., may be regarded as of order zero, and spoken of as total, as distinct from partial, correlations. 6. If the regressions Bus... m bugs...» 6b. be assigned the “best ” values, as determined by the method of least squares, the difference between the actual value of x; and the value assigned by the right-hand side of the regression-equation (1), that is, the error of estimate, will be denoted by x5; ,.. . .; ¢.c as a defini- tion we have L193...n=% 7 Dinse) np 7 bis2s...n%s adler Diniz loin)" . (3) where x, x, . . . . x, are assigned any one set of observed values. Such an error (or residual, as it is sometimes called) denoted by a symbol with p secondary suffixes, will be termed a deviation of the pth order. Finally, we will define a generalised standard-deviation O13 . . . . » DY the equation N.ol, Sl aE Ns ih ) , - . (4) N being, as usual, the number of observations. A standard- deviation denoted by a symbol with p secondary suffixes will be termed a standard-deviation of the pth order, the standard- deviations oy a, etc., being regarded as of order zero, the standard- deviations ay, 04; €tc., (cf. eqn. (d) of § 3) of the first order, and 0 on. 7. From the reasoning of § 3 it follows that the “least-square” values of the partial regressions b;,3 . . . . a etc, will be given by equations of the form Sy —bm....a Xt... . + bins... ns Ta) = (mr, EE SE ETE IT § being very small. That is, neglecting the term in &? Sao(2, x bios ..n-Tgt a bins . . .. m1 Tn) =0, or, more briefly, in terms of the notation of equation (3), (xy. 2195. ...2n)=0. : (5) There are a large number of these equations, (n — 1) for determin- ing the coefficients by, . . .. a» etc., (n— 1) again for determining FON

Access restriction

Copyright

Full text: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation