The work of the Stock Exchange

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1831284952

URN:: urn:nbn:de:zbw-retromon-225876

Document type:: Monograph

Author:: Meeker, James Edward http://d-nb.info/gnd/126597340

Title:: The work of the Stock Exchange

Edition:: Revised edition

Place of publication:: New York

Publisher:: The Ronald Press Company

Year of publication:: [1930]

Scope:: XVI, 720 Seiten; Illustrationen, Diagramme

Digitisation:: 2022

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Chapter II. Organized security markets and their economic functions

Collection:: Economics Books

XIL—PARTIAL CORRELATION. which is the value found by the previous indirect method of Chapter IX. From the fact that &,, is determined so as to make the value of 3(a, — b,,7,)? the least possible, the method of determination is sometimes called the method of least squares. Evidently all the remaining results of Chapter IX. follow from this, and notably we have for 01.9 the minimum value of s,,, the standard-deviation of errors of estimate of =0(1 -mp?) : . (a) 4. Now apply the same method to the regression-equation for m variables. Writing the equation in terms of deviations, it follows from reasoning precisely similar to that given above that no constant term need be entered on the right-hand side. For the partial regression-coefficients (the coefficients of the z’s on the right) a special notation will be used in order that the exact position of each coefficient may be rendered quite definite. The first subscript affixed to the letter 4 (which will always be used to denote a regression) will be the subscript of the z on the left (the dependent variable), and the second will be the subscript of the « to which it is attached ; these may be called the primary subscripts. After the primary subscripts, and separated from them by a point, are placed the subscripts of all the remaining variables on the right-hand side as secondary subscripts. The regression-equation will therefore be written in the form Ty =bos, n-Tg+byun,, n.23+ sre Oinos... m1" Zn i {) The order in which the secondary subscripts are written is, it should be noted, quite indifferent, but the order of the primary subscripts is material; eg. b,, _ , and boys. denote quite distinct coefficients, x, being the dependent variable in the first case and ro in the second. A coefficient with » secondary subscripts may be termed a regression of the pth order. The regressions b,,, by1s byg bg, ete., in the case of two variables may be regarded as of order zero, and may be termed total as distinct from partial regressions. 5. In the case of two variables, the correlation-coefficient Tyg may be regarded as defined by the equation 719 = (b19.07)% We shall generalise this equation in the form Tam... .0=0un... inban,.. in : +) This is at present a pure definition of a new symbol, and it remains to be shown that ry, may really be regarded as, 239

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