The story of Pittsburgh: Petroleum and natural gas : in two parts, part two

Petroleum and natural gas : in two parts, part two (Vol. 1, nr. 11)

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Multivolume work

Identifikator:: 1831622599

Document type:: Multivolume work

Title:: The story of Pittsburgh

Place of publication:: Pittsburgh

Publisher:: First National Bank

Year of publication:: 1919-1930

Collection:: Economics Books

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Volume

Identifikator:: 1831623528

URN:: urn:nbn:de:zbw-retromon-239829

Document type:: Volume

Title:: Petroleum and natural gas : in two parts, part two

Volume count:: Vol. 1, nr. 11

Place of publication:: Pittsburgh

Publisher:: First National Bank

Year of publication:: 1924

Scope:: [ca. 38] Seiten

Digitisation:: 2022

Collection:: Economics Books

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CHAPTER XII. PARTIAL CORRELATION, 1-2, Introductory explanation—3. Direct deduction of the formule for two variables—4. Special notation for the general case : generalised re- gressions—5. Generalised correlations—6. Generalised deviations and standard-deviations—7-8. Theorems concerning the generalised pro- duct-sums—9. Direct interpretation of the generalised regressions— 10-11. Reduction of the generalised standard-deviation—12. Reduc- tion of the generalised regression—13. Reduction of the generalised correlation-coefficient—14. Arithmetical work : Example i. : Example ii.—15. Geometrical representation of correlation between three variables by means of a model—16. The coefficient of n-fold correlation —17. Expression of regressions and correlations of lower in terms of those of higher order—18. Limiting inequalities between the values of correlation-coefficients necessary for consistence—19. Fallacies. 1. In Chapters IX.-XI. the theory of the correlation-coefficient for a single pair of variables has been developed and its applications illustrated. But in the case of statistics of attributes we found It necessary to proceed from the theory of simple association for a single pair of attributes to the theory of association for several attributes, in order to be able to deal with the complex causation characteristic of statistics; and similarly the student will find it impossible to advance very far in the discussion of many problems in correlation without some knowledge of the theory of multiple correlation, or correlation between several variables. In such a problem as that of illustration i., Chap. X., for instance, it might be found that changes in pauperism were highly correlated (positively) with changes in the out-relief ratio, and also with changes in the proportion of old ; and the question might arise how far the first correlation was due merely to a tendency to give out- relief more freely to the old than the young, 7.e. to a correlation between changes in out-relief and changes in proportion of old. The question could not at the present stage be answered by work- ing out the correlation-coefficient between the last pair of variables, for we have as yet no guide as to how far a correlation between 290

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