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

. THEORY OF STATISTICS. theory or by previous experience, it may be possible to throw that relation into the form Y=24 + B.¢(X), where 4 and B are the only unknown constants to be determined. If a correlation-table be then drawn up between ¥ and ¢(X) instead of ¥ and JX, the regression will be approximately linear. Thus in Table V. of the last chapter, if X be the rate of discount and Y the percentage of reserves on deposits, a diagram of the curves of regression, or curves on which the means of arrays lie, suggests that the relation between X and Y is approximately of the form X(Y -B)=4, 4 and B being constants ; that is, XY=4+ BX. Or, if we make XY a new variable, say Z, Z=4+ BX. Hence, if we draw up a new correlation-table between X and Z the regression will probably be much more closely linear. If the relation between the variables be of the form Y= ADZ we have log Y=1og 4 + X. log B, and hence the relation between log ¥ and X is linear. Similarly, if the relation be of the form X¥=4 we have log Y=1log 4 —n. log X, and so the relation between log Y¥ and log X is linear By means of such artifices for obtaining correlation-tables in which the regression is linear, it may be possible to do a good deal in difficult cases whilst using elementary methods only. The advanced student should refer to ref. 17 for a different method of treatment. 19. The only strict method of calculating the correlation coefficient is that described in Chapter IX. from the formula po SOIL Approximations to this value may, however, be N.c,0, 202

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