An Introduction to the theory of statistics

Bibliographic data

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

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

IX.—CORRELATION. RR and CC given by the regression equations (a) and (3). In doing this it is as well to determine a point at each end of both lines, and then to check the work by seeing that they meet in the mean of the whole distribution. Thus RR is determined from (a) by the points ¥Y=0, X=19-13 and Y=6, X=1391: CC is determined from (%) by the points X=12, ¥=564 and X=21, ¥ =114. Marking in these points, and drawing the lines, they will be found to meet in the mean, X=15'94, Y=367. The diagram gives a very clear idea of the distribution ; clearly the regression is as nearly linear as may be with so very scattered a distribution, and there are no very exceptional observations. The most exceptional districts are Brixworth and St Neots with rather low earnings but very low pauperism, and Glendale and Wigton with the highest earnings but a pauperism well above the lowest— over 2 per cent. 16. When a classified correlation-table is to be dealt with, the procedure is of precisely the same kind as was used in the calcula- tion of a standard deviation, the same artifices being used to shorten the work. That is to say, (1) the product-sum is calculated in the first instance with respect to an arbitrary origin, and is afterwards reduced to the value it would have with respect to the mean; (2 the arbitrary origin is taken at the centre of a class-interval ; (3 the class-interval is treated as the unit of measurement throughout the arithmetic. Let deviations from the arbitrary origin be denoted by £7, and let £7 be the co-ordinates of the mean. Then ¢=z +E g=y+7 - En=xy+ Ey +e + Gi. Therefore, summing, since the second and third sums on the right vanish, being the sums of deviations from the mean, (én) = Z(xy) + NE7, or bringing 2(zy) to the left, (wy) = 3(&) - Ne3. That is, in terms of mean-products, using »’ to denote the mean- product for the arbitrary origin, r=p -5&. In any case where the origin from which deviations have been measured is not the mean, this correction must be used. It will sometimes give a sensible correction even for work in the form of 18,

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation