Open AccessOn the partial correlation ratio
Publication year - 1915
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1915.0041
Subject(s) - partial correlation , mathematics , correlation coefficient , linear regression , correlation ratio , statistics , correlation , regression analysis , pearson product moment correlation coefficient , measure (data warehouse) , regression , geometry , computer science , database
(1) In a paper communicated to the Royal Society in 1903 I gave very briefly in a footnote the properties of thecorrelation ratio . These properties were discussed more at length in my memoir, “On the General Theory of Skew Correlation and Non-linear Regression,” published in 1905. The two papers dealt only with thetotal correlation ratio , or the relation between two variates without consideration of any other correlated variates. The introduction of the correlation ratio enabled the measure of the relationship between two variates to be expressed by a single number, measuring its total intensity, in cases where the regression line was of any form. The ratio passed into the usual correlation coefficient when the regression line became straight. This correlation ratio has been generally accepted by statisticians as a useful measure of relationship in cases of skew correlation and non-linear regression. Shortly after the appearance of the above memoirs I generalised this coefficient in a manner comparable with the generalisation of the coefficient of correlation, namely, by the definitions of themultiple correlation ratio and of thepartial correlation ratio . These ratios correspond to the multiple correlation coefficient and the partial correlation coefficient in multiple linear regression. Their importance is very considerable, as they enable us to measure the intensity of association between two variates when other correlated variates are considered as constant without any assumption that the regression is linear, still less that the frequencies follow the normal (or Laplace-Gaussian) surface. I had not intended to discuss the results of the present paper before the probable errors had been provided, but the recent revival of interest in skew regression, and its fundamental importance in all higher statistical inquiry, justifies, at least, the publication of those formulæ which are fundamental to the subject. (2) I deal first with the problem of three variates, although the extension to any number is not hard to make.