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XX.—On the Theory of Statistical Regression

Published online by Cambridge University Press:  15 September 2014

M. S. Bartlett
M. S. Bartlett
Affiliation:
Queens' College, Cambridge
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Extract

1. The product moment distribution in the general case of p normal variates, obtained in 1928 (1), and again in 1933 (2), has been awaiting further analysis. Some indication has already been given (Wishart, 1928) that new results might be expected from it; in the particular case of two variates obtained previously by Fisher (3), it has been used to deduce the distributions of the correlation coefficient (3), co-variance (4), and regression coefficient (5). In the general case, it has been used by Wilks (6) to furnish a proof of Fisher's distribution of the multiple correlation coefficient (7), and also in connection with his idea of a generalized variance (8). Further analysis appears to be most fruitful in studying statistical regression in general. It is shown in Part I of this paper that the product moment distribution can be split up into a chain of independent factors. Most of the known distributions related to regression or partial correlation are simply obtained, in a manner which clearly indicates the relations they bear to one another; the distribution of a partial regression coefficient of any order is also readily derived.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 53 , 1934 , pp. 260 - 283
Copyright
Copyright © Royal Society of Edinburgh 1934

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References

References to Literature

1.Wishart, J., 1928. Biometrika, vol. xx, A, pp. 32–52.CrossRefGoogle Scholar
2.Wishart, J., and Bartlett, M. S., 1933. Proc. Camb. Phil. Soc., vol. xxix, pp. 260–270.CrossRefGoogle Scholar
3.Fisher, R. A., 1915. Biometrika, vol. x, pp. 507–521.Google Scholar
4.Pearson, K., Jeffery, G. B., and Elderton, E. M., 1929. Biometrika, vol. xxi, pp. 164–193.Google Scholar
5. Romanovsky, V., 1926. Bulletin de l'Academie des Sciences de l' U.R.S.S., p. 646.Google Scholar
Pearson, K., 1926. Proc. Roy. Soc., A, vol. cxii, pp. 1–14.Google Scholar
6.Wilks, S. S., 1932. Annals Math. Statistics, pp. 196–203.Google Scholar
7.Fisher, R. A., 1928. Proc. Roy. Soc., A, vol. cxxi, pp. 654–673.Google Scholar
8.Wilks, S. S., 1932. Biometrika, vol. xxiv, pp. 471–494.CrossRefGoogle Scholar
9.Yule, G. U., 1907. Proc. Roy. Soc., A, vol. lxxix, pp. 182–193.Google Scholar
10.Ingham, A. E., 1933. Proc. Camb. Phil. Soc., vol. xxix, pp. 271–276.CrossRefGoogle Scholar
11.Fisher, R. A., 1925. Metron, vol. v, No. 3, pp. 90–104.Google Scholar
12.Wishart, J., and Bartlett, M. S., 1932. Proc. Camb. Phil. Soc., vol. xxviii, pp. 455–459.CrossRefGoogle Scholar
13.Fisher, R. A., 1924. Metron, vol. iii, Nos. 3–4, pp. 329–333.Google Scholar
14.Fisher, R. A., 1930. Statistical Methods for Research Workers (3rd ed.).Google Scholar
15.Fisher, R. A., 1924. Phil. Trans., B, vol. ccxiii, pp. 89–142.Google Scholar
16.Fisher, R. A., 1922. Journ. Roy. Stat. Soc., vol. lxxxv, pp. 597–612.CrossRefGoogle Scholar