Was This in Your Statistics Textbook? VI. Regression and Covariance

Abstract

SUMMARYThis paper concludes the series with comments on regression, covariance analysis, and correlation. The importance of choosing a regression function, whether linear or non-linear, appropriate to problem and data is emphasized and the nature of parameter estimation is outlined. The merits of transformation of variates and the importance of introducing a proper number of parameters are briefly discussed. Common misunderstandings of the meaning of ‘the regression of y on x’ for experimental data are related to the analysis of covariance.Regression with two or more regressors increases the computations but does not alter principles. Adjustment of means by use of covariance analysis is a much under-exploited technique in its direct sense; it also offers a computationally convenient way of handling missing observations and related problems. An attempt is made to overcome the confusions of interpretation between the regression equations of y on x and of x on y. A final section warns against misuses of correlation coefficients; the opportunities for misuse are too many for brief summary, yet such coefficients can be helpful when interpreted with care.