Significance of Correlation and Regression Results
The sampling significance of correlation and regression measures
Early in this book it was pointed out that when any statistical measure, such as an average, is determined from a sample selected from a universe under study, the true value of that measure in the universe might be different from the value shown by the sample. Methods were discussed which enable one to estimate how far the average from such a sample may vary from the true average, for a stated proportion of such samples. Such estimates enable one to judge how much confidence may be placed in an average calculated from a given sample.
Different Types of Sampling Models. The applicability of sampling concepts to correlation coefficients differs widely according to the nature of the universe from which the sample is selected and the manner in which sample values of the independent variables are obtained. The interpretation of regression coefficients is much less dependent upon the shape of the underlying universe (if any) or the manner in which sample values of the independent variables are chosen; however, estimates of the reliability of regression coefficients are influenced by these factors. For convenience of exposition we shall distinguish between two principal situations or "models"--the correlation model and the regression model.1____________________
Compare M. G. Kendall, "Regression, structure and functional relationship", Part I, Biometrika, Vol. 38, pp. 11-25, June, 1951.
Kendall distinguishes between (1) situations in which values of the independent