Repeated Linear Regression and Variance Components of a Population with Binomial Frequencies

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Abstract
When a variable takes the values 0, 1, 2, [long dash], n, with binomial frequencies, the variance is npq. This paper deals with a more general population where the variable takes the values Y0, Y1, Y2, [long dash], Yn with binomial frequencies. It is shown that the variance of such a Y variable may be subdivided into n components by a very simple procedure. The first component is due to the first order differences Y1 - Y0, Y2 - Y1, etc.; the second component is due to the second order differences (Y2 -Y1) - (Y1 - Y0) = Y2 - 2Y1 + Y0, etc., and so on. An application of this method to break up the genotypic variance of autotetraploids into 4 components is given.

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