
Accession Number : AD0695449
Title : LINEAR REGRESSION ON PROPORTIONS.
Descriptive Note : Technical rept.,
Corporate Author : JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS
Personal Author(s) : Watson,G. S.
Report Date : JAN 1969
Pagination or Media Count : 8
Abstract : In linear regression of a single dependent variable y on k regressor variables x1,x2,...,xk, it is sometimes assumed that the regressors satisfy a certain linear restraint c1x1+c2x2+...+ckxk = d. For example, when the regressors are proportions, we may require that the proportions add to one. If n > k observations are taken jointly on the variables (y,x1,x2,...,xk), the regression matrix X may verge on singularity. When a desk calculator is employed and we use the usual formula 9for the residual sum of squares, roundoff errors may result in reducing the calculated residual sum of squares to a value so small that it may severly bias the analysis. In the present paper, an alternative formula for the residual sum of squares is suggested. This formula provides a way of overcoming the numerical inaccuracy problem mentioned above.
Descriptors : (*REGRESSION ANALYSIS, NUMERICAL ANALYSIS), (*NUMERICAL ANALYSIS, ACCURACY), DEOXYRIBONUCLEIC ACIDS, LEAST SQUARES METHOD, STOCHASTIC PROCESSES, MATRICES(MATHEMATICS), ANALYSIS OF VARIANCE, ERRORS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE