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, round-off 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