LINEAR REGRESSION ON PROPORTIONS.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0695449
Entities
People
- G. S. Watson
Organizations
- Johns Hopkins University