Confidence Bounds for the General Linear Model.
Abstract
In this paper, for the general linear model Y = X beta + e, we consider the construction of confidence bounds about the entire regression line. To accomplish this we exploit a powerful theorem of Scheffe. A procedure often encountered is one in which a set of confidence intervals about E(y,x) or prediction intervals for future observations are determined and then the end points are connected in such a fashion as to describe an envelope. The belief is that what has been accomplished is precisely what Scheffe's theorem allows one to do. In addition, we present some extensions concerning confidence bounds about combinations of regression lines and suggest a useful application of these results. Specifically, we propose to use the confidence bounds about the difference of regression lines to make a quantitative assessment of when and where independent sets of data characterizing the same phenomena are in agreement or disagreement.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1977
- Accession Number
- ADA041035
Entities
People
- J. Richard Moore
- Malcolm S. Taylor
Organizations
- Ballistic Research Laboratory