Criteria for Judging Adequacy of Estimation by an Approximating Response Function.
Abstract
In response surface methodology the true functional form f(x) is usually not known and the response must be approximated by means of a graduating function g(x) (for example, by a polynomial in x) over the region of interest. The relationship between an observation y and the graduating function g(x) is therefore y = g(x) + beta + epsilon, where beta = f(x) - g(x). In the report, a measure (gamma sub m) of the variation accounted for by g(x) in relation to the size of the error of estimate of g(x) and a measure (gamma sub l) of the discrepancy introduced due to the bias term beta in relation to the error of estimate of the response are suggested. Furthermore the interpolation efficiency omega = 1/(1 + (gamma sub l, sup 2)/(gamma sub m, sup 2)) is defined. This is a measure of the amount of change accounted for by the graduating function g(x) compared with the change occurring in the true function f(x) over the region of interest R. Methods for estimating the criteria are discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1973
- Accession Number
- AD0769627
Entities
People
- George E. P. Box
- John Wetz
Organizations
- University of Wisconsin–Madison