
Accession Number : AD0671799
Title : ON A PROBLEM OF FIXING THE LEVEL OF INDEPENDENT VARIABLES IN A LINEAR REGRESSION FUNCTION.
Descriptive Note : Technical rept.,
Corporate Author : NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
Personal Author(s) : Takeuchi,Kei
Report Date : JUN 1968
Pagination or Media Count : 29
Abstract : Suppose that a linear regression model Y = beta'x + U is given. It is desirable to fix x so as to make E(Y) = beta'x as near to some prescribed level c as possible. Asymptotic consideration leads to a solution of the type x circumflex = (cM(beta circumflex)/(beta circumflex')M(beta circumflex) + k(sigma circumflex)squared) where beta circumflex is the least square estimator of beta, and (sigma circumflex)squared is the unbiased estimator of sigma squared = V(U). Under the assumption of normality for the distribution of U, an exact formula for the first two moments of the error beta'(x circumflex) is given, and by expanding the formula for the mean square error it is recommended that k be chosen to be equal to max (5p,0) where p is the dimension of the x vector. (Author)
Descriptors : (*REGRESSION ANALYSIS, OPTIMIZATION), STATISTICAL FUNCTIONS, STATISTICAL DISTRIBUTIONS, STOCHASTIC PROCESSES, DECISION THEORY, MATHEMATICAL MODELS, LEAST SQUARES METHOD
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE