ON A PROBLEM OF FIXING THE LEVEL OF INDEPENDENT VARIABLES IN A LINEAR REGRESSION FUNCTION.

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 (5-p,0) where p is the dimension of the x vector. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1968
Accession Number
AD0671799

Entities

People

  • Kei Takeuchi

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computing-Related Activities
  • Data Science
  • Estimators
  • Information Science
  • Mathematics
  • Normality
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Facility/Structural Engineering.
  • Regression Analysis.