Advertisement

Hector pp 83-86 | Cite as

On optimal designs for straight line regression with nonconstant variance

  • W. Bischoff
  • W. Fieger
Conference paper

Abstract

For estimating the unknown parameters α,β of the straight line regression y = α +β t by the wellknown method of least squares, we consider n (n ≥ 2) measurements Y1,…,Yn which are disturbed by errors zi·in measuring, for the control variables t1,…,tn. The measured values
$$\text{y}_\text{i} = \alpha + \beta \text{t}_\text{i} + \text{z}_\text{i} ,\;\text{i}\;\text{ = }\;\text{1,} \ldots \text{,n}$$
are realizations of the stochastic model
$$\text{Y}_\text{i} = \alpha + \beta \text{t}_\text{i} + \text{z}_\text{i} ,\;\text{i}\;\text{ = }\;\text{1,} \ldots \text{,n}$$
where Zl,…,Zn are independent random variables with mean value E(Zi) = 0, i = l,…,n. We suppose that the control variables t1,…,tn can be selected from a fixed interval [Tl,T2]. The collection (t1,…,tn) of the n control variables t1,…,tn is called the design of the experiment.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Krafft, O. (1978). Lineare statistische Modelle und optimale Versuchsplanung, Vandenhoeck und Ruprecht.Google Scholar
  2. Silvey, S.D. (1980), Optimal Design, Chapman and Hall.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • W. Bischoff
    • 1
  • W. Fieger
    • 1
  1. 1.Institut für Mathematische StatistikUniversität KarlsruheKarlsruheGermany

Personalised recommendations