Hector pp 83-86 | Cite as

On optimal designs for straight line regression with nonconstant variance

  • W. Bischoff
  • W. Fieger
Conference paper


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.


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  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

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