Chapter 2. Designs for Simple Linear Regression

  1. Martijn P. F. Berger1 and
  2. Weng Kee Wong2

Published Online: 27 MAY 2009

DOI: 10.1002/9780470746912.ch2

An Introduction to Optimal Designs for Social and Biomedical Research

An Introduction to Optimal Designs for Social and Biomedical Research

How to Cite

Berger, M. P. F. and Wong, W. K. (2009) Designs for Simple Linear Regression, in An Introduction to Optimal Designs for Social and Biomedical Research, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470746912.ch2

Author Information

  1. 1

    Department of Methodology and Statistics, Maastricht University, The Netherlands

  2. 2

    Department of Biostatistics, School of Public Health, University of California, Los Angeles, USA

Publication History

  1. Published Online: 27 MAY 2009
  2. Published Print: 29 MAY 2009

ISBN Information

Print ISBN: 9780470694503

Online ISBN: 9780470746912

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Keywords:

  • designs for simple linear regression;
  • scatter plot, visualizing relationship between random variables X and Y;
  • variance–covariance matrix, determining shape and form of confidence ellipsoid;
  • E-optimality criterion, minimizing squared length of ‘largest’ axis of confidence ellipsoid;
  • values of independent variable X, having upper and lower limit xmax and xmin;
  • radiation-dosage design

Summary

This chapter contains sections titled:

  • Design problem for a linear model

  • Designs for radiation-dosage example

  • Relative efficiency and sample size

  • Simultaneous inference

  • Optimality criteria

  • Relative efficiency

  • Matrix formulation of designs for linear regression

  • Summary