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Trend-surface-analysis_UNWIN

Trend-surface-analysis_UNWIN - AN INTRODUCTION TO TREND...

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AN INTRODUCTION TO TREND SURFACE ANALYSIS D.Unwin ISSN 0305-6142 ISBN 0 902246 51 8 © 1978 David J. Unwin
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CONCEPTS AND TECHNIQUES IN MODERN GEOGRAPHY No. 5 AN INTRODUCTION TO TREND SURFACE ANALYSIS by David J. Unwin (University of Leicester) CONTENTS Page I INTRODUCTION (i) Pre-requisites and purpose 3 (ii) Spatial series 3 II MATHEMATICAL DEVELOPMENT (i) The method of least squares 5 (ii) A simple example 9 (iii) A matrix formulation 15 (iv) Extension to other surface shapes 16 (v) Properties of least squares estimates and assumptions made 19 (vi) Significance testing in trend surface analysis 21 III AN EXAMPLE OF A PRACTICAL APPLICATION: DAVIES AND GAMM (1969) (i) Introduction 26 (ii) Hypothesis under test 26 (iii) Results 26 IV PROBLEMS AND PITFALLS IN TREND SURFACE ANALYSIS (i) Introduction 30 (ii) Data suitability 31 (iii) Trend specification 32 (iv) Significance testing 33 CATMOG (Concepts and Techniques in Modern Geography) CATMOG has been created to fill a teaching need in the field of quantitative methods in undergraduate geography courses. These texts are admirable guides for the teachers, yet cheap enough for student purchase as the basis of class- work. Each book is written by an author currently working with the technique or concept he describes. 1. An introduction to Markov chain analysis - L. Collins 2. Distance decay in spatial interactions - P.J. Taylor 3. Understanding canonical correlation analysis - D. Clark 4. Some theoretical and applied aspects of spatial interaction shopping models - S. Openshaw 5. An introduction to trend surface analysis - D. Unwin 6. Classification in geography - R.J. Johnston 7. An introduction to factor analytical techniques - J.B. Goddard & A. Kirby 8. Principal components analysis - S. Daultrey 9. Causal inferences from dichotomous variables - N. Davidson 10. Introduction to the use of logit models in geography - N. Wrigley 11. Linear programming: elementary geographical applications of the transportation problem - A. Hay 12. An introduction to quadrat analysis - R.W. Thomas 13. An introduction to time-geography - N.J. Thrift 14. An introduction to graph theoretical methods in geography - K.J. Tinkler 15. Linear regression in geography - R. Ferguson 16. Probability surface mapping. An introduction with examples and Fortran programs - N. Wrigley 17. Sampling methods for geographical research - C. Dixon & B. Leach 18. Questionnaires and interviews in geographical research - C. Dixon & B. Leach Other titles in preparation This series, Concepts and Techniques in Modern Geography is produced by the Study Group in Quantitative Methods, of the Institute of British Geographers. For details of membership of the Study Group, write to the Institute of British Geographers, I Kensington Gore, London, S.W.7. The series is published by Geo Abstracts, University of East Anglia, Norwich, NR4 7TJ, to whom all other enquiries should be addressed.
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