LINEAR REGRESSION MODELS, ANALYSIS AND APPLICATIONS

LINEAR REGRESSION MODELS, ANALYSIS AND APPLICATIONS

CONTENTS

PREFACE

Chapter 1 WEIGHTING AND TRANSFORMING DATA IN LINEAR REGRESSION

ABSTRACT

INTRODUCTION

WEIGHTING DATA

RANDOM ERRORS AND NOISE

MODELLING THE VARIANCES AS A FUNCTION OF THE DEPENDENT OR INDEPENDENT VARIABLE

VARIATION OF PRECISION WITH CONCENTRATION

APPLICATIONS

Enzymatic Kinetics: Lineweaver-Burk, Hones or Eadie- Hofstee?

TRANSFORMING DATA

TRANSFORMATIONS TO SIMPLIFY RELATIONSHIPS

TRANSFORMATIONS TO LINEARIZE THE MODEL

TRANSFORMATIONS TO STABILIZE VARIANCES

TRANSFORMATION BASED ON SAMPLE DATA OBSERVATIONS: BOX-COX METHOD

APPLICATIONS

Equilibrium Constant for the Heterogeneous Reaction: CoTiO3 = Co + TiO2 + CO2

The CO2 Vapour Pressure versus Temperature Case

CONCLUSION

REFERENCES

Chapter 2 REGRESSION THROUGH THE ORIGIN

ABSTRACT

INTRODUCTION

WEIGHTED REGRESSION THROUGH THE ORIGIN

STANDARD ERRORS IN REGRESSION THROUGH THE ORIGIN

CONFIDENCE INTERVALS IN REGRESSION THROUGH THE ORIGIN

INVERSE EXTRAPOLATION: REVERSE USE OF THE REGRESSION LINE THROUGH THE ORIGIN

GOODNESS OF FIT

COMPARISON BETWEEN MODELS WITH AND WITHOUT INTERCEPT

CAUTION CONCERNING ABOUT R2

CONSTRAINED (CALIBRATION) EQUATIONS

STRAIGHT LINE IN THE CASE OF ACCUMULATIVE ERRORS

ERRORS IN VARIABLES METHOD

Adcock’s Regression though the Origin

Deming Regression

Orthogonal Generalized Regression

ROBUST REGRESSION THROUGH THE ORIGIN

Least Median of Squares through the Origin (L1 Regression)

Least Absolute Deviation Regression through the Origin (L1 Regression)

Deepest Regression through the Origin in Analytical Chemistry

POLYNOMIAL REGRESSION

ANALYTICAL APPLICATIONS OF REGRESSION THROUGH THE ORIGIN

FINAL COMMENTS

REFERENCES

Chapter3LINEARREGRESSIONFORINTERVAL-VALUEDDATAINKC(R)

Abstract

1.Introduction

2.TheProposedModel

2.1ModelSpecification

2.2LeastSquaresEstimate(LSE)

2.3SumsofSquaresandCoefficientofDetermination

2.4PositiveRestrictionandGoodness-of-fit

3.PropertiesofLSE

4.Simulation

5.ARealDataApplication

Conclusion

Appendix:Proofs

ProofofProposition1

5.1ProofofTheorem1

5.2ProofofTheorem2

5.3ProofofTheorem3

5.4ProofofProposition2

5.5ProofofTheorem4

6.AppendixII:Lemmas

References

Chapter 4 LINEAR REGRESSION VERSUS NON-LINEAR REGRESSION IN MATHEMATICAL MODELING OF ADSORPTION PROCESSES

ABSTRACT

INTRODUCTION

COMMENTS ON ARTICLES STATING THAT NON-LINEAR REGRESSION IS BETTER THAN LINEAR REGRESSION IN ADSORPTION ISOTHERM MODELING

MODELING BY LINEAR AND NON-LINEAR REGRESSIONS OF EQUILIBRIUM ISOTHERMS IN ADSORPTION OF HEAVY METAL IONS ONTO SURFACE-FUNCTIONALIZED POLYMER BEADS

CONCLUSION

REFERENCES

INDEX

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