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Fitting Models to Data: Residual Analysis, a Primer

In: Uncertainty Quantification and Model Calibration

Author

Listed:
  • Julia Martin
  • David Daffos Ruiz De Adana
  • Alberto Romero Gracia
  • Agustin G. Asuero

Abstract

The aim of this chapter is to show checking the underlying assumptions (the errors are independent, have a zero mean, a constant variance and follows a normal distribution) in a regression analysis, mainly fitting a straight-line model to experimental data, via the residual plots. Residuals play an essential role in regression diagnostics; no analysis is being complete without a thorough examination of residuals. The residuals should show a trend that tends to confirm the assumptions made in performing the regression analysis, or failing them should not show a tendency that denies them. Although there are numerical statistical means of verifying observed discrepancies, statisticians often prefer a visual examination of residual graphs as a more informative and certainly more convenient methodology. When dealing with small samples, the use of the graphic techniques can be very useful. Several examples taken from scientific journals and monographs are selected dealing with linearity, calibration, heteroscedastic data, errors in the model, transforming data, time-order analysis and non-linear calibration curves.

Suggested Citation

  • Julia Martin & David Daffos Ruiz De Adana & Alberto Romero Gracia & Agustin G. Asuero, 2017. "Fitting Models to Data: Residual Analysis, a Primer," Chapters, in: Jan Peter Hessling (ed.), Uncertainty Quantification and Model Calibration, IntechOpen.
    • Handle: RePEc:ito:pchaps:118800
    DOI: 10.5772/68049
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    More about this item

    Keywords

    least squares method; residual analysis; weighting; transforming data;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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