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Determining Uncertainties in Fitted Curves

In: Introduction to Statistics in Metrology

Author

Listed:
  • Stephen Crowder

    (Sandia National Laboratories)

  • Collin Delker

    (Sandia National Laboratories)

  • Eric Forrest

    (Sandia National Laboratories)

  • Nevin Martin

    (Sandia National Laboratories)

Abstract

This chapter discusses methods of fitting curves to measured data while accounting for uncertainty in the data. We start with equations for the best linear fit and uncertainties in the slope and intercept. A short discussion of linear fits when there is uncertainty in the x-values is presented next. Confidence and prediction bands are presented for expressing uncertainty in the fitted line and uncertainty in predictions made using the fitted line. Goodness-of-fit metrics are used to assess model adequacy. A summary of techniques for fitting nonlinear equations to data is given, including formulas for nonlinear confidence and prediction bands. In this chapter “nonlinear equation” means an equation that is nonlinear in the independent variable. Finally, a case study applying curve fitting to a calibration drift problem is provided with a short discussion of how to choose optimal calibration intervals based on predicted drift.

Suggested Citation

  • Stephen Crowder & Collin Delker & Eric Forrest & Nevin Martin, 2020. "Determining Uncertainties in Fitted Curves," Springer Books, in: Introduction to Statistics in Metrology, chapter 0, pages 227-265, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-53329-8_10
    DOI: 10.1007/978-3-030-53329-8_10
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