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NIST StRD Pontius: quadratic calibration of a load cell (40 points, certified values)

ToolRegression and Curve Fitting
SourceNational Institute of Standards and Technology (2012). Statistical Reference Datasets: Linear Regression. NIST, Gaithersburg, MD. Pontius dataset, certified values (copy in References/Regression-StRD/Pontius.dat).
LevelProfessional

Problem

Pontius's 40 load-cell deflections at loads from 150,000 to 3,000,000 are to be fitted by the quadratic y = B0 + B1 x + B2 x². The loads span seven orders of magnitude relative to the curvature term, so the fit is a test of numerical conditioning. Report the coefficients, their standard deviations, the residual standard deviation and R².

Inputs to Enter

  • Model: polynomial, degree 2; data: the 40 Pontius pairs pasted with x (load) first and y (deflection) second
  • Confidence 95 %
Open the Regression and Curve Fitting tool

Answers

  • B0 = 6.73565789473684 × 10⁻⁴ (SD 1.07938612033077 × 10⁻⁴)
  • B1 = 7.32059160401003 × 10⁻⁷ (SD 1.57817399981659 × 10⁻¹⁰)
  • B2 = −3.16081871345029 × 10⁻¹⁵ (SD 4.86652849992036 × 10⁻¹⁷)
  • Residual SD = 2.05177424076185 × 10⁻⁴, R² = 0.999999900178537, regression SS = 15.6040343244198, F = 185,330,865.995752

Notes

Paste the data (x first) and choose Polynomial, degree 2. The tool fits on the centred predictor and reports the coefficients in the original x; reproduced to 1e-8 relative (test_regression.php).

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