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NIST StRD Norris: straight-line calibration of an ozone monitor (36 points, certified values)

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

Problem

Norris's 36 calibration readings of an ozone monitor against the NIST reference values are to be fitted by a straight line y = B0 + B1 x. Report the coefficients with their standard deviations, the residual standard deviation, R² and the analysis-of-variance table to the NIST certified precision, and the fitted value at x = 500 with its confidence and prediction intervals.

Inputs to Enter

  • Model: linear with intercept; data: the 36 Norris pairs with x (reference) first and y (reading) second (loaded by default)
  • Confidence 95 %, predict at x₀ = 500
Open the Regression and Curve Fitting tool (loaded with this example)

Answers

  • B0 = −0.262323073774029 (SD 0.232818234301152), B1 = 1.00211681802045 (SD 0.000429796848199937)
  • Residual SD = 0.884796396144373, R² = 0.999993745883712
  • Regression SS = 4,255,954.13232369, residual SS = 26.6173985294224 on 34 df, F = 5,436,385.54079785
  • Fitted value at x = 500: 500.796 (−0.262323 + 1.00211682 · 500); the tool's interval half-widths follow the closed forms s √(1/n + (x₀ − x̄)²/S_xx) and s √(1 + 1/n + …) with t_0.975,34 = 2.0322

Notes

The tool's default data set is Norris (x column first, the NIST file lists y first); press Submit. Reproduced to 1e-9 relative or better (test_regression.php).

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