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Comparison of linear fits to Pearson's data

Pearson's data (K. Pearson, Philosophical Magazine, 2, 559 (1901)) is often used for testing the accuracy of a linear fit. This is a worst-case set of data with errors in both x and y coordinates.

The data is as follows:

xdxydy
0.00.035.91.0
0.90.035.40.74
1.80.0444.40.5
2.60.0354.60.35
3.30.073.50.22
4.40.113.70.22
5.20.132.80.12
6.10.222.80.12
6.50.742.40.1
7.41.01.50.044

When plotted, the data looks like this:

One test of a fitting algorithm is to swap the x and y data and their respective errors. The slope of the two fits should be reciprocal. The Chixy2 value should in theory be exactly the same as the Chiyx2 value.

Below is a comparison of the results of a linear fit of Pearson's data from several sources. As can be seen from the results, Glove gives the correct answer and is the only one that we could find that does so. (FFIT, which comes close, is the precursor of Glove.)

Comparison of Fitting Algorithms

Program Bxy sigmaBxy Byx 1/Byx Chi2xy/(N-2) Chi2yx/(N-2) Bxy/(1/Byx)
Williamson Paper3 -0.48050.05766-2.0810-0.48054  0.999921
Glove -0.479570.05487-2.08519-0.479571.5086111.5086111.000002
Glove Eff.Variance -0.462390.05956-1.81673-0.550441.4272611.7601260.840032
FFIT Add'l Opt Q -0.4799130.04315-2.0826780.480151.5087651.5087730.999504
FFIT Eff. Variance -0.462810.0574-1.81764-0.550161.519661.6845870.841228
FFIT Linear2 -0.6152410.029215-1.568851-0.637414.39754875.410020.965221
Origin y-weighted2 -0.615240.06126-1.56885-0.63741  0.965219
Origin unweighted -0.539580.04213-1.76713-0.56589  0.953508
Excel Linest fcn1 -0.539580.042127-1.76713-0.565890.8006642.6221960.953508
Sigmaplot1 -0.53960.0421-1.7671-0.56590.80072.62220.953527
Sigmaplot weight2 -0.55030.0454-1.6092-0.621430.21560.37820.885543
Lin. Reg. www site1 -0.540.04-1.77-0.560.82.60.96
Axum 4.01 -0.540.04-1.77-0.560.82.620.96
Kaleidegraph 3.01 -0.539580.042127-1.7671-0.56590.100080.3277750.953492
Kaleidegraph 3.02 -0.6152410.029215-1.56885-0.637414.3975575.410.965221
Kaleidegraph EV -0.46240.05956-1.8167-0.5504491.4273751.760250.840042

Notes:
1. unweighted
2. y-weighting only
3. J. H. Williamson, Can. J. Phys., 46, 1845 (1968).