Edward T. Peltzer
Model I and Model II Regressions

## Results for Model I and Model II Regressions

Here are the results from my MATLAB® shell-script routines for fitting a line to the example dataset (see the file: data.txt) using the various linear regression models:

Model I
Regressions
M-fileSlopeInterceptCorrelation
Coefficient
Y-on-XLsqfity.m   1.2931 ± 0.0598      9.3670 ± 1.4750   0.9014
X-on-YLsqfitx.m1.5916 ± 0.07363.0908 ± 1.89450.9014
Weighted Y-on-XLsqfityw.m   1.3322 ± 0.00644.4067 ± 0.07380.8973
Weighted Y-on-XLsqfityz.m   1.3322 ± 0.06304.4067 ± 0.72200.8973
Model II
Regressions
M-fileSlopeInterceptCorrelation
Coefficient
Major axisLsqfitma.m1.4896 ± 0.06825.2356 ± 1.64550.9014
Geometric meanLsqfitgm.m1.4346 ± 0.06136.3917 ± 1.51280.9014
Least-squares-bisector    Lsqbisec.m   1.4320 ± 0.06136.4477 ± 1.51140.9014
Least-squares-cubic    Lsqcubic.m    1.4948 ± 0.06495.2594 ± 0.62270.9583

Footnotes to table:

1. All parameters were calculated with equations from Bevington and Robinson (1992). Their standard deviations for the slope and intercept seem very small when compared to the uncertainties calculated with the other regression equations.
2. Revised weighted model I regression: equations for the slope and intercept were again taken from Bevington and Robinson (1992), however, the standard deviations in these parameters are calculated according to equations derived by York (1966). The uncertainties calculated this way seem more in line with those calculated by the other regressions.
3. The least-squares-bisector algorithm follows the suggestion of Sprent and Dolby (1980) that in the case of model II regressions, an equally strong case can be made for the line that bisects the minor angle between the two model I regressions: Y-on-X and X-on-Y. The uncertainties in the slope and intercept are calculated according to the equations derived by York (1966) in a manner analogous to that used for the geometric mean regression.