Artículo
Bruzzone, H.; Moreno, C. "When errors in both coordinates make a difference in the fitting of straight lines by least squares" (1998) Measurement Science and Technology. 9(12):2007-2011
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Abstract:
The problem of assessing the incidence of the x errors on the fitting parameters and their uncertainties in straight-line fittings is addressed. The case in which the x and y errors are proportional to each other is studied in detail. Limits for the maximum expected variation of the fitting values due to the inclusion of the x errors are given in terms of the standard fitting results, namely those obtained disregarding the x errors. Closed expressions for the parameters' values and their uncertainties are also given in terms of the standard fitting results. The main inaccuracies of the standard fitting are investigated analytically. The general case of point-dependent errors is also briefly discussed.
Registro:
| Documento: | Artículo |
| Título: | When errors in both coordinates make a difference in the fitting of straight lines by least squares |
| Autor: | Bruzzone, H.; Moreno, C. |
| Filiación: | Inst. de Física del Plasma, Fac. de Ciencias Exactas y Naturales, Ciudad Universitaria, Pab. 1, Buenos Aires 1428, Argentina Colorado State University, Engineering Research Center, Fort Collins, CO 80523, United States |
| Palabras clave: | Errors in both coordinates; Errors in x; Least-squares; Linear regression; Straight-line fitting; Straight-line fitting; Curve fitting; Error analysis; Least squares approximations; Regression analysis; Measurement errors |
| Año: | 1998 |
| Volumen: | 9 |
| Número: | 12 |
| Página de inicio: | 2007 |
| Página de fin: | 2011 |
| DOI: | http://dx.doi.org/10.1088/0957-0233/9/12/012 |
| Título revista: | Measurement Science and Technology |
| Título revista abreviado: | Meas. Sci. Technol. |
| ISSN: | 09570233 |
| CODEN: | MSTCE |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09570233_v9_n12_p2007_Bruzzone |
Referencias:
- Barker, D.R., Diana, L.M., Simple method for fitting data when both variables have uncertainties (1974) Am. J. Phys., 42, pp. 224-227
- Bevington, P.R., (1969) Data Reduction and Error Analysis for the Physical Sciences, , New York: McGraw-Hill
- Boggs, P.T., Byrd, R.H., Schnabel, R.B., A stable and efficient algorithm for nonlinear orthogonal distance regression (1987) SIAM J. Sci. Statist. Comput., 8, pp. 1052-1078
- Forbes, A.B., Generalised regression problems in metrology (1993) Numerical Algorithms, 5, pp. 523-533. , New York: Baltzer
- Gill, P.E., Murray, W., Wright, M.H., (1981) Practical Optimization, , London: Academic
- Macdonald, J.R., Thompson, W.J., Least-squares fitting when both variables contain errors: Pitfalls and possibilities (1992) Am. J. Phys., 60, pp. 66-73
- Moreno, C., Bruzzone, H., Parameters' variances of a least-squares determined straight-line with errors in both coordinates (1993) Meas. Sci. Technol., 4, pp. 635-636
- Pearson, K., On lines and planes of closest fit to systems of points in space (1901) Phil. Mag., 2, pp. 559-572
- Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., (1992) Numerical Recipes: The Art of Scientific Computing 2nd Edn, , New York: Cambridge University Press
- Williamson, J.H., Least-squares fitting of a straight line (1968) Can. J. Phys., 46, pp. 1845-1847
- York, D., Least-squares fitting of a straight line (1966) Can. J. Phys., 44, pp. 1079-1086
Citas:
---------- APA ----------
Bruzzone, H. & Moreno, C. (1998) . When errors in both coordinates make a difference in the fitting of straight lines by least squares. Measurement Science and Technology, 9(12), 2007-2011.http://dx.doi.org/10.1088/0957-0233/9/12/012
---------- CHICAGO ----------
Bruzzone, H., Moreno, C. "When errors in both coordinates make a difference in the fitting of straight lines by least squares" . Measurement Science and Technology 9, no. 12 (1998) : 2007-2011.http://dx.doi.org/10.1088/0957-0233/9/12/012
---------- MLA ----------
Bruzzone, H., Moreno, C. "When errors in both coordinates make a difference in the fitting of straight lines by least squares" . Measurement Science and Technology, vol. 9, no. 12, 1998, pp. 2007-2011.http://dx.doi.org/10.1088/0957-0233/9/12/012
---------- VANCOUVER ----------
Bruzzone, H., Moreno, C. When errors in both coordinates make a difference in the fitting of straight lines by least squares. Meas. Sci. Technol. 1998;9(12):2007-2011.http://dx.doi.org/10.1088/0957-0233/9/12/012
