Orthogonal regression: A teaching perspective

International Journal of Mathematical Education in Science and Technology

Volumn 43, Issue 1, 2012, Pages 134-143

  Carr, James R ^a  

^a UNIVERSITY OF NEVADA   (United States)

Author keywords

data visualization; errors in variables; geyser eruption data; least squares; major axis; orthogonal regression; reduced major axis

Indexed keywords

EID: 84855868765     PISSN: 0020739X     EISSN: 14645211     Source Type: Journal    
DOI: 10.1080/0020739X.2011.573876     Document Type: Article

References (25)

1. Weisberg, S. 1985. Applied Linear Regression,2nd ed, New York: John Wiley and Sons.
2. Chatterjee, S, Handcock, MS and Simonoff, JS. 1995. A Casebook for a First Course in Statistics and Data Analysis, New York: John Wiley and Sons.
3. Rinehart, JS and Murphy, A. 1969. Observations of pre- and post-earthquake performance of Old Faithful geyser. J. Geophys. Res., 74: 574-575.
4. Imbrie, J. 1956. The place of biometrics in taxonomy. Bull. Am. Mus. Nat. Hist., 108(2): 211-252.
5. Miller, RL and Kahn, JS. 1962. Statistical Analysis in the Geological Sciences, New York: Wiley.
6. Davis, JC. 1986. Statistics and Data Analysis in Geology,2nd ed, New York: Wiley.
7. Cheng, CL and van Ness, JW. 1999. Statistical Regression with Measurement Error, New York: Arnold, London (co-published in the USA by Oxford University Press.
8. Adcock, RJ. 1878. A problem in least squares. Analyst, 5: 53-54.
9. Pearson, K. 1901. On lines and planes of closest fit to systems of points in space. Philos. Mag., 2(6): 559-572.
10. Kermack, KA and Haldane, JBS. 1950. Organic correlation and allometry. Biometrika, 37: 30-41.
11. York, D. 1966. Least-squares fitting of a straight line. Can. J. Phys., 44: 1079-1086.
12. Kruskal, WH. 1953. On the uniqueness of the line of organic correlation. Biometrics, 9(1): 47-58.
13. Till, R. 1974. Statistical Methods for the Earth Scientist: An Introduction, New York: John Wiley and Sons.
14. Fuller, WA. 1987. Measurement Error Models, New York: John Wiley and Sons.
15. Cheng, CL and van Ness, JW. 1988. Generalized M-estimators for errors in variables regression. Ann. Stat., 20: 385-397.
16. Bickel, PJ and Ritov, Y. 1987. Efficient estimation in the errors in variables model. Ann. Stat., 15: 513-540.
17. Burr, D. 1988. On errors-in-variables in binary regression - Berkson case. J. Am. Stat. Assoc., 83: 739-743.
18. Schafer, DW and Purdy, K. 1996. Likelihood analysis for errors-in-variables regression with replicate measurement. Biometrika, 83: 813-824.
19. Carroll, RJ and Ruppert, D. 1996. The use and misuse of orthogonal regression in linear errors-in-variables models. Am. Stat., 50(1): 1-6.
20. McCartin, BJ. 2003. A geometric characterization of linear regression. Statistics, 37(2): 101-117.
21. Vincente de Julián-Ortiz, J, Pogliani, L and Besalú, E. 2010. Two-variable linear regression: Modelling with orthogonal least-squares analysis. J. Chem. Educ., 87(9): 994-995.
22. Li, HC. 1984. A generalized problem of least squares. Am. Math. Mon., 91(2): 135-137.
23. Shuchat, A. 1985. Generalized least squares and eigenvalues. Am. Math. Mon., 92(9): 656-659.
24. Hall, T. 1970. Carl Friedrich Gauss (translated by A. Froderberg), Cambridge, MA: MIT Press.
25. Carroll, RJ, Ruppert, D, Stefanski, LA and Crainiceanu, CM. 2006. Measurement Error in Nonlinear Models: A Modern Perspective,2nd ed, London: Chapman and Hall.