Minimizing the Effects of Collinearity in Polynomial Regression

Industrial and Engineering Chemistry Research

Volumn 36, Issue 10, 1997, Pages 4405-4412

  Shacham, Modechai ^a   Brauner, Neima ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MEASUREMENT ERRORS; POLYNOMIALS;

COLLINEARITY; POLYNOMIAL REGRESSION;

REGRESSION ANALYSIS;

EID: 0031257864     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie970236k     Document Type: Article

References (15)

1. Abramovitz, M.; Stegun, I. A. Handbook of Mathematical Functions; Dover: New York, 1972.
2. Belsley, D. A. Condition Diagnostics: Collinearity and Weak Data in Regression; John Wiley: New York, 1991.
3. Box, G. E.; Draper, N. R. Empirial Model Building and Response Surfaces; Wiley: New York, 1987.
4. Bradley, R. A.; Srivastava, S. S. Correlation in Polynomial Regression. Am. Stat. 1979, 33, 11-14.
5. Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Hemisphere Publishing Co.: New York, 1989.
6. Forsythe, G. E. Generation and Use of Orthogonal Polynomials for Data-Fitting with Digital Computer. J. Soc. Ind. Appl. Math. 1957, 5, 74-87.
7. Giaugue, W. F.; Wiebe, R. The Heat Capacity of Hydrogen Bromide from 15°K to its Boiling Point and its Heat of Vaporization. Am. Chem. 1928, 50, 2193-2203.
8. Gunns, R. F. Towards a balanced assessment of collinearity diagnostics. Am. Stat 1984, 38 (2), 79-82.
9. Mandel, J. Evaluation and Control of Measurements, Quality and Reliability; Marcel Dekker, Inc.: New York, 1991.
10. Math Works, Inc. The Student Edition of MATLAB; Prentice Hall: Englewood Cliffs, N. J., 1992.
11. Reid, R. C.; Prausnitz, J. M.; Sherwood T. K. Properties of Gases and Liquids, 3rd ed.; McGraw Hill: New York, 1977.
12. Seber, G. A. F. Linear Regression Analysis; Wiley: New York, 1977.
13. Shacham, M.; Cutlip, M. B. POLYMATH 4.0 User's Manual; CACHE Corporation: Austin, TX, 1996.
14. Wagner, W. New Vapor Pressure Measurements for Argon and Nitrogen and a New Method for Establishing Rational Vapor Pressure Equations. Cryogenics 1973, 13, 470.
15. Wold, S.; Ruhe, A.; Wold, H.; Dunn, W. J., III. The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses. SIAM J. Stat. Comput. 1984, 5 (3), 735-743.