Page 151 - Modern Analytical Chemistry

1400-CH05 9/8/99 4:00 PM Page 134

134 Modern Analytical Chemistry

Nimura, Y.; Carr, M. R. “Reduction of the Relative Error in the Harris, D. C. “Nonlinear Least-Squares Curve Fitting with
Standard Additions Method,” Analyst 1990, 115, 1589–1595. Microsoft Excel Solver,” J. Chem. Educ. 1998, 75, 119–121.
The following paper discusses the importance of weighting Lieb, S. G. “Simplex Method of Nonlinear Least-Squares—A
experimental data when using linear regression Logical Complementary Method to Linear Least-Squares
Karolczak, M. “To Weight or Not to Weight? An Analyst’s Analysis of Data,” J. Chem. Educ. 1997, 74, 1008–1011.
Dilemma,” Curr. Separations 1995, 13, 98–104. Machuca-Herrera, J. G. “Nonlinear Curve Fitting with
Algorithms for performing a linear regression with errors in both Spreadsheets,” J. Chem. Educ. 1997, 74, 448–449.
x and y are discussed in Zielinski, T. J.; Allendoerfer, R. D. “Least Squares Fitting of
Irvin, J. A.; Quickenden, T. L. “Linear Least Squares Treatment Nonlinear Data in the Undergraduate Laboratory,” J. Chem.
When There Are Errors in Both x and y,” J. Chem. Educ. 1983, Educ. 1997, 74, 1001–1007.
60, 711–712. More information on multivariate regression can be found in
Kalantar, A. H. “Kerrich’s Method for y = ax Data When Both y Lang, P. M.; Kalivas, J. H. “A Global Perspective on Multivariate
and x Are Uncertain,” J. Chem. Educ. 1991, 68, 368–370. Calibration Methods,” J. Chemometrics 1993, 7, 153–164.
Macdonald, J. R.; Thompson, W. J. “Least-Squares Fitting When Kowalski, B. R.; Seasholtz, M. B. “Recent Developments in
Both Variables Contain Errors: Pitfalls and Possibilities,” Am. Multivariate Calibration,” J. Chemometrics 1991, 5 129–145.
J. Phys. 1992, 60, 66–73. An additional discussion on method blanks is found in the
Ogren, P. J.; Norton, J. R. “Applying a Simple Linear Least- following two papers.
Squares Algorithm to Data with Uncertainties in Both Cardone, M. J. “Detection and Determination of Error in
Variables,” J. Chem. Educ. 1992, 69, A130–A131. Analytical Methodology. Part II. Correction for Corrigible
The following paper discusses some of the problems that may be Systematic Error in the Course of Real Sample Analysis,” J.
encountered when using linear regression to model data that have Assoc. Off. Anal. Chem. 1983, 66, 1283–1294.
been mathematically transformed into a linear form. Cardone, M. J. “Detection and Determination of Error in
Chong, D. P. “On the Use of Least Squares to Fit Data in Linear Analytical Methodology. Part IIB. Direct Calculational
Form,” J. Chem. Educ. 1994, 71, 489–490. Technique for Making Corrigible Systematic Error
The analysis of nonlinear data is covered in the following papers. Corrections,” J. Assoc. Off. Anal. Chem. 1985, 68, 199–202.

5 J REFERENCES

1. Battino, R.; Williamson, A. G. J. Chem. Educ. 1984, 61, 51–52. 9. Bonate, P. J. Anal. Chem. 1993, 65, 1367–1372.
2. Ebel, S. Fresenius J. Anal. Chem. 1992, 342, 769. 10. (a) Sharaf, M. A.; Illman, D. L.; Kowalski, B. R. Chemometrics,
3. ACS Committee on Environmental Improvement “Guidelines for Wiley-Interscience: New York, 1986; (b) Deming, S. N.; Morgan,
Data Acquisition and Data Quality Evaluation in Environmental S. L. Experimental Design: A Chemometric Approach, Elsevier:
Chemistry,” Anal. Chem. 1980, 52, 2242–2249. Amsterdam, 1987.
4. Moody, J. R.; Greenburg, P. R.; Pratt, K. W.; et al. Anal. Chem. 1988, 11. Beebe, K. R.; Kowalski, B. R. Anal. Chem. 1987, 59,
60, 1203A–1218A. 1007A–1017A.
5. Committee on Analytical Reagents, Reagent Chemicals, 8th ed., 12. Cardone, M. J. Anal. Chem. 1986, 58, 433–438.
American Chemical Society: Washington, DC, 1993. 13. Cardone, M. J. Anal. Chem. 1986, 58, 438–445.
6. Cardone, M. J.; Palmero, P. J.; Sybrandt, L. B. Anal. Chem. 1980, 52, 14. Wojciechowski, M; Balcerzak, J. Anal. Chim. Acta 1991, 249,
1187–1191. 433–445.
7. Draper, N. R.; Smith, H. Applied Regression Analysis, 2nd ed. Wiley: 15. Troost, J. R.; Olavesen, E. Y. Anal. Chem. 1996, 68, 708–711.
New York, 1981. 16. Franke, J. P.; de Zeeuw, R. A.; Hakkert, R. Anal. Chem. 1978, 50,
8. (a) Miller, J. N. Analyst 1991, 116, 3–14; and (b) Sharaf, M. A.; Illman, 1374–1380.
D. L.; Kowalski, B. R. Chemometrics, Wiley-Interscience: New York,
1986; pp. 126–127.