[16] Nonlinear least-squares analysis

doi:10.1016/S0076-6879(85)17018-7

Methods in Enzymology

Volume 117, 1985, Pages 301-342

https://doi.org/10.1016/S0076-6879(85)17018-7 Get rights and content

Publisher Summary

This chapter highlights one of the methods for the analysis of experimental data, along with the assumptions, advantages, and disadvantages of the method. The most important experimental detail to understand for any parameter estimation procedure is the sources and magnitudes of the random and nonrandom experimental errors superimposed on the data. Moreover, computers are not oracles. The investigator needs to be continually aware that the output of any computer program is no better than what goes into it. It is important to realize that a computer is in essence the same as any other instrument in a laboratory. To obtain optimal results it must be used correctly. To use it correctly, the user must understand the assumptions which went into the development of the computer programs and their limitations.

References (41)

M.L. Johnson et al.
P.J. Munson et al.
Anal. Biochem.
(1980)
M.L. Johnson et al.
Biophys. J.
(1981)
M.L. Johnson
Biophys. J.
(1983)
M.L. Johnson et al.
Biophys. J.
(1977)
C.R. Kahn et al.
J. Biol. Chem.
(1974)
M.L. Johnson et al.
J. Biol. Chem.
(1978)
I. Isenberg
Biophys. J.
(1983)
M.E. Magar
Data Analysis in Biochemistry and Biophysics
J.A. Nelder et al.
Comput. J.
(1965)

D.W. Marquardt

SIAM J. Appl. Math

(1963)

H.O. Hartley

Technometrics

(1961)

F.B. Hildebrand

Introduction to Numerical Analysis

M.L. Johnson et al.

M.E. Magar

Data Analysis in Biochemistry and Biophysics

Y. Bard

Nonlinear Parameter Estimation

G.D.P. Box

Ann. N.Y. Acad. Sci.

(1960)

L. Endrenyi et al.

Acta Biol. Med. Ger.

(1973)

G.K. Ackers et al.

M.L. Johnson et al.

Biochemistry

(1982)

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[16] Nonlinear least-squares analysis

Publisher Summary

Anal. Biochem.

Biophys. J.

Biophys. J.

Biophys. J.

J. Biol. Chem.

J. Biol. Chem.

Biophys. J.

Data Analysis in Biochemistry and Biophysics

Comput. J.

SIAM J. Appl. Math

Technometrics

Introduction to Numerical Analysis

Data Analysis in Biochemistry and Biophysics

Nonlinear Parameter Estimation

Ann. N.Y. Acad. Sci.

Acta Biol. Med. Ger.

Biochemistry