Nonlinear Least-Squares Curve Fitting with Microsoft Excel Solver

Harris, Daniel C.

doi:10.1021/ed075p119

Cited by 251 publications

(223 citation statements)

References 17 publications

(20 reference statements)

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“…Excel's Solver, 20 and for estimating the precision of the resulting parameters, 21 In past years finding that minimum was a formidable problem.…”

Section: First-order Kinetics By Nonlinear Least Squaresmentioning

confidence: 99%

Linear or Nonlinear Least-Squares Analysis of Kinetic Data?

Perrin

2017

J. Chem. Educ.

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Abstract. The disadvantages of the usual linear least-squares analysis of first-and second-order kinetic data are described, and nonlinear least-squares fitting is recommended as an alternative. Keywords. Kinetics, Graduate Education/Research, ReactionsA common task in chemical kinetics is to extract the rate constant from the time dependence of concentrations. We first consider a reaction where reactant A is converted to product B, as in eq 1, and where the rate of reaction (rate of product formation or rate of reactant disappearance) is proportional to the concentration of reactant A, as in eq 2. Such a reaction is said to follow firstorder kinetics, because the rate is proportional to only one concentration.Alternatively, the rate may also be proportional to the concentration of another species C with proportionality constant k', as in eq 3. However, if C is a catalyst, so that its concentration remains constant, or if C is in large excess, so that its depletion is negligible, its concentration does not deviate from its initial concentration [C] 0 , and eq 3 can be simplified to eq 2 by setting k'[C] 0 equal to k. Such a reaction is said to follow pseudo-first-order kinetics, and k is often called a rate coefficient, rather than a rate constant, because its value changes with [C] 0 . In either case the solution to eq 2 is given by eq 4, where [A] 0 is the initial concentration of A.

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“…Excel's Solver, 20 and for estimating the precision of the resulting parameters, 21 In past years finding that minimum was a formidable problem.…”

Section: First-order Kinetics By Nonlinear Least Squaresmentioning

confidence: 99%

Linear or Nonlinear Least-Squares Analysis of Kinetic Data?

Perrin

2017

J. Chem. Educ.

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“…Treatments of the spectrophotometric data (each 5 nm) obtained during the titrations, as a function of the H + concentration, were conducted to the computer program. 35 The program allows calculation of stability constants for different stoichiometry models. The degree of refinement then guides the user to a choice between models.…”

Section: Stabilities Of Amp Complexesmentioning

confidence: 99%

“…The method of determining εM was previously described 17 and its values at different wavelengths are used in this work. Using a suitable computer program 35 we fitted the data to the final equation for estimating the formation constant of Eq. (3).…”

Section: Stabilities Of Amp Complexesmentioning

confidence: 99%

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Complexation of Thallium(I) with Adenosine 5′-Monophosphate in Aqueous Methanol Solutions

2005

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The development of various kinds of approaches to hydrophobic hydration is necessary for a better understanding of its key role in controlling biochemical processes in water. 1,2 In the last few years, several experimental and theoretical works dealing with the effect of solvent on many reactions have been published. [3][4][5] Most of these papers are concerned with the effect of solvent on reaction rates. There is surprisingly little work, involving the effect of solvent on the thermodynamics and complexation of some biologically important ligands. [6][7][8] Various empirical solvent polarity parameters have been used to describe the influence of solvents on physicochemical solute properties. 9One particularly useful set consists of complementary Lewis acid-base solvent parameters, now known for most common organic solvents.10,11 It was found for example, by analysis of the variation of Kamlet-Taft's, β and α values, 12 for mixtures of methanol and other organic solvents, that one important factor influencing the basicity or acidity of solvent mixtures is due to an order/disorder process, particularly in binary mixtures of protic solvents with non-hydrogen bond donor (non-HBD) solvents. 12,13 Nucleotides play a key role in almost all kinds of metabolic processes. Much effort was devoted to the complexes of AMP, adenosine 5′-monophosphate, with metal ions. The properties and structures of binary complexes of most metal ion-AMP systems in aqueous solution are now relatively well described.14,15 Depending on the kind of metal ion involved, coordination occurs not only to the phosphate chain but also to N-1, leading thus to macrochelates.Thallium has been recognized as a toxic element for many years. It produces a variety of adverse effects in human beings. This element acts on the central nervous system and induces an inflammatory response. 16,17 However, the metabolic action and mechanism and fate of thallium toxicity are still not well understood, though there is some experimental evidence that suggests sulfur-containing compounds have been the main detoxifying drug in the case of poisoning. 17,18 Since thallium(I) shows marked similarities to that of potassium cation, 19 its interaction with nucleotides, the monomeric units of DNA and RNA, would be of major biochemical interest.This work deals with the study of thallium(I) complexes by AMP and the determination their stability constants in different solutions of methanol + water to show how the solvent and their mixtures with various dielectric constants affect the complexation.Recently, more attention has been paid to binary solvent mixtures in this field. 20-22 Solute-solvent interactions are much more complex in mixed solvent systems than in pure solvents, due to the possibility of preferential solvation by any of the solvents present in the mixtures. Moreover, the solvent-solvent interactions produced in solvent mixtures can affect the solutesolvent interactions and therefore they can also affect preferential solvations. 23At present, there are two more imp...

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“…In addition, spreadsheets have the merits of wide accessibility and powerful computation in terms of fitting nonlinear models. For these reasons, spreadsheets such as Microsoft Excel are widely suggested to make nonlinear parameter estimation (Harris 1998;Smith et al 1998;Wraith and Or 1998;Brown 2001;Berger 2007).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of parameter uncertainties in nonlinear regression using Microsoft Excel Spreadsheet

Xie

Chau

et al. 2015

Environ Syst Res

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Background: Nonlinear relationships are common in the environmental discipline. Spreadsheet packages such as Microsoft Excel come with an add-on for nonlinear regression, but parameter uncertainty estimates are not yet available. The purpose of this paper is to use Monte Carlo and bootstrap methods to estimate nonlinear parameter uncertainties with a Microsoft Excel spreadsheet. As an example, uncertainties of two parameters (α and n) for a soil water retention curve are estimated. Results: The fitted parameters generally do not follow a normal distribution. Except for the upper limit of α using the bootstrap method, the lower and upper limits of α and n obtained by these two methods are slightly greater than those obtained using the SigmaPlot software which linearlizes the nonlinear model. Conclusions: Since the linearization method is based on the assumption of normal distribution of parameter values, the Monte Carlo and bootstrap methods may be preferred to the linearization method.

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Nonlinear Least-Squares Curve Fitting with Microsoft Excel Solver

Cited by 251 publications

References 17 publications

Linear or Nonlinear Least-Squares Analysis of Kinetic Data?

Linear or Nonlinear Least-Squares Analysis of Kinetic Data?

Complexation of Thallium(I) with Adenosine 5′-Monophosphate in Aqueous Methanol Solutions

Evaluation of parameter uncertainties in nonlinear regression using Microsoft Excel Spreadsheet

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