Excel curve fitting

Mortimer, R. G., 1999. Mathematics for Physical Chemistry, 2nd ed. Academic Press, San Diego, CA. [This book contains an introduction to computer use with brief comments, references and sources to BASIC, Excel, graphics, curve fitting, and Mathematica.]... 

It is worthwhile indicating that the values of o, fitted excellently a third-degree curve expressed by ... 

From Ref. 22) the values of the composite moduli in the direction of the fibers were taken for various fiber-volume contents, whereas the mesophase volume fractions Uj were determined from the experimental values of these quantities for certain values of uf s, by applying the approximate multilayer model introduced by Ref. 4). These values fitted excellently a second degree curve expressed by ... 

The parameters are easily determined by using computer software. In Microsoft Excel, the data are put into columns A and B and the graph is created as for a linear curve fit. This time, though, when adding the trendline, choose the polynomial icon and use 2 (which gives powers up to and including x ). The result is... 

The best-fitting set of parameters can be found by minimization of the objective function (Section 13.2.8.2). This can be performed only by iterative procedures. For this purpose several minimization algorithms can be applied, for example, Simplex, Gauss-Newton, and the Marquardt methods. It is not the aim of this chapter to deal with non-linear curve-fitting extensively. For further reference, excellent papers and books are available [18]. 

To dearly distinguish between these two modes of solvent penetration of the gel, we immersed poly(acrylamide-co-sodium methacrylate) gels swollen with water and equilibrated with either pH 4.0 HQ or pH 9.2 NaOH solution into limited volumes of solutions of 10 wt % deuterium oxide (DzO) in water at the same pHs. By measuring the decline in density of the solution with time using a densitometer, we extracted the diffusion coefficient of D20 into the gel using a least squares curve fit of the exact solution for this diffusion problem to the data [121,149]. The curve fit in each case was excellent, and the diffusion coefficients obtained were 2.3 x 10 5cm2/s into the ionized pH 9.2 gel and 2.4 x 10 5 cm2/s into the nonionized pH 4.0 gel. These compare favorably with the self diffusion coefficient of D20, which is 2.6 x 10 5 cm2/s, since the presence of the polymer can be expected to reduce the diffusion coefficient about 10% in these cases [150], In short, these experiments show that individual solvent molecules can rapidly redistribute between the solution and the gel by a Fickian diffusion process with diffusion coefficients slightly less than in the free solution. 

Please verify for yourself that this equation is correct. If one does not know Cmax or cannot make a reasonable guess, then one must use nonlinear curve fitting techniques, the simplest of which is the Solver tool in Excel. 

Curve-fitting computation technique was applied for the calculation of formation constants of calcium lactate in methanol-water, ethanol-water, and glucose-water systems (60) with excellent results. In the calculation of the average formation constant Kav( = (Ki K2)i), P turned out to be about 190 for the methanol-water system, 192 for the ethanol-water system, and 185 for the glucose-water system. The value of b was 204. 

Excel provides several ways to find the coefficients that provide the best fit of a function to a set of data points — a process sometimes referred to as curve fitting. The "best fit" of the curve is considered to be foimd when the sum of the squares of the deviations of the data points from the calculated curve is a minimum. In the field of statistics, finding the least-squares best-fit parameters that describe a data set is known as regression analysis. In this chapter you ll learn how to perform simple and multiple linear regression... 

In this chapter you ll learn how to use the Solver, Excel s powerful optimization package, to perform non-linear least-squares curve fitting. 

Microsoft Excel or Sigma Plot (Jandel Scientific, Corte Madera, CA) or any database software that allows curve fitting. 

Spreadsheet Applications. Applications of Microsoft Excel in Analytical Chemistry, by Stanley R. Crouch and F. James Holler, treats in detail the spreadsheet approaches summarized in the text. This supplement contains 16 chapters that lead the student from basic concepts and operations to using spreadsheets for simulations, curve fitting, data smoothing, curve resolution, and many other topics. Topics in this companion book are correlated with topics in the text. See pages xvii and xviii for a correlation chart. Summaries in the text point to specific chapters and sections in the companion book. For added value and convenience, this ancillary can be packaged with the text. Contact your Thomson Brooks/Cole representative for details. 

Straight line curve fit using Excel, Appendix E, p. 294. 

If the parameters enter the equation linearly, then the minimization problem reduces to a set of linear equations which are solved easily by Excel and MATLAB. The effectiveness of the curve fit is often reported as values of the linear correlation coefficient squared, r. The linear correlation coefficient is defined as (Press et al., 1986, p. 484) ... 

Figure E.I. Linear curve fit to data in Table E.l using Excel.

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