Fitting in Excel

As a last example, we demonstrate the versatility of the Solver by performing a -fitting of the emission data taken from Data Em iss ion. m (p.191). In order to keep the Excel spreadsheet reasonably concise, we selected the data at one wavelength only (500nm). At this wavelength, the correct amplitudes for the two species are 500 and 50 with lifetimes of 10 and 30 time units. Data are available from times 0 to 100 time units. 

An additional observation for photon counting data there are no fractions of photons and thus the count can only include integer numbers. Thus the measurements in column B are rounded down to the nearest integer. It seems to be reasonable to do the same with the calculated values in column C. However, a test in Excel reveals that such an attempt does not work. The reason is, that the solver s Newton-Gauss algorithm requires the computation of the derivatives of the objective (x2 or ssq) with respect to the parameters. A rounding would destroy the continuity of the function and effectively wipe out the derivatives. 

---

Rather than writing a short program in Matlab for this result, we demonstrate how to perform the task of a straight line fit in Excel. Excel actually provides several ways of performing the job of fitting the best line through a set of data pairs. The most convenient is probably the Add Trendline. .. tool which delivers the result in a few clicks. 

Open the file kinetics B (the file kinetics B.stat-mr contains a more detailed description of the statistics for the fitting in Excel format). 

Kemmer G. Keller S. (2010). Nonlinear least-squares data fitting in Excel spreadsheets. Nat Protoc., 5,267-281. 

Polypropylene Polypropylene (PP) pipe and fittings have excellent resistance to most common organic and mineral acids and their salts, strong and weak alkahes, and many organic chemicals. They are available in sizes V2 through 6 in, in Schedules 40 and 80, but are not covered as such by ASTM specifications. 

From this figure it is clear that a much better fit is obtained. The fluid temperatures during the summer season 2001 and in the winter season 2001-2002 are still too high. This can be explained by taking into account that the real ambient temperatures during those years have not been used in the model, only average atmospheric temperatures. Fit in the winter season 2002-2003 is excellent. 

As indicated in Chapter 4.2.1, Straight Line Fit, the Excel function LINEST is a more general function than the rRENDLINE. In addition to allowing the... 

The spreadsheet in Figure 4-62 is heavily matrix based (see Chapter 2, for an introduction to basic matrix functions in Excel). It is the only way to keep the structure reasonably simple. The matrix C in cells A21 C31 is computed in the usual way, see equation (4.63) the parameters required to compute the concentration matrix are in cells Q4 S4, they include the initial concentration for species A and the two rate constants that are to be fitted. In cells E 16 018 the computation of the best absorptivity matrix A for any given concentration matrix C, is done as a matrix equation, as demonstrated in The Pseudo-Inverse in Excel (p.146). Similarly the matrix Ycaic in cells E21 031 is written as the matrix product CA. Even the calculation of the square sum of the residuals in cell R7 is written in a compact way, using the Excel function SUMXMY2, especially designed for this purpose. We refer to... 

A much more satisfactory random network model has been discussed by Alben and Boutron 82h They used a model, proposed by Polk 78> for Ge(as), scaled to fit the observed nearest neighbor 00 distance of H20(as), and with H atoms added to the OO bonds according to the Pauling ice rule that guarantees the presence of only H20 molecules 65>. In the Polk model the bond length is everywhere the same and the 000 angles are distributed with root mean square deviation of 7° about 109°. For the case of Ge(as), the observed and model radial distribution functions are in excellent agreement. 

As shown in Fig. 2.43b, the enthalpy of absorption and desorption calculated from the Van t Hoff plots using the mid-plateau pressures of PCT curves in Fig. 2.43a, which are listed in Table 2.18, is equal to -72 and 83 kJ/mol, respectively. The value of entropy is 138 and 151 J/mol K for absorption and desorption, respectively. The enthalpy value for absorption is very close to the values found in the literature for MgHj as discussed in Sect. 2.1.2 and 2.1.3. Surprisingly, however, the enthalpy of desorption at 83 kJ/mol is much greater than the former and also greater than the enthalpy of desorption of the as-received and activated MgH as shown in Fig. 2.11. The coefficients of fit are excellent and give good credibility to the obtained values. 

There are many excellent texts on nutrition. This chapter, therefore, focuses not on nutrition per se but on how biochemistry helps us understand well established and less well established aspects of nutrition and how such knowledge fits in with other subjects discussed in this text. There is now considerable medical and lay interest in what is meant by healthy and unhealthy diets. Nutrition has become a major issue in the medical sciences and in clinical practice. It is also of concern to politicians, particularly in the link between nutrition and Western diseases such as cardiovascular disease, obesity, cancer and neurological problems. In this chapter an attempt is made to provide a biochemical basis for discussion of nutrition and development of these conditions. To this end, biochemical explanations for nutritional advice and the recommendations from national bodies are provided. Similarly, explanations for the recommendations designed for different populations, different conditions and activities (physical and mental activity, the elderly, the young, during pregnancy and space flight) are discussed. Finally, the biochemistry of malnutrition, undemutrition and ovemutrition is discussed. 

For both cluster ions, the ZTRID rates for Equations (24) and (25) at room temperature (Table 6) were analyzed by the master equation method, the ab initio calculated IR intensities being used, to give the fitted values of Eq displayed in the Table. In addition, the temperature dependence of Equation (25) was fitted to the master equation simulation (the E approach), to give an independent value of Ef (0.31 eV) in excellent agreement with the value from the approach (0.32 eV). These values were corrected to 298 K by use of Equations (3) and (4) to give the BDE values displayed as AH (ZTRID). 

Lang s result from the numerical theory is in excellent agreement with the general theory in the previous section. If both tip state and sample state are. 9-wave states, the tunneling conductance should have a spherical distribution, and the apparent radius should equal the nominal distance between the two nuclei. The radius obtained from the figure fits well with this expectation. 

---