Curve Fitting Toolbox

The parameters in the adsorption isotherms were estimated from the experimental equilibrium data using MATLAB Curve Fitting Toolbox. The comparison of experimental and estimated data by Langmuir, Freundlich, Redlich-Peterson and combined Langmuir-Freundlich models for the investigated systems are presented in Figures 1 to 3 for six investigated systems. 

NOTE We will show how to proceed with curve-fitting process showing both the old and new look of the MATLAB Curve Fitting Toolbox. In general. Fig. 5.2q will be reserved for the old look and Fig. 5.2b for the new look whenever there is a difference worth mentioning. 

Figure 5.15a. b show the old and new look main windows for the Curve Fitting Toolbox. 

Figure 5.15(a) The main window for the MATLAB Curve Fitting Toolbox (old look). 

Second, define the dependent (y) and independent (x) variables. Click the Data button (shown as a framed button in Fig. 5.15). Figure 5.16 shows the data window that defines thex andy variables. With the new look of MATLAB Curve Fitting Toolbox, you define the dependent variable (y), the independent variable (x), the model main category, and the method t e from the drop-down lists (shown as framed boxes in Fig. 5.15bL... 

Fourth, click the Close button to finish the data input step. Figure 5.17 shows the main window of the Curve Fitting Toolbox, after finishing the data input step. 

Figure 5.17 The MATLAB Curve Fitting Toolbox is ready for the next step, i.e., the fitting step, after properly defining the x and y variables.

Twelfth, click the OK button (shown as a framed button in Fig. 5.24). MATLAB will return to the main Fit Editor window as shown in Fig. 5.25a. Figure 5.25b shows the new look of the Curve Fitting Toolbox window where the user selects Custom Equation from the main category drop-down list and then enters the expression fory = f x a, b, c). 

Figure 5.25(a) The old look of the MATLAB Curve Fitting Toolbox, where it is ready to start the process of curve fitting or nonlinear regression. 

Figure 5.25(b) The new look of the MATLAB Curve Fitting Toolbox. After successfully entering the syntax error-free model (i.e., y = f(x)), MATLAB will either start the process of curve fitting or wait for the user s command if the Auto fit option is de-selected. 

Based on the aforementioned results, the model with the estimated parameters is definitely a misfit, as also shown in Fig. 5.26. The same terrible situation will occur with the new look MATLAB Curve Fitting Toolbox (see Fig. 5.25bl. 

Figure 5.5Qq shows the 95% confidence interval which brackets (or sandwiches) the curve. From a statistics point of view, the 95% confidence interval means that out of 100 samples being measured fory, at the given x 95 of them will have a value ofy that lies within the range ofy, (i.e., between lower f(x,) and upper / (x,)) at the given x,. For the new look of the MATLAB Curve Fitting Toolbox (see Fig. 5.25bi. click on the Tools menu, followed by the Prediction Bounds submenu, and pick up, for example, a 95% confidence interval so that the 95% confidence envelope will sandwich the curve, as shown in Fig. 5.30b. 

Finally, from the File menu in the main window of the Curve Fitting Toolbox, you may choose Generate Code from the drop-down list to create the M-file, which when executed will create a plot similar to the plot in the main Curve Fitting Toolbox, using the data that you provide as input. You can use this function with the same data you used with the MATLAB Curve Fitting Toolbox or different data sets. You may want to edit the function to customize the code. 

Figure S.34 shows the default main window of the MATLAB Surface Fitting Toolbox, which is similar to that of Fig. 5.25b (a new look for the MATLAB Curve Fitting Toolbox).

Figure 5.34 The default main window of the MATLAB Surface/Curve Fitting Toolbox.

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