Computational Example of Nonlinear Regression

In the development of a new dmg, you are investigating the previously unknown reaction between two compounds X and Y to produce a valuable intermediary Z. One of the important tasks is to characterise the reaction properties. Luckily, X and 

Y are relatively easy to produce and so that multiple runs and trials could be performed. At each of the temperatures, three separate runs were performed. The results obtained are shown in Table 3.8. It is desired to fit Arrhenius s equation to this data set and determine the reaction constant and activation energy. Perform both linear and nonlinear regressions and compare the results using a = 0.05. 

The results will be presented without showing all the detailed calculations as they are relatively straightforward. From Example 3.1, we have that Arrhenius s reaction can be linearised as 

Therefore, the confidence for A can be written as [297, 301] cm s . It should be mentioned that the confidence interval is not symmetric about the mean value. This is because the exponential function does not preserve distance. 

For Ea, the mean value can be computed as = —8.314 x —178.84 = 1,486.91. The confidence interval becomes 2.208 78 x 8.314 = (—)18.36. Therefore, the confidence interval for is 1,490 18 J moU. Notice that, in this case, the confidence interval remains symmetric about the mean value. Model validation graphs will be shown combined with the nonlinear regression results. 

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