B

Figure 3.4 Graphic output for nonlinear regression analysis summarized in Table 3.6 for steady state voltammetry data with a constant background fit using a model not considering background: (a) points are experimental data, line computed from regression analysis; (b) nonrandom deviation plot.

Figure 3.4 Graphic output for nonlinear regression analysis summarized in Table 3.6 for steady state voltammetry data with a constant background fit using a model not considering background: (a) points are experimental data, line computed from regression analysis; (b) nonrandom deviation plot.

Table 3.7 Results of the Model in Eq. (3.6) with Background Term Fit onto Steady State Voltammetry Data with Background

Parameter/statistic

Initial value

True value"

Final value

Error

1.01

1.000

0.983

1.7%

b2

36.0

38.92

39.68

2.0%

b,

-0.21

-0.200

-0.1996

0.2%

b4

-0.22

-0.200

-0.267

34%

b5

0.01

0.005

0.0051

2%

SD

(ev = 0.005)

0.0033

Deviation plot

Random

" Data generated by using eq. (3.6) with absolute normally distributed noise at 0.5% of the maximum y.

the fit without background parameters (cf. Table 3.6). The data points all fall on the regression line (Figure 3.5), the deviation plot is random, and SD < ey. The error in the background slope b4 is relatively large because its value is small and it contributes little to the total signal. Information

-E, mV

Figure 3.5 Graphic output for nonlinear regression analysis summarized in Table 3.7 for steady state voltammetry data with a constant background fit using the correct model: (a) points are experimental data, line computed from regression analysis; (b) random deviation plot.

Figure 3.5 Graphic output for nonlinear regression analysis summarized in Table 3.7 for steady state voltammetry data with a constant background fit using the correct model: (a) points are experimental data, line computed from regression analysis; (b) random deviation plot.

about this parameter is not well represented in the data. Also, b4 is partly correlated with b\. Partial correlation between parameters can cause an increase in their errors. Effects of correlation, that is, the dependence of one parameter in the model on another parameter, will be discussed in more detail later in this chapter.

The model in eq. (3.6) for steady state voltammetry was constructed by adding a background term to a theoretical expression describing the faradaic response caused by the electrode reaction. In this example, we employed a linear background, but the same general conclusions would be drawn from data with any mathematical form of the background. We shall see in the applications chapters that adding a background term to a theoretical expression for the sample response is a useful approach to model building in a variety of situations.

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