Lag plot

Kinetic data from Table 2-5 for the reaction between Puvl and Ulv. The time lag plot, right, was constructed according to Eq. (2-42) with r = 300 s. The direct plot according to Eq. (2-33) shows the curve fitted by nonlinear least squares. 

When experimental data are collected over time or distance there is always a chance of having autocorrelated residuals. Box et al. (1994) provide an extensive treatment of correlated disturbances in discrete time models. The structure of the disturbance term is often moving average or autoregressive models. Detection of autocorrelation in the residuals can be established either from a time series plot of the residuals versus time (or experiment number) or from a lag plot. If we can see a pattern in the residuals over time, it probably means that there is correlation between the disturbances. 

Here, z0 and p0 are just two positive numbers. There are obviously two possibilities case (a) z0 > po, and case (b) z0 < p0. Sketch the magnitude and phase lag plots of Gc for both cases. Identify which case is the phase-lead and which case is the phase-lag compensation. What types of classical controllers may phase-lead and phase-lag compensations resemble ... 

Figure 2. Specimen effect for the time lag plotted as a function of gas.

Appropriate statistical tests such as lag plot or autocorrelation plot should be used, which effectively show the randoirmess of the data residuals [11, 12], When the number of lifetimes is beheved to be known, the mechanism and rate matrix of the process can be estimated and the latter model can be applied. 

The code in Listing 8.3 also illustrates a lag plot on lines 16 through 18 for the Gaussian data. The lag plot for this data set is shown in Figures 8.6. It is readily seen that the lag data is clustered around a zero mean value wifli no evidence of any visual pattern in the data and this is consistent with an ideal Gaussian random variable. 

Lag plot of Gaussian random numbers (10000 data points). 

Figure 8.14. Lag Plot of Measurement value i vs. Measurement value i-1.

Predicted values and data points Residuals vs x 3 Residuals vs y Lag plot of residuals Histogram plot of residuals Distribution plot of residuals... 

Figure 9.4 Lag plot of residual values for Figure 9.1 data and Eq. (9.4) model...

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