Q-residuals

Q Residual of phase-equilibrium X Feedback-reset time s t... 

The PCA prediction scores and residuals can then be used to generate two common quality metrics for conveying the abnormality of the measured response namely the Hotelling statistic and the Q residual statistic, which are defined below ... 

Figure 12.27 (A) Scatter plot of the Hotelling P and Q residual statistics associated with the samples in the process spectroscopy calibration data set, obtained from a PCA model built on the data after obvious outliers were removed. The dashed lines represent the 95% confidence limit of the respective statistic. (B) The spectra used to generate the plot in (A), denoting one of the outlier samples.

As a result, it is critical to evaluate process samples in real-time for their appropriateness of use with the empirical model. For models built using PC A, PLS, PCR and other factor based methods, the mechanism for such a model health monitor is already built into the model. Equations 12.21 and 12.22 can be used to calculate Hotelling and Q residual statistics for each process sample using the sample s on-line analytical profile (xp) and the loadings (P) and scores (T) of the model. An abnormally high value would indicate... 

An interesting feature of compound 5 is the structure of the [QHQ]+ cation. A displacement ellipsoid plot of one of the two independent Q residues is shown in Figure 1. In... 

The 43-unit mass difference between modified and unmodified peptides appeared because of acetylation of lysine along with deamidation of either asparagine (N) or glutamine (Q) residues present in... 

Figure 5.13. Multivariate statistical indicators for combinatorial production of melt polycarbonate in one of the 96-microreactor arrays (A) control chart (B) Q residual control chart (dotted lines in A and B) 95% confidence limits.

Setting Ax = Ay, rearranging, and setting the resultant equation = q residual, the following results. 

Also from the so-called Q-residuals plot (error plot), it can be seen (Fig. 21.2) that some batches behave in an abnormal way and should be removed from the data set, because they have an exceptionally large error contribution to the PC model. 

To see whether the two PC model describes all countries equally well, the error or Q-residual for all countries can be plotted. This is shown in Figure 22.7. As can be seen, India and the USA have the largest contribution to the error. 

The residuals from regression models can be plotted per object, for individual variables per object or per variable. A critical limit for the residuals per object may be estimated based on F- or Q-residual statistics and used as a cut-off value. One other alternative is to plot residuals against the value of the y-variable to check that the residuals are not depending on the value of Y (Figure 7). 

This plot shows the distance from the objects to the model centre as Leverage or Hotelling s on the abscissa and the Q-residual X-variance or F-residuals on the ordinate. 

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