In fact it can be seen how both the empirical distribution of standardized residuals, Figure 4 top panel, and the 99% confidence interval, Figure 4 bottom panel, for the ARMA-GARCH and the ARMAX-GARCH model behave similarly.
Despite the scarcity of observations along this profile, model-predicted displacements in both horizontal and vertical directions agree well with the first-order pattern of the residuals (Figure 6b,c,d).
The random numbers (e it ) generated for the trees in a particular 5-year growth period were assumed to be correlated (Pasanen 1998), resulting in both auto- and cross-correlated time series of growth residuals (Figure 1).
The apparent difference among the graphs relative to solitary and clustered deer was confirmed by the distribution of residuals (Figure 3B).
Following removal of the two peptide outliers, the variance components analysis yields no significant random effects factors with respect to the residuals (Figure 5).
The residuals (Figure 1) provide an alternative view of how different the fitted line is from the actual data, and it also reveals why the r2 values can appear statistically favorable (close to 1.0) despite being visually sub-optimal.
These conclusions were further supported by three additional statistical methods, including analysis of adjusted residuals (Figure S1) [33], "detection rate" ROC curves (Figure S2) [34], and the gene set enrichment score statistic proposed by Subramanian et al. [35] (i.e., "GSEA analysis", see Figure S3).
A root-to-tip regression of the VP60 ML tree, including AY269825, revealed that both AY269825 and FR823354 were potential outliers (highest residuals, Figure 6).
Simultaneously, with removing stripes, this process also decomposes an image into pattern and noise (residuals): Figure 8 shows reconstruction of hb expression from the "unstriped" components 1 4, alongside the striped components (strongly affected by ftz) 5 12 and the residuals.
