Trend lines

An additional advantage derived from plotting the residuals is that it can aid in detecting a bad data point. If one of the points noticeably deviates from the trend line, it is probably due to a mistake in sampling, analysis, or reporting. The best action would be to repeat the measurement. However, this is often impractical. The alternative is to reject the datum if its occurrence is so improbable that it would not reasonably be expected to occur in the given set of experiments. 

The presence of errors within the underlying database fudher degrades the accuracy and precision of the parameter e.stimate. If the database contains bias, this will translate into bias in the parameter estimates. In the flash example referenced above, including reasonable database uncertainty in the phase equilibria increases me 95 percent confidence interval to 14. As the database uncertainty increases, the uncertainty in the resultant parameter estimate increases as shown by the trend line represented in Fig. 30-24. Failure to account for the database uncertainty results in poor extrapolations to other operating conditions. 

No trend line is needed to determine the formation pressure. However, petrophysical data are required to refine the results. A computer is mandatory to implement the technique. 

Another technique based on shale resistivity was proposed by Alixant [124]. This technique does not use a normal trend line or empirical correlations and is based solely on the shale resistivity. The procedure is as follows ... 

Demonstration. The transition zone is clearly indicated at 12,000 ft. The trend line is determined as an exponential function. The difference between the trend line value (2.48 g/cm ) and the measured value (2.28 g/cm ) at 13,000 ft can be correlated to the formation pressure gradient using the empirical correlation curve established by Boatman and shown in Figure 4-337 [101]. 

Probability Plots. To distinguish between background distributions and human activity, trace element data were probability plotted using the method of Velz (10), The plots produce two separate trend lines, the intersection of which distinguishes natural from anthropogenic concentrations. Figure 10 is an illustration of the resulting plots for zinc (38),... 

The Y-axis represents the magnitude of the friction signal force and the X-axis is the load. The slope of the trend line is dehned as the friction factor (friction force signal/load) which is used to express the relative friction coefficient (friction force/load). Experiments that have been done in the same monolayer L-B him but different scan ranges give similar results as shown in Fig. 24 and Fig. 25. The friction factors of this monolayer L-B him, 0.0265 and 0.0203, are similar. The topographies of these two areas are shown in Fig. 26. 

Figure 4.39. Variability of back calculated concentrations Concbc- For each concentration range five calibration points were measured, over which a separate regression was run (not shown). Placebo tablets were spiked to the same concentrations and measured in triplicate (short horizontal lines gray trend lines in background). Ten repeat determinations of actual product (vertical bars = Mean + SD) were done. The bold lines pertain to compound A in all concentration ranges, the thin lines to compound B (middle concentration range only).

Figure 16. Carbonyl C PECD from enantiomers of camphor. The experimentally derived data (Ref. [56]) for the (iS)-enantiomer have been negated prior to plotting on expectation that they will then fall on the same trend line as the (/ )-enantiomer data. The CMS-Xa and B-spline calculations (Ref. [57]) for the (R)-camphor enantiomer are included for comparison. The inset shows the (R)-camphor structure.

In this instance, the (5)-enantiomer data have been negated prior to plotting. From previous discussion of the antisymmetry of the parameters under enantiomer exchange (e.g., Section III.A) it is recognized that it is then to be expected that the (R)- and (5)-enantiomer data should fall on the same experimental trend line. That they do indeed do so shows, as was argued in the Section IV.A for fenchone, that the behavior is at least qualitatively in accord with a pure electric dipole model. Furthermore, combining two distinct data sets [(/ )- and (5)-enantiomers] in this manner provides a consistency check on the reproducibility of the PECD data. It seems good practice to include measurement of both enantiomers, where this is feasible, in an experimental study. 

The reaction of seawater with country rocks is also a possible but unlikely explanation. Tertiary volcanic sediments in the vicinity of Kuroko deposits are altered and tend to have lost both Ca and Sr (Farrell and Holland, 1983). The ratio of Sr loss to Ca loss is roughly equal to the Sr/Ca ratio in seawater. If seawater was the altering medium, its Sr/Ca ratio was probably not strongly affected by the alteration process. The 87sr/86si- ratio would be intermediate between an initial value of 0.7088 and ca. 0.740 — the Sr/ Sr ratio of unaltered Tertiary volcanics of the Hokuroku basin. It is unlikely, therefore, that this type of alteration can account for the Sr content and for the isotopic composition of Sr in the anhydrites at the upper end of the trend line in Fig. 1.49. On the other hand, mixing of seawater with solutions which have a Sr/Ca ratio much smaller than that of seawater could have led to the deposition of Kuroko anhydrites. 

Data points are the high precision ( 2%c) measurements of Stuiver and Quay (9). Note the excellent agreement between the high precision data of Stuiver and the trend line generated from the lower precision (ca. 5V) data of the composite data set. Maxima occur between a.d. 1020-1080, 1290-1320, 1420-1530, 1660-1710, 1790-1830 or on the average, every ca. 190 years. The pronounced minimum between aj>. 1100 and 1240 corresponds to the Medieval Warm epoch. 

Figure 5.14 Correlation of net H-bond energy (A2shb, squares) and principal n-a stabilization energy (AEn a,(2), circles) with intermolecular charge transfer (Qcr) cf. Table 5.15. (Approximate trend-lines are shown for each quantity to aid visualization.)...

Fig. 2. Percent quartz in C horizon (dashed trend line) and weight percent Al (filled boxes) in C horizon soils along the W-E transect (truncated box plot boxes include 50% of data, extent of lines include 80% of data solid line is the median). Geochemical data shown by the box plots were grouped into 10 areas (vertical dashed lines, numbers at top of plot) defined by commonalities of physiographic features.

Fig. 3. Percent feldspar in C horizon (dashed trend line) and weight percent Na in C horizon soils along the W-E transect (filled boxes). Plot specifics as in Figure 2. 

Fig. 4. Trend line for PMPE (dashed line) plotted with a bar anchor plot of the log A-horizon/C-horizon Al ratios (dark boxes) for the W-E transect.

Fig. 7. Dependence of the relative abundance of the most common folds on the proteome size. Trend lines are shown for the P-loop and PP-loop NTPases.

Figure 9.14 shows that the score T1 for the acoustic model and T1 for the process data have similar trend lines for the start-up procedure on the 20 February 2001, however the acoustic T1 has a significantly faster response than T1 for the process data when the fluidized bed is filled with granules. 

Fig. 3. Zr/Al203 vs. Nb/AbOs plot confirms that unit G is separate and geochemically unique. Trend lines for units B, C, F, and G are shown in figure. Zr/Nb ratios for units B, C, D, E, and Gare 14.77, 19.01, 15.07, 14.22, 15.13, 14.23, and 8.19 respectively.

Figure 2.9 Plots with trend lines of the conventional enthalpies of hydration of the Group 1 cations and Group 17 anions against their ionic radii also included are the values of the conventional enthalpies of hydration of the Group 1 calions minus 1110 kj mol 1 and the conventional enthalpies of hydration of the Group 17 anions plus 1110 kj mol-1...

Trend lines are shown which emphasize that the values for AhydFF (M +, g)conv and AhydH (X, g)conv vary with ionic radius. This is to be expected from simple electrostatic arguments. The smaller ions would be expected to have greater interactions with water than the larger ones. 

That the trend lines coincide almost completely is some justification of the empirical approach. 

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