Scatter plot

A scatter plot provides a quick visual summary of where numerous data points exist in two-dimensional space. Scatter plots are commonly used to investigate positive or negative correlation between two variables plotted on the X and Y axes. 

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Figure 2 Scatter plot of clustering results Figure 3 Definition of Damage Stages...

Figure 4 Scatter plot for the resulting partition for the example of CFRP pressure vessel.

Besides these main categories, a large number of hybrid visualization techniques also exist, which arc combinations of the methods described. Well-known hybrid approaches arc the 2D or 3D glyph displays. These techniques combine the multidimensional representation capabilities of icon-based methods with the easy and intuitive representations of scatter-plot displays, Therefore these techniques can also be frequently found within chemical data analysis applications. 

Spectral features and their corresponding molecular descriptors are then applied to mathematical techniques of multivariate data analysis, such as principal component analysis (PCA) for exploratory data analysis or multivariate classification for the development of spectral classifiers [84-87]. Principal component analysis results in a scatter plot that exhibits spectra-structure relationships by clustering similarities in spectral and/or structural features [88, 89]. 

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

Lateral density fluctuations are mostly confined to the adsorbed water layer. The lateral density distributions are conveniently characterized by scatter plots of oxygen coordinates in the surface plane. Fig. 6 shows such scatter plots of water molecules in the first (left) and second layer (right) near the Hg(l 11) surface. Here, a dot is plotted at the oxygen atom position at intervals of 0.1 ps. In the first layer, the oxygen distribution clearly shows the structure of the substrate lattice. In the second layer, the distribution is almost isotropic. In the first layer, the oxygen motion is predominantly oscillatory rather than diffusive. The self-diffusion coefficient in the adsorbate layer is strongly reduced compared to the second or third layer [127]. The data in Fig. 6 are qualitatively similar to those obtained in the group of Berkowitz and coworkers [62,128-130]. These authors compared the structure near Pt(lOO) and Pt(lll) in detail and also noted that the motion of water in the first layer is oscillatory about equilibrium positions and thus characteristic of a solid phase, while the motion in the second layer has more... 

MCBase offers the possibility to load the original CAMPUS data of different suppliers from version 3.0 and higher into one database, which allows direct comparison. It has been developed in close cooperation with the CAMPUS consortium. For more information see http //www.m-base.de/. MCBase is user friendly and offers extremely efficient handling of material data. All CAMPUS options are available define search profiles define and sort tables print tables and data sheets curve overlay scatter plots. In addition MCBase 4.1 offers search in curves search for comparable grades text search update via Internet calculation of simulation parameters. A French version of MCBase is available from the distribution agent in France. 

Scatter plots of temperature atx/d = 15 in turbulent Cl-14/air jet flames with Reynolds numbers of 13,400 (Flame C) and 44,800 (Flame F). The stoichiometric mixture fraction is = 0.351. The line shows the results of a laminar counterflow-flame calculation with a strain parameter of a = 100 s and is included as a visual guide. (From Barlow, R.S. and Frank, J.H., Proc. Combust. Inst, 27,1087,1998. With permission.)... 

One of the most challenging aspects of modeling turbulent combustion is the accurate prediction of finite-rate chemistry effects. In highly turbulent flames, the local transport rates for the removal of combustion radicals and heat may be comparable to or larger than the production rates of radicals and heat from combustion reactions. As a result, the chemistry cannot keep up with the transport and the flame is quenched. To illustrate these finite-rate chemistry effects, we compare temperature measurements in two piloted, partially premixed CH4/air (1/3 by vol.) jet flames with different turbulence levels. Figure 7.2.4 shows scatter plots of temperature as a function of mixture fraction for a fully burning flame (Flame C) and a flame with significant local extinction (Flame F) at a downstream location of xld = 15 [16]. These scatter plots provide a qualitative indication of the probability of local extinction, which is characterized... 

Figure 7.2.12 shows scatter plots of instantaneous measurements of temperature and CH4 mole fraction obtained at a height of 5 mm and at several radial locations, which are color-coded in the figure. The foremost observable characteristics are that there are no samples richer than 0.2 in the mixture fraction (1.0 being pure fuel) and that many samples remain at room temperature even within the limits of flammability. Many... 

Scatter plots of temperature and CH4 mole fraction versus mixture fraction in a model gas turbine combustor. (From Meier, W., Duan, X.R., and Weigand, R, Combust. Flame, 144, 225, 2006. With permission.)... 

Fig. 35.3. Scatter plot of 16 olive oils scored by two sensory panels (Dutch panel lower case British panel upper case). The combined data are shown after Procrustes matching and projection onto the principal plane of the average configuration.

Fig. 36.6. Scatter plot of dependent variable (X-content) versus the first four principal components.

Common Clinical Trial Graphs 200 Scatter Plot 200 Line Plot 201 Bar Chart 202 Box Plot 203 Odds Ratio Plot 203... 

Scatter plots are used widely in clinical trial research, as they are intuitive to read and have many applications. We often look for a drug s effect on some parameter (Y axis) over time (X axis). Also, change-from-baseline scatter plots are useful when you plot the baseline on the X axis and the follow-up value on the Y axis. You will see an example of this graph later in this chapter. 

Note that for box and survival plots, PROC GPLOT is listed as an alternative. Although PROC BOXPLOT and PROC LIFETEST produce excellent graphs by themselves, sometimes it is necessary to make modifications to the output in a way that these procedures cannot handle directly. When modifications are needed, PROC GPLOT is an excellent choice. Also note that PROC REG and PROC UNIVARIATE are listed as options for scatter plots and box plots, respectively, as they can be useful in producing lower-resolution graphics for statistical appendices. 

Here is the SAS program that creates the preceding scatter plot. Notes follow the program. 

Program 6.1 Laboratory Data Scatter Plot Using PROC GPLOT... 

Due to the mainly qualitative nature of PCA, DFA, and HCA, the role of PyMS in microbiology has been somewhat restricted. For example, using these clustering methods, the use of PyMS to identify microorganisms can be a subjective process because it relies on the interpretation of complex scatter plots and dendrograms. Furthermore the qualitative nature of PCA, DFA, and FICA prevents the application of PyMS to quantitative microbial analysis, while limitations also arise from batch-to-batch variation of PyMS data.80... 

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