2.1.3 Scatter Plot

The X-Y scatter plot is one of the most powerful tools for exploratory data analysis. GRAPHID includes a host of features to enhance the basic scatter plot. These features are:

• Multi-window option for simultaneous plotting of several scatter plots. This option allows the visualization of relationships between several variables at a time, for example, the predictors of a regression model to look for multicollinearity.
• Identification of cases in a scatter plot. This option is particularly useful to identify the outlier cases.
• Regression lines: Three different types of regression lines can be displayed on each scatter plot:

· Local regression

· Local mean

· Local median.

These are nonparametric regression lines, which are constructed through smoothing with order statistics (k- nearest neighbor smoothing). The number of neighbors is to be decided by the researcher.

• Histograms of variables can be plotted on the diagonal windows of the multi-window scatter plot, to visualize the distributions of different variables.
• Density plots are essentially smooth versions of histograms. They provide smooth estimates of probability density curve. Order statistics can be used for constructing nonparametric density estimates. Let i be the number of points in a gate of width r corresponding to the point X (i) and let I (i) =X (i+ r) – X ( i – r),. The density of the point X (i) = I (i)/2 r.