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Multiple numerical variables can be analyzed using:
a) 3-D plots: 3-D Scatter Plot, Contour Plot, Surface Plot
c) Factor Analysis / Principal Components Analysis
The 3D scatter plot displays trivariate points plotted in an X-Y-Z grid. It is particularly useful for investigating the relationships among these variables.
Figure 1 Relationship between height, weight and BMI
Contour plots are topographical maps drawn from three-dimensional data. One variable is represented on the horizontal axis and a second variable is represented on the vertical axis. The third variable is represented by isolines (lines of constant value). These plots are often useful in data analysis, especially when you are searching for minimums and maximums in a set of trivariate data.
Figure 2 Relationship between height, weight and BMI
Surface plots are diagrams of three-dimensional data. Rather than showing the individual data points, surface plots show a functional relationship between a designated dependent variable (Y), and two independent variables (X1 and X2). The plot is a companion plot to the contour plot. It is important to understand how these plots are constructed. A two-dimensional grid of X1 and X2 is constructed. The range of this grid is equal to the range of the data. Next, a Y value is calculated for each grid point. This Y value is a weighted average of all data values that are “near” this grid point. (The number of points averaged is user specified.) The three-dimensional surface is constructed using these averaged values. Hence, the surface plot does not show the variation at each grid point. These plots are useful in regression analysis for viewing the relationship among a dependent and two independent variables. Remember that multiple regression assumes that this surface is a perfectly flat surface. Hence, the surface plot lets you visually determine if multiple regression is appropriate.
Figure 3 Relationship between height, weight and BMI