Each observation is represented in the plot as a series of connected line segments. In this plot, the coordinate axes are all laid out horizontally, instead of using orthogonal axes as in the usual Cartesian graph. The most straight-forward multivariate plot is the parallel coordinates plot. However, there are other alternatives that display all the variables together, allowing you to investigate higher-dimensional relationships among variables. The scatter plot matrix only displays bivariate relationships. However, there may be important patterns in higher dimensions, and those are not easy to recognize in this plot. This array of plots makes it easy to pick out patterns in the relationships between pairs of variables. There is also a handful of 5 cylinder cars, and rotary-engined cars are listed as having 3 cylinders. The points in each scatter plot are color-coded by the number of cylinders: blue for 4 cylinders, green for 6, and red for 8. We'll use the number of cylinders to group observations. We'll illustrate multivariate visualization using the values for fuel efficiency (in miles per gallon, MPG), acceleration (time from 0-60MPH in sec), engine displacement (in cubic inches), weight, and horsepower. In this example, we'll use the carbig dataset, a dataset that contains various measured variables for about 400 automobiles from the 1970's and 1980's. This example explores some of the ways to visualize high-dimensional data in MATLAB®, using Statistics and Machine Learning Toolbox™. However, many datasets involve a larger number of variables, making direct visualization more difficult. It's also possible to visualize trivariate data with 3D scatter plots, or 2D scatter plots with a third variable encoded with, for example color. Such data are easy to visualize using 2D scatter plots, bivariate histograms, boxplots, etc. Many statistical analyses involve only two variables: a predictor variable and a response variable. This example shows how to visualize multivariate data using various statistical plots.
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