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Chapter 69. The PRINCOMP Procedure > Getting Started: PRINCOMP Procedure - Pg. 5139

Getting Started: PRINCOMP Procedure ! 5139 perpendicular distances from each data point to the subspace. This is in contrast to the geo- metric interpretation of least squares regression, which minimizes the sum of squared vertical distances. For example, suppose you have two variables. Then, the first principal component minimizes the sum of squared perpendicular distances from the points to the first principal axis. This is in contrast to least squares, which would minimize the sum of squared vertical distances from the points to the fitted line. Principal component analysis can also be used for exploring polynomial relationships and for mul- tivariate outlier detection (Gnanadesikan 1977), and it is related to factor analysis, correspondence analysis, allometry, and biased regression techniques (Mardia, Kent, and Bibby 1979). Getting Started: PRINCOMP Procedure The following data provide crime rates per 100,000 people in seven categories for each of the 50 states in 1977. Since there are seven numeric variables, it is impossible to plot all the variables simultaneously. Principal components can be used to summarize the data in two or three dimen- sions, and they help to visualize the data. The following statements produce Figure 69.1 through Figure 69.5.