Example of Principal Components Analysis

A bank requires eight pieces of information from loan applicants: income, education level, age, length of time at current residence, length of time with current employer, savings, debt, and number of credit cards. A bank administrator wants to analyze this data to determine the best way to group and report it. The administrator collects this information for 30 loan applicants.

The administrator performs a principal components analysis to reduce the number of variables to make the data easier to analyze. The administrator wants enough components to explain 90% of the variation in the data.

  1. Open the sample data, LoanApplicant.MTW.
  2. Choose Stat > Multivariate > Principal Components.
  3. In Variables, enter C1-C8.
  4. Click OK.

Interpret the results

The first principal component accounts for 44.3% of the total variance. The variables that correlate the most with the first principal component (PC1) are Age (0.484), Residence (0.466), Employ (0.459), and Savings (0.404). The first principal component is positively correlated with all four of these variables. Therefore, increasing values of Age, Residence, Employ, and Savings increase the value of the first principal component. The first four principal components explain 90.7% of the variation in the data. Therefore, the administrator decides to use these components to analyze loan applicants.

Principal Component Analysis: Income, Education, Age, Residence, Employ, ...

Eigenanalysis of the Correlation Matrix Eigenvalue 3.5476 2.1320 1.0447 0.5315 0.4112 0.1665 0.1254 0.0411 Proportion 0.443 0.266 0.131 0.066 0.051 0.021 0.016 0.005 Cumulative 0.443 0.710 0.841 0.907 0.958 0.979 0.995 1.000
Eigenvectors Variable PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 Income 0.314 0.145 -0.676 -0.347 -0.241 0.494 0.018 -0.030 Education 0.237 0.444 -0.401 0.240 0.622 -0.357 0.103 0.057 Age 0.484 -0.135 -0.004 -0.212 -0.175 -0.487 -0.657 -0.052 Residence 0.466 -0.277 0.091 0.116 -0.035 -0.085 0.487 -0.662 Employ 0.459 -0.304 0.122 -0.017 -0.014 -0.023 0.368 0.739 Savings 0.404 0.219 0.366 0.436 0.143 0.568 -0.348 -0.017 Debt -0.067 -0.585 -0.078 -0.281 0.681 0.245 -0.196 -0.075 Credit cards -0.123 -0.452 -0.468 0.703 -0.195 -0.022 -0.158 0.058
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