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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.
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.
| 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 |
| 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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