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# Variance of Components

Six variables measured on 100 genuine and 100 counterfeit old Swiss Franc bank notes. The following six variables were measured: Length of the bank note (X1); Height of the bank note measured on the left (X2); Height of the bank note measured on the right (X3); Distance of inner frame to the lower border (X4); Distance of inner frame to the upper border (X5); Length of the diagonal (X6). The type of bank note was also recorded (X7) as "Genuine" or "Counterfeit."
Explain the following using SPSS.

a) How many components do you need to adequately describe the data in X1 to X6? Explain why.

b) What is the variance of the first component? How much of the total variation in the data (X1 to X6) is accounted for by the first component?

c) Display the loadings of the first two components. Explain clearly what they tell you about the relationship between the original variables (X1 to X6) and the first two components.

d) Use a graphical display to compare the first component scores of the genuine and counterfeit bank notes. Do you find any pattern? Explain

#### Solution Preview

a. How many components do you need to adequately describe the data in X1 to X6? Explain why.

We need two components as only two components have Eigen Value above 1.

See attachment for graph

b. What is the variance of the first component? How much of the ...

#### Solution Summary

The variance of components are provided. How many components are needed to adequately describe the data in X1 to X6 is determined.

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