What is the variance of the first component

Question

Discuss the below:

Q: 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

Length	LeftHeight	RightHeight	LowerDist	UpperDist	Diagonal	Type
214.8	131	131.1	9	9.7	141	Genuine
214.6	129.7	129.7	8.1	9.5	141.7	Genuine
214.8	129.7	129.7	8.7	9.6	142.2	Genuine
214.8	129.7	129.6	7.5	10.4	142	Genuine
215	129.6	129.7	10.4	7.7	141.8	Genuine
215.7	130.8	130.5	9	10.1	141.4	Genuine
215.5	129.5	129.7	7.9	9.6	141.6	Genuine
214.5	129.6	129.2	7.2	10.7	141.7	Genuine
214.9	129.4	129.7	8.2	11	141.9	Genuine
215.2	130.4	130.3	9.2	10	140.7	Genuine
215.3	130.4	130.3	7.9	11.7	141.8	Genuine
215.1	129.5	129.6	7.7	10.5	142.2	Genuine
215.2	130.8	129.6	7.9	10.8	141.4	Genuine
214.7	129.7	129.7	7.7	10.9	141.7	Genuine
215.1	129.9	129.7	7.7	10.8	141.8	Genuine
214.5	129.8	129.8	9.3	8.5	141.6	Genuine
214.6	129.9	130.1	8.2	9.8	141.7	Genuine
215	129.9	129.7	9	9	141.9	Genuine
215.2	129.6	129.6	7.4	11.5	141.5	Genuine
214.7	130.2	129.9	8.6	10	141.9	Genuine
215	129.9	129.3	8.4	10	141.4	Genuine
215.6	130.5	130	8.1	10.3	141.6	Genuine
215.3	130.6	130	8.4	10.8	141.5	Genuine
215.7	130.2	130	8.7	10	141.6	Genuine
215.1	129.7	129.9	7.4	10.8	141.1	Genuine
215.3	130.4	130.4	8	11	142.3	Genuine
215.5	130.2	130.1	8.9	9.8	142.4	Genuine
215.1	130.3	130.3	9.8	9.5	141.9	Genuine
215.1	130	130	7.4	10.5	141.8	Genuine
214.8	129.7	129.3	8.3	9	142	Genuine
215.2	130.1	129.8	7.9	10.7	141.8	Genuine
214.8	129.7	129.7	8.6	9.1	142.3	Genuine
215	130	129.6	7.7	10.5	140.7	Genuine
215.6	130.4	130.1	8.4	10.3	141	Genuine
215.9	130.4	130	8.9	10.6	141.4	Genuine
214.6	130.2	130.2	9.4	9.7	141.8	Genuine
215.5	130.3	130	8.4	9.7	141.8	Genuine
215.3	129.9	129.4	7.9	10	142	Genuine
215.3	130.3	130.1	8.5	9.3	142.1	Genuine
213.9	130.3	129	8.1	9.7	141.3	Genuine
214.4	129.8	129.2	8.9	9.4	142.3	Genuine
214.8	130.1	129.6	8.8	9.9	140.9	Genuine
214.9	129.6	129.4	9.3	9	141.7	Genuine
214.9	130.4	129.7	9	9.8	140.9	Genuine
214.8	129.4	129.1	8.2	10.2	141	Genuine
214.3	129.5	129.4	8.3	10.2	141.8	Genuine
214.8	129.9	129.7	8.3	10.2	141.5	Genuine
214.8	129.9	129.7	7.3	10.9	142	Genuine
214.6	129.7	129.8	7.9	10.3	141.1	Genuine
214.5	129	129.6	7.8	9.8	142	Genuine
214.6	129.8	129.4	7.2	10	141.3	Genuine
215.3	130.6	130	9.5	9.7	141.1	Genuine
214.5	130.1	130	7.8	10.9	140.9	Genuine
215.4	130.2	130.2	7.6	10.9	141.6	Genuine
214.5	129.4	129.5	7.9	10	141.4	Genuine
215.2	129.7	129.4	9.2	9.4	142	Genuine
215.7	130	129.4	9.2	10.4	141.2	Genuine
215	129.6	129.4	8.8	9	141.1	Genuine
215.1	130.1	129.9	7.9	11	141.3	Genuine
215.1	130	129.8	8.2	10.3	141.4	Genuine
215.1	129.6	129.3	8.3	9.9	141.6	Genuine
215.3	129.7	129.4	7.5	10.5	141.5	Genuine
215.4	129.8	129.4	8	10.6	141.5	Genuine
214.5	130	129.5	8	10.8	141.4	Genuine
215	130	129.8	8.6	10.6	141.5	Genuine
215.2	130.6	130	8.8	10.6	140.8	Genuine
214.6	129.5	129.2	7.7	10.3	141.3	Genuine
214.8	129.7	129.3	9.1	9.5	141.5	Genuine
215.1	129.6	129.8	8.6	9.8	141.8	Genuine
214.9	130.2	130.2	8	11.2	139.6	Genuine
213.8	129.8	129.5	8.4	11.1	140.9	Genuine
215.2	129.9	129.5	8.2	10.3	141.4	Genuine
215	129.6	130.2	8.7	10	141.2	Genuine
214.4	129.9	129.6	7.5	10.5	141.8	Genuine
215.2	129.9	129.7	7.2	10.6	142.1	Genuine
214.1	129.6	129.3	7.6	10.7	141.7	Genuine
214.9	129.9	130.1	8.8	10	141.2	Genuine
214.6	129.8	129.4	7.4	10.6	141	Genuine
215.2	130.5	129.8	7.9	10.9	140.9	Genuine
214.6	129.9	129.4	7.9	10	141.8	Genuine
215.1	129.7	129.7	8.6	10.3	140.6	Genuine
214.9	129.8	129.6	7.5	10.3	141	Genuine
215.2	129.7	129.1	9	9.7	141.9	Genuine
215.2	130.1	129.9	7.9	10.8	141.3	Genuine
215.4	130.7	130.2	9	11.1	141.2	Genuine
215.1	129.9	129.6	8.9	10.2	141.5	Genuine
215.2	129.9	129.7	8.7	9.5	141.6	Genuine
215	129.6	129.2	8.4	10.2	142.1	Genuine
214.9	130.3	129.9	7.4	11.2	141.5	Genuine
215	129.9	129.7	8	10.5	142	Genuine
214.7	129.7	129.3	8.6	9.6	141.6	Genuine
215.4	130	129.9	8.5	9.7	141.4	Genuine
214.9	129.4	129.5	8.2	9.9	141.5	Genuine
214.5	129.5	129.3	7.4	10.7	141.5	Genuine
214.7	129.6	129.5	8.3	10	142	Genuine
215.6	129.9	129.9	9	9.5	141.7	Genuine
215	130.4	130.3	9.1	10.2	141.1	Genuine
214.4	129.7	129.5	8	10.3	141.2	Genuine
215.1	130	129.8	9.1	10.2	141.5	Genuine
214.7	130	129.4	7.8	10	141.2	Genuine
214.4	130.1	130.3	9.7	11.7	139.8	Counterfeit
214.9	130.5	130.2	11	11.5	139.5	Counterfeit
214.9	130.3	130.1	8.7	11.7	140.2	Counterfeit
215	130.4	130.6	9.9	10.9	140.3	Counterfeit
214.7	130.2	130.3	11.8	10.9	139.7	Counterfeit
215	130.2	130.2	10.6	10.7	139.9	Counterfeit
215.3	130.3	130.1	9.3	12.1	140.2	Counterfeit
214.8	130.1	130.4	9.8	11.5	139.9	Counterfeit
215	130.2	129.9	10	11.9	139.4	Counterfeit
215.2	130.6	130.8	10.4	11.2	140.3	Counterfeit
215.2	130.4	130.3	8	11.5	139.2	Counterfeit
215.1	130.5	130.3	10.6	11.5	140.1	Counterfeit
215.4	130.7	131.1	9.7	11.8	140.6	Counterfeit
214.9	130.4	129.9	11.4	11	139.9	Counterfeit
215.1	130.3	130	10.6	10.8	139.7	Counterfeit
215.5	130.4	130	8.2	11.2	139.2	Counterfeit
214.7	130.6	130.1	11.8	10.5	139.8	Counterfeit
214.7	130.4	130.1	12.1	10.4	139.9	Counterfeit
214.8	130.5	130.2	11	11	140	Counterfeit
214.4	130.2	129.9	10.1	12	139.2	Counterfeit
214.8	130.3	130.4	10.1	12.1	139.6	Counterfeit
215.1	130.6	130.3	12.3	10.2	139.6	Counterfeit
215.3	130.8	131.1	11.6	10.6	140.2	Counterfeit
215.1	130.7	130.4	10.5	11.2	139.7	Counterfeit
214.7	130.5	130.5	9.9	10.3	140.1	Counterfeit
214.9	130	130.3	10.2	11.4	139.6	Counterfeit
215	130.4	130.4	9.4	11.6	140.2	Counterfeit
215.5	130.7	130.3	10.2	11.8	140	Counterfeit
215.1	130.2	130.2	10.1	11.3	140.3	Counterfeit
214.5	130.2	130.6	9.8	12.1	139.9	Counterfeit
214.3	130.2	130	10.7	10.5	139.8	Counterfeit
214.5	130.2	129.8	12.3	11.2	139.2	Counterfeit
214.9	130.5	130.2	10.6	11.5	139.9	Counterfeit
214.6	130.2	130.4	10.5	11.8	139.7	Counterfeit
214.2	130	130.2	11	11.2	139.5	Counterfeit
214.8	130.1	130.1	11.9	11.1	139.5	Counterfeit
214.6	129.8	130.2	10.7	11.1	139.4	Counterfeit
214.9	130.7	130.3	9.3	11.2	138.3	Counterfeit
214.6	130.4	130.4	11.3	10.8	139.8	Counterfeit
214.5	130.5	130.2	11.8	10.2	139.6	Counterfeit
214.8	130.2	130.3	10	11.9	139.3	Counterfeit
214.7	130	129.4	10.2	11	139.2	Counterfeit
214.6	130.2	130.4	11.2	10.7	139.9	Counterfeit
215	130.5	130.4	10.6	11.1	139.9	Counterfeit
214.5	129.8	129.8	11.4	10	139.3	Counterfeit
214.9	130.6	130.4	11.9	10.5	139.8	Counterfeit
215	130.5	130.4	11.4	10.7	139.9	Counterfeit
215.3	130.6	130.3	9.3	11.3	138.1	Counterfeit
214.7	130.2	130.1	10.7	11	139.4	Counterfeit
214.9	129.9	130	9.9	12.3	139.4	Counterfeit
214.9	130.3	129.9	11.9	10.6	139.8	Counterfeit
214.6	129.9	129.7	11.9	10.1	139	Counterfeit
214.6	129.7	129.3	10.4	11	139.3	Counterfeit
214.5	130.1	130.1	12.1	10.3	139.4	Counterfeit
214.5	130.3	130	11	11.5	139.5	Counterfeit
215.1	130	130.3	11.6	10.5	139.7	Counterfeit
214.2	129.7	129.6	10.3	11.4	139.5	Counterfeit
214.4	130.1	130	11.3	10.7	139.2	Counterfeit
214.8	130.4	130.6	12.5	10	139.3	Counterfeit
214.6	130.6	130.1	8.1	12.1	137.9	Counterfeit
215.6	130.1	129.7	7.4	12.2	138.4	Counterfeit
214.9	130.5	130.1	9.9	10.2	138.1	Counterfeit
214.6	130.1	130	11.5	10.6	139.5	Counterfeit
214.7	130.1	130.2	11.6	10.9	139.1	Counterfeit
214.3	130.3	130	11.4	10.5	139.8	Counterfeit
215.1	130.3	130.6	10.3	12	139.7	Counterfeit
216.3	130.7	130.4	10	10.1	138.8	Counterfeit
215.6	130.4	130.1	9.6	11.2	138.6	Counterfeit
214.8	129.9	129.8	9.6	12	139.6	Counterfeit
214.9	130	129.9	11.4	10.9	139.7	Counterfeit
213.9	130.7	130.5	8.7	11.5	137.8	Counterfeit
214.2	130.6	130.4	12	10.2	139.6	Counterfeit
214.8	130.5	130.3	11.8	10.5	139.4	Counterfeit
214.8	129.6	130	10.4	11.6	139.2	Counterfeit
214.8	130.1	130	11.4	10.5	139.6	Counterfeit
214.9	130.4	130.2	11.9	10.7	139	Counterfeit
214.3	130.1	130.1	11.6	10.5	139.7	Counterfeit
214.5	130.4	130	9.9	12	139.6	Counterfeit
214.8	130.5	130.3	10.2	12.1	139.1	Counterfeit
214.5	130.2	130.4	8.2	11.8	137.8	Counterfeit
215	130.4	130.1	11.4	10.7	139.1	Counterfeit
214.8	130.6	130.6	8	11.4	138.7	Counterfeit
215	130.5	130.1	11	11.4	139.3	Counterfeit
214.6	130.5	130.4	10.1	11.4	139.3	Counterfeit
214.7	130.2	130.1	10.7	11.1	139.5	Counterfeit
214.7	130.4	130	11.5	10.7	139.4	Counterfeit
214.5	130.4	130	8	12.2	138.5	Counterfeit
214.8	130	129.7	11.4	10.6	139.2	Counterfeit
214.8	129.9	130.2	9.6	11.9	139.4	Counterfeit
214.6	130.3	130.2	12.7	9.1	139.2	Counterfeit
215.1	130.2	129.8	10.2	12	139.4	Counterfeit
215.4	130.5	130.6	8.8	11	138.6	Counterfeit
214.7	130.3	130.2	10.8	11.1	139.2	Counterfeit
215	130.5	130.3	9.6	11	138.5	Counterfeit
214.9	130.3	130.5	11.6	10.6	139.8	Counterfeit
215	130.4	130.3	9.9	12.1	139.6	Counterfeit
215.1	130.3	129.9	10.3	11.5	139.7	Counterfeit
214.8	130.3	130.4	10.6	11.1	140	Counterfeit
214.7	130.7	130.8	11.2	11.2	139.4	Counterfeit
214.3	129.9	129.9	10.2	11.5	139.6	Counterfeit