Consider the criminological data of Table 7.1 (Example 7.1):
(a) Repeat the analysis using (1) the matrix YTY and (ii) the cosine matrix (Section 2.4). Compare your results.
(b) Ahamad (1967) gives the following population values of the 13- to 19-year age group, in thousands:
![](https://test.transtutors.com/qimg/53717d19-1b5c-4a67-a85b-5012df8f5a3d.png)
Express the data of Table 7.1 per thousand and repeat the analysis using the correlation matrix. Compare your results-is there a significant change in the interpretation? Explain.
![](https://test.transtutors.com/qimg/620982bf-23ce-4b4d-a3a0-7c3ce3d7c48b.png)
Example 7.1
Using published data for p= 18 offence categories Ahamad (1967) has carried out a principal component analysis of the number of offences committed in each category, per year, during the period 1950-1963. The variables are defined as follows and the data matrix is given in Table 7.1. Since n p
Y1 = Homicide
Y2 = Woundings
Y3= Homosexual offences
Y4 = Heterosexual offences
Y5 = Breaking and entering
Y6 = Robbery
Y7 = Larceny
Y8 = Fraud and false pretence
Y9 = Receiving
Y10= Malicious injury to property
Y11 = Forgery
Y12 = Blackmail
Y13 = Assault
Y14 = Malicious damage
Y15 = Revenue laws
Y16= Intoxication laws
Y17 = Indecent exposure
Y18 = Taking motor vehicle without consent