Consider the criminological data of Table 7.1 (Example 7.1):

(a) Repeat the analysis using (1) the matrix Y^TY 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:

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.

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