Assignment 5

In an investigation of the relationship between the perceived risk of crime and actual crime the following data were obtained. The variables y1, y2 and y3 are responses to questions to the subjects about how likely they thought it was that they would be victims of robbery, burglary or vandalism respectively over the next year. x1 is the number of self-reported prior victimizations in the last year, x2 is the subject's age, x3 is the sex of the subject and x4 is rate of personal and property crime in the subject's neighborhood. I do not have information about the sample size or the coding of x3. All I can give you is the correlation matrix:

y1  1.0
y2  0.575  1.0
y3  0.540  0.598  1.0
x1  0.169  0.240  0.246  1.0
x2 -0.014 -0.144 -0.128 -0.184  1.0
x3 -0.023 -0.088 -0.092 -0.148  0.236  1.0
x4  0.224  0.215  0.182  0.168 -0.027 -0.102  1.0

The objective is to find a compact model which describes the relationship between the x variables and the y variables. Give an interpretation of the model you choose.