The FBI’s Uniform Crime Reporting (UCR) program gathers crime data from more than 17,000 law enforcement agencies throughout the United States. The Crime data set contains crime counts for several years in Iowa. Crimes are listed by type of crime (murder, burglary, larceny, etc.).
a. Conduct PCA on the crime variables in this data set. What percentage of the variation can be explained by the top two principal components?
b. How would you interpret these two principal components in terms of crime characteristics?
c. Some may suggest simply totaling the crime rates, in essence giving a weight of 1 to every unstandardized variable. Give an example where calculating a “Total” value may be more appropriate than using PCA. Give an example where using PCA may be more appropriate than calculating a “Total” value.
d. Repeat Parts A and B using a rate instead of using the raw numbers of crimes in each category. Explain why either counts or rates would be more appropriate.