The crime index refers to the number of incidents of crime. The numbers of burglaries, aggravated assaults,

The €œcrime index€ refers to the number of incidents of crime. The numbers of burglaries, aggravated assaults, and all types of crime per 100,000 Americans are shown in Table 27 for various years.

a. Let A be the crime index of aggravated assaults for the year that is t years since 1990. Can the data be modeled well by a linear model? If yes, find such a model. If no, explain why not.
b. Let B be the crime index of burglaries for the year that is t years since 1990. Can the data be modeled well by a linear model? If yes, find such a model. If no, explain why not.
c. Let C be the crime index of all types of crime for the year that is t years since 1990. Can the data be modeled well by a linear model? If yes, find such a model. If no, explain why not.
d. Economist Steven D. Levitt believes crime and the econ- omy are not related. The U.S. economy performed well from 1993 to 2000 and from 2003 to 2008 and did poorly from 2000 to 2003 and from 2008 to 2012. Explain why the aggravated-assault data support Levitt€™s theory.
e. Explain why the burglary data are less supportive (than the aggravated-assault data) of Levitt€™s theory.
f. Explain why the data for all types of crime support Levitt€™s theory.

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Table 27 Crime Indexes Crime Index (number of incidents per 100,000 people) Aggravated Assault All Types of Crime Burglary Year 1993 1995 1997 1999 2001 1100 987 919 770 742 741 441 418 382 334 319 295 291 10,974 10.550 9855 8533 8134 7801 7496 6947 6585 6492 2007 726 718 701 670 265 242 242 2011 2012