The Federal Bureau of Investigation (FBI), as part of its internal security mission, serves as a database for all the reported crimes committed in the United States. One question that might be of interest is does having more police officers reduce the number of homicides? To investigate this claim, the 2013 data from the twenty largest municipal cities was supplied by the FBI's Uniform Crime Report. Below are two observations from the dataset: > head (cities) City Pop Homicides Police Density MedHome Mayor 1 New York 8175.133 335 4.2595 27016.30 5.5390 2 Chicago 2695.598 414 4.4309 11843.58 1.8310 1 The variables included in the study are: Name of city Population of city in 1,000s of people Number of homicides in the year 2013 Number of police officers per 1,000 people Number of people per square mile Median home price in $100,000 1 if city has a “Strong Mayor" form of government; 0 if not City Рop Homicides Police Density MedHome Мayor Model: log(µ;) = Bo + B1Police; + B2MedHome; + B3I(Mayor;) +log(Pop;) mod1 glm (Homicides * Police + MedHome + Mayor, family=poisson, offset=log(Pop)) Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.19745 0.35530 -6.185 1.31e-05 Police 0.05424 0.11390 0.476 0.640352 i MedHome -0.28076 0.05630 -4.987 0.000134 Мayor 0.60000 0.31171 1.925 0.072219 (Dispersion parameter for poisson family taken to be 1)
The Federal Bureau of Investigation (FBI), as part of its internal security mission, serves as a database for all the reported crimes committed in the United States. One question that might be of interest is does having more police officers reduce the number of homicides? To investigate this claim, the 2013 data from the twenty largest municipal cities was supplied by the FBI's Uniform Crime Report. Below are two observations from the dataset: > head (cities) City Pop Homicides Police Density MedHome Mayor 1 New York 8175.133 335 4.2595 27016.30 5.5390 2 Chicago 2695.598 414 4.4309 11843.58 1.8310 1 The variables included in the study are: Name of city Population of city in 1,000s of people Number of homicides in the year 2013 Number of police officers per 1,000 people Number of people per square mile Median home price in $100,000 1 if city has a “Strong Mayor" form of government; 0 if not City Рop Homicides Police Density MedHome Мayor Model: log(µ;) = Bo + B1Police; + B2MedHome; + B3I(Mayor;) +log(Pop;) mod1 glm (Homicides * Police + MedHome + Mayor, family=poisson, offset=log(Pop)) Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.19745 0.35530 -6.185 1.31e-05 Police 0.05424 0.11390 0.476 0.640352 i MedHome -0.28076 0.05630 -4.987 0.000134 Мayor 0.60000 0.31171 1.925 0.072219 (Dispersion parameter for poisson family taken to be 1)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question
![The Federal Bureau of Investigation (FBI), as part of its internal security mission,
serves as a database for all the reported crimes committed in the United States. One question
that might be of interest is does having more police officers reduce the number of homicides? To
investigate this claim, the 2013 data from the twenty largest municipal cities was supplied by the
FBI's Uniform Crime Report. Below are two observations from the dataset:
> head (cities)
City
Pop Homicides
Police
Density MedHome Mayor
1
New York
8175.133
335
4.2595
27016.30
5.5390
1
2
Chicago
2695.598
414
4.4309
11843.58
1.8310
The variables included in the study are:
Name of city
Population of city in 1,000s of people
Number of homicides in the year 2013
Number of police officers per 1,000 people
Number of people per square mile
Median home price in $100,000
1 if city has a "Strong Mayor" form of government; 0 if not
City
Рор
Homicides
Police
Density
MedHome
Мayor
Model: log(u;) = Bo + B1Police; + B2MedHome; + B3I(Mayor;) + log(Pop;)
mod1
glm (Homicides ~ Police + MedHome + Mayor, family=poisson, offset=log (Pop))
Coefficients:
Estimate Std. Error z value Pr(>]z|)
(Intercept) -2.19745
0.35530
-6.185 1.31e-05
Police
0.05424
0.11390
0.476 0.640352
i
MedHome
-0.28076
0.05630
-4.987 0.000134
Мayor
0.60000
0.31171
1.925 0.072219
(Dispersion parameter for poisson family taken to be 1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2db349d-44e2-4dc0-ad50-be44fa6802da%2Fa5565cee-ee37-49e4-8d3d-0394dac9e5dc%2Fe3usrch_processed.png&w=3840&q=75)
Transcribed Image Text:The Federal Bureau of Investigation (FBI), as part of its internal security mission,
serves as a database for all the reported crimes committed in the United States. One question
that might be of interest is does having more police officers reduce the number of homicides? To
investigate this claim, the 2013 data from the twenty largest municipal cities was supplied by the
FBI's Uniform Crime Report. Below are two observations from the dataset:
> head (cities)
City
Pop Homicides
Police
Density MedHome Mayor
1
New York
8175.133
335
4.2595
27016.30
5.5390
1
2
Chicago
2695.598
414
4.4309
11843.58
1.8310
The variables included in the study are:
Name of city
Population of city in 1,000s of people
Number of homicides in the year 2013
Number of police officers per 1,000 people
Number of people per square mile
Median home price in $100,000
1 if city has a "Strong Mayor" form of government; 0 if not
City
Рор
Homicides
Police
Density
MedHome
Мayor
Model: log(u;) = Bo + B1Police; + B2MedHome; + B3I(Mayor;) + log(Pop;)
mod1
glm (Homicides ~ Police + MedHome + Mayor, family=poisson, offset=log (Pop))
Coefficients:
Estimate Std. Error z value Pr(>]z|)
(Intercept) -2.19745
0.35530
-6.185 1.31e-05
Police
0.05424
0.11390
0.476 0.640352
i
MedHome
-0.28076
0.05630
-4.987 0.000134
Мayor
0.60000
0.31171
1.925 0.072219
(Dispersion parameter for poisson family taken to be 1)
Transcribed Image Text:a. The offset term is set to be log(Pop). If this offset term was not included in the model, what
would we be modeling with respect to the response instead?
b. Write out the estimated model and state the random, systematic, and link components in this
model.
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