Assignment:
Q1. We studied variability of crime rates and police expenditures in the eastern and Midwestern United States. We’ve now been asked to investigate the hypothesis that the number of crimes is related to police expenditures per capita because states with higher crime rates are likely to increase their police force, thereby spending more on the number of officers on the street.
|
State
|
Number of Crimes
|
Police Protection Expenditures per
Capita (Dollars), per 10,000 People
|
|
Maine
|
2,875
|
122.5
|
|
New Hampshire
|
2,282
|
141.8
|
|
Vermont
|
2,819
|
102.8
|
|
Massachusetts
|
3,262
|
218.7
|
|
Rhode Island
|
3,583
|
179.2
|
|
Connecticut
|
3,389
|
193.6
|
|
New York
|
3,279
|
292.4
|
|
New Jersey
|
3,400
|
236.6
|
|
Pennsylvania
|
3,114
|
171.2
|
|
Ohio
|
3,997
|
179.4
|
|
Indiana
|
3,766
|
124.5
|
|
Illinois
|
4,515
|
224.4
|
|
Michigan
|
4,325
|
172.3
|
|
Wisconsin
|
3.296
|
196.6
|
|
Minnesota
|
3,598
|
166.8
|
|
Iowa
|
3,224
|
135.8
|
|
Missouri
|
4,578
|
153.9
|
|
North Dakota
|
2,394
|
102.9
|
|
South Dakota
|
2,644
|
115.3
|
|
Nebraska
|
4,108
|
128.8
|
|
Kansas
|
4,439
|
161.6
|
a) Construct a scatter diagram of the number of crimes and police expenditures per capita, with number of crimes as the predictor variable. What can you say about the relationship between these two variables based on the scatter plot?
b) Find the least-squares regression equation that predicts police expenditures per capita from the number of crimes. What is the slope? What is the intercept?
c) Calculate the coefficient of determination (r²), and provide interpretation.
d) If the number of crimes increased by 100 for a state, by how much would you predict police expenditures per capita to increase?
e) Does it make sense to predict police expenditures per capita when the number of crimes is equal to zero? Why or why not?
Q2. We investigated the relationship between infant mortality rate and GNP in South America. The birth rates (number of live births per 1,000 inhabitants) in these same countries are shown in the following table:
|
Country
|
Birth Rate in 1999
|
GNP per Capita in 1997 ($)
|
|
Argentina
|
19
|
8,030
|
|
Bolivia
|
32
|
1,010
|
|
Brazil
|
20
|
4,630
|
|
Chile
|
18
|
4,990
|
|
Colombia
|
24
|
2,740
|
|
Ecuador
|
24
|
1,520
|
|
Paraguay
|
30
|
1,760
|
|
Peru
|
25
|
2,440
|
|
Uruguay
|
17
|
6,070
|
|
Venezuela
|
25
|
3,530
|
a) Construct a scatter plot for GNP and birth rate and one for infant mortality rate and birth rate. Do you think each can be characterized by a linear relationship?
b) Calculate the coefficient of determination and correlation coefficient for each relationship.
c) Use this information to describe the relationship between the variables.
Provide complete and step by step solution for the question and show calculations and use formulas.