Does familiarity with neighbors lead to lower crime rates? A researcher has theorized that if neighbors know each other, then the crime rates will be lower than in communities in which neighbors do not have a relationship. When communities grow quickly the closeness of the community degrades. A study was done to see if there is a relationship between the crime rate and the percentage change in neighborhood population. 10 neighborhoods in a large metropolis were studied. The results are as follows.
|
Percentage Change in Neighborhood Population
|
29
|
2
|
11
|
17
|
7
|
6
|
51
|
13
|
19
|
7
|
|
Crime Rate (Crime per 1000 population)
|
173
|
35
|
132
|
127
|
69
|
53
|
223
|
104
|
99
|
45
|
1. Identify the Explanatory (X) and Response (Y) variable.
2. Find Persons Correlation Coefficient and determine if there exists a significant linear relationship.
3. Make a scatter plot of the data. Does the scatter plot support the decision from problem 2?
4. Find the Least Squares Regression Line for the data.
5. What percentage of variation in the crime rate that is explained by the linear relationship between the crime rate and the percentage of change in neighborhood population? (Hint: Coefficient of Determination)
6. Use the least squares regression line to predict the crime rate for a neighborhood with a change in population of 45 percent.