The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asks the Chief of Police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The Chief gathered the following sample information.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![11. The city council of Pine Bluffs is considering increasing the number of police in an effort
to reduce crime. Before making a final decision, the council asks the Chief of Police to
survey other cities of similar size to determine the relationship between the number of
police and the number of crimes reported. The Chief gathered the following sample
information.
City
Police
Number of Crimes
Oxford
15
17
Starkville
17
13
Danville
25
Athens
27
Holgate
17
Carey
12
21
Whistler
11
19
Woodville
22
6.
a. If we want to estimate crimes based on the number of police, which variable is the
dependent variable, and which is the independent variable?
According to the regression output shown below:
. reg y x
Source
df
MS
Number of obs -
8
F( 1,
6) -
19.49
Model
222.393634
1
222.393634
Prob > F
0.0045
Residual
68.4813665
6.
11.4135611
R-squared
0.7646
Adj R-squared -
0.7253
Total
290.875
7
41.5535714
Root MSE
3.3784
Coef.
Std. Err.
P>|t|
[95% Conf. Interval]
-.9596273
.2173962
-4.41
0.004
-1.491577
-.4276779
cons
29.3882
4.143381
7.09
0.000
19.24971
39.52669
b. write the regression equation.
c. Interpret the coefficient -0.9596273, does it surprise you that the relationship is inverse?
с.
d. What is the coefficient of determination? What does this statistic tell you?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1667e4df-8d7f-4dd9-b2ab-1c01b04b5b86%2Ffb018b32-8c17-4d73-b992-753f6cc8fcc6%2Fm17h91_processed.png&w=3840&q=75)
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