The city council of Pine Bluffs is considering increasing the number of police i
ID: 3158957 • Letter: T
Question
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 asked 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 Determine the regression equation (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.) Estimate the number of crimes for a city with 25 police officers (Round your answer to 4 decimal places.) Interpret the regression equation.Explanation / Answer
The regression model is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.845282644
R Square
0.714502748
Adjusted R Square
0.666919872
Standard Error
3.681734865
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
203.5439703
203.544
15.01596
0.008217718
Residual
6
81.33102972
13.55517
Total
7
284.875
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
40.6496199
7.538852428
5.392017
0.001676
22.20271259
59.09652722
Number of Police
-1.06081548
0.273755743
-3.87504
0.008218
-1.73067165
-0.390959311
Part a
The regression equation is given as below:
Y = 40.6496 – 1.0608*X
Part b
Number of crimes = 40.6496 – 1.0608*25 = 14.1296
Part c
For each policeman added, the number of crimes goes decreases by one.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.845282644
R Square
0.714502748
Adjusted R Square
0.666919872
Standard Error
3.681734865
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
203.5439703
203.544
15.01596
0.008217718
Residual
6
81.33102972
13.55517
Total
7
284.875
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
40.6496199
7.538852428
5.392017
0.001676
22.20271259
59.09652722
Number of Police
-1.06081548
0.273755743
-3.87504
0.008218
-1.73067165
-0.390959311
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