The city council of Pine Bluffs is considering increasing the number of police i
ID: 3152854 • 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.
7
a.
Determine the regression equation. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)
Estimate the number of crimes for a city with 21 police officers. (Round your answer to 4 decimal places.)
City Police Number of Crimes City Police Number of Crimes Oxford 12 17 Holgate 15 6 Starksville 15 13 Carey 8 18 Danville 20 6 Whistler 6 21 Athens 22 7 Woodville 177
a.
Determine the regression equation. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)
= + X b.Estimate the number of crimes for a city with 21 police officers. (Round your answer to 4 decimal places.)
Number of crimes c. Interpret the regression equation. For each policeman added, the number of crimes goes (Click to select)downup by one.Explanation / Answer
a.
Mean of X = X / n = 14.375
Mean of Y = Y / n = 11.875
(Xi - Mean)^2 = 213.88
(Yi - Mean)^2 = 264.88
(Xi-Mean)*(Yi-Mean) = -213.63
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = -213.63 / 213.88 = -0.9988
bo = Y / n - b1 * X / n
bo = 11.875 - -0.9988*14.375 = 26.2332
Y = bo + b1 X
Y'=26.2332-0.9988*X
b.
When crimes for a city with 21 police officers,
Y' = 26.2332-0.9988*(21) = 5.2584
c.
For each policeman added, the number of crimes goes down by one.
Police No.of Crimes (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 12 17 5.641 26.266 -12.17 15 13 0.391 1.266 0.7 20 6 31.641 34.516 -33.05 22 7 58.141 23.766 -37.17 15 6 0.391 34.516 -3.67 8 18 40.641 37.516 -39.05 6 21 70.141 83.266 -76.42 17 7 6.891 23.766 -12.8Related Questions
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