The city council of Pine Bluffs is considering increasing the number of police i

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.

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 28 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 (UP or DOWN) by one.

City Police Crimes Oxford 16 14 Straksville 19 13 Danville 24 6 Athens 27 7 Holgate 19 6 Carey 14 17 Whistler 13 20 Woodville 21 8

Explanation / Answer

a. Line of Regression Y on X i.e Y = bo + b1 X

Mean of X = X / n =    19.125
Mean of Y = Y / n =   11.375
(Xi - Mean)^2 =   162.91
(Yi - Mean)^2 =   203.87
(Xi-Mean)*(Yi-Mean) =   -156.37
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = -156.37 / 162.91 = -0.96  
bo = Y / n - b1 * X / n  
bo = 11.375 - -0.96*19.125 = 29.73  
  
Y = bo + b1 X  
  
Y'=29.73-0.96*X  

b.

Estimate the number of crimes for a city with 28 police officers = Y'=29.73-0.96* (28) = 2.85

c.

it will down by one

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 16 14 9.77 6.89 -8.2 19 13 0.02 2.64 -0.2 24 6 23.77 28.89 -26.2 27 7 62.02 19.14 -34.45 19 6 0.02 28.89 0.67 14 17 26.27 31.64 -28.83 13 20 37.52 74.39 -52.83 21 8 3.52 11.39 -6.33

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