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. Determine the regression equation. (Round your answer to 4 decimal places. Negative values should be indicated by a minus sign.) Y = + X Estimate the number of crimes for a city with 26 police officers. (Round your answer to 4 decimal places.) Number of crimes Interpret the regression equation. For each policeman added, the number of crimes goes by one

Explanation / Answer

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

Mean of X = X / n =    25.25
Mean of Y = Y / n =   13
(Xi - Mean)^2 =   113.5
(Yi - Mean)^2 =   188
(Xi-Mean)*(Yi-Mean) =   -113
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = -113 / 113.5 = -0.9956  
bo = Y / n - b1 * X / n  
bo = 13 - -0.9956*25.25 = 38.1388  
  
Y = bo + b1 X  
  
Y'=38.1388-0.9956*X  

b.

No.of crimes = Y' = 38.1388-0.9956*(26) = 12.2532

c.

it goes down by one

Police No.ofCrimes (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 23 15 5.063 4 -4.5 25 11 0.063 4 0.5 29 8 14.063 25 -18.75 32 11 45.563 4 -13.5 25 8 0.063 25 1.25 21 19 18.063 36 -25.5 20 22 27.563 81 -47.25 27 10 3.063 9 -5.25

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