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

ID: 3355833 • 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 amounts should be indicated by a minus sign.)

Estimate the number of crimes for a city with 29 police officers. (Round your answer to 4 decimal places.)

Explanation / Answer

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

calculation procedure for regression

mean of X = X / n = 17.125

mean of Y = Y / n = 13.375

(Xi - Mean)^2 = 180.87504

(Yi - Mean)^2 = 227.88

(Xi-Mean)*(Yi-Mean) = -173.37503

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= -173.37503 / 180.87504

= -0.95853

bo = Y / n - b1 * X / n

bo = 13.375 - -0.95853*17.125 = 29.78991

value of regression equation is, Y = bo + b1 X

Y'=29.7899-0.9585* X

when x = 29

Y'=29.7899-0.9585* 29

= 1.9934

For each policeman added, the number of crimes goes down by one.

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 14 16 9.76563 6.89063 -8.20313 17 15 0.01563 2.64063 -0.20313 22 7 23.76563 40.64063 -31.07813 25 10 62.01563 11.39063 -26.57813 17 8 0.01563 28.89063 0.67188 12 20 26.26563 43.89063 -33.95313 10 22 50.76563 74.39063 -61.45313 20 9 8.26563 19.14063 -12.57813

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

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

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