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.

City	Police				Number of Crimes				City				Police				Number of Crimes
Oxford		19				16				Holgate				21				6
Starksville		21				12				Carey				15				18
Danville		27				6				Whistler				13				21
Athens		29				7				Woodville				25				8

Click here for the Excel Data File

1. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)

2. Estimate the number of crimes for a city with 23 police officers. (Round your answer to the nearest whole number.)

3. Interpret the regression equation.

Answer 1

a.

Sum of X = 170
Sum of Y = 94
Mean X = 21.25
Mean Y = 11.75
Sum of squares (SS_X) = 219.5
Sum of products (SP) = -207.5

Regression Equation = ŷ = bX + a

b = SP/SS_X = -207.5/219.5 = -0.9453

a = M_Y - bM_X = 11.75 - (-0.95*21.25) = 31.8383

ŷ = -0.9453X + 31.8383

b. For x=23,

ŷ = (-0.9453*23) + 31.8383=10.0964=10

c. For every increase in x, there is -0.9453 decrease in y, this is slope value.

For x=0, y value will be 31.8383