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		18				17				Holgate				19				7
Starksville		19				13				Carey				14				21
Danville		28				4				Whistler				13				25
Athens		31				7				Woodville				24				5

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

2. y_______ + _________X

3. Estimate the number of crimes for a city with 26 police officers. (Round your answer to the nearest whole number.)

4. Interpret the regression equation.

Answer 1

Using Minitab, (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output -

The regression equation is

The estimated number of crimes for a city with 26 police officers

d) For a unit increase in number of police officers, the estimated number of crimes for a city will decrease by 1.044 units.

For a city with no police officer, the estimated number of crimes for a city will be 34.05 units.