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 # of Crimes	City
Oxford	12	17
Starksville	15	13
Danville	20	6
Athens	22	7
Holgate	15	6
Carey	8	18
Whistler	6	21
Woodville	17	7

a) Determine the regression equation

b) estimate the number of crimes for a city with 21 police officers

Answer 1

(a)

The following data are passed:

X	Y
12	17
15	13
20	6
22	7
15	6
8	18
6	21
17	7

The independent variable is X, and the dependent variable is YY In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	12	17	204	144	289
	15	13	195	225	169
	20	6	120	400	36
	22	7	154	484	49
	15	6	90	225	36
	8	18	144	64	324
	6	21	126	36	441
	17	7	119	289	49
Sum =	115	95	1152	1867	1393

Based on the above table, the following is calculated:

Therefore, we find that the regression equation is:

(b)

When X = 21