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 15 17 Holgate 17 7 Starksville 17 13 Carey 12 21 Danville 25 5 Whistler 11 19 Athens 27 7 Woodville 22 6

1. Determine the standard error of estimate

2. Determine the coefficient of determination

3. Interpret the coefficient of determination

Answer 1

SST=Syy=		290.8750
SSE =Syy-(Sxy)2/Sxx=		68.481
SSR =(Sxy)2/Sxx =		222.3936

1)

	s2 =SSE/(n-2)=	11.4136
std error of estimate σ              =	=se =√s2=	3.3784

2)

Coefficient of determination R^2 =SSR/SST=222.394/290.875 =

0.7646

3)

coefficient of determination indicate that 76.46 % variation in number of crimes can be explained by independent variable( number of police ) in the city,