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.

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. Which variable is the dependent variable and which is the independent variable? Hint: Which of the following makes sense: Cities with more police have fewer crimes, or cities with fewer crimes have less police?

2, Fill in the blanks below

x¯x¯
y¯y¯
Sx
Sy
Coefficient of correlation
Coefficient of determination

Answer 1

1)

number of police is  independent variable

and  number of crimes is dependent variable  

since we assume that presence of police reduces crime,.

2()

	n=	8.0000
	X̅=ΣX/n	18.250
	Y̅=ΣY/n	11.875
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	5.874
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	6.446
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	-33.1071
	r=Cov/(Sx*Sy)=	-0.8744

from above:

x¯x¯	18.250
y¯y¯	11.875
Sx	5.8737
Sy	6.4462
Coefficient of correlation	-0.8744
Coefficient of determination =0.7646