Question

Given the data below, Number of Police Officers 4 6 8 9 10 12 12 13 15 20 26 28 Number of Crimes 49 42 38 31 24 24 28 23 21 19 12 14

a) Test for correlation coefficient at the 5% level of significance and make a conclusion

b) Testing the significance of the slope of the regression line at the 5% level of significance and make a conclusion

c) What is the regression equation? What is the standard error of regression?

d) If number of X increases to 50, what would we predict Y to be?

Answer 1

a)

null hypothesis:		ρ	=	0
Alternate Hypothesis:		ρ	≠	0

correlation coefficient r=		Sxy/(√Sxx*Syy)               =		-0.8863
test statistic:                t=		r*(√(n-2)/(1-r2))	=	-6.0534

p value =0.0001

as p value is lower then 0.05 level we reject null hypothesis and conclude that there is significant linear relationship

b)

from above ; test statsitic t=-6.053

p value =0.0001

as p value is lower then 0.05 level we reject null hypothesis and conclude that there is significant linear relationship

c)

regression equation:Yhat=44.9415+(-1.3147)*x

standard error of regression =5.4293

d)

predicted Y=44.9415+(-1.3147)*50=-20.7935 ( which is not posible)