Question

Question 4

A researcher wants to know the relationship between murder and robbery. The researcher recorded the number of murders and robberies per 100,000 population for a random selection of cities. Help the researcher to find the relationship between the two variables.

Murders, x 2.4 2.7 5.6 2.6 2.1 3.3 6.6 5.7
Robberies, y 25 14 151 91 80 49 173 96
       
a. Calculate the correlation coefficient, R. Interpret the calculated value of R.      
b. Briefly comment on the relationship between the two variables based on the correlation
coefficient, R.        (1 Mark)
c. Calculate the slope, b.      
d. Calculate the intercept, a.      
e. Write the regression equation.          (1 Mark)

Answer 1

A)
S.NO.	X	Y	Xn-ẋ	Yn-ẏ	(Xn-ẋ)^2	(Yn-ẏ)^2	(Xn-ẋ)/Sx X (Yn-ẏ)/Sy
1	2.4	25	-1.475	-59.875	2.175625	3585.016	0.8762
2	2.7	14	-1.175	-70.875	1.380625	5023.266	0.8262
3	5.6	151	1.725	66.125	2.975625	4372.516	1.1317
4	2.6	91	-1.275	6.125	1.625625	37.51563	-0.0775
5	2.1	80	-1.775	-4.875	3.150625	23.76563	0.0859
6	3.3	49	-0.575	-35.875	0.330625	1287.016	0.2047
7	6.6	173	2.725	88.125	7.425625	7766.016	2.3826
8	5.7	96	1.825	11.125	3.330625	123.7656	0.2014
Total	31	679			22.395	22218.88	5.6312
	ẋ=31/8	3.875
	ẏ=679/8	84.875
	Sx=√22.395/7	1.789
	Sy=√22218.88/7	56.339
Formula	R=1/n-1∑[(Xn-ẋ)/Sx X (Yn-ẏ)/Sy}]=5.6312/7	0.804
Answer	R=0.804
R is positive and close to 1, which means there is strong relation between murder and robbery
B)
Positive correlation mean that both the variables move in the same direction.