Question

Below is a set of data from a sample of n = 11: X 3 6 10 12 4 9 15 18 7 5 8 Y 9 18 30 36 12 27 45 54 21 15 24 Answer the following questions: (a) Calculate the covariance. (b) Calculate the coefficient of correlation. (c) What conclusions can you reach about the relationship between X and Y? Explain.

Answer 1

a) The covariance is given by

From data we get n= 11, = 8.82, = 26.45, s_x = 4.67, s_y = 13.995

x	y	(x- )	(y- )
3	9	-5.82	-17.45	101.559
6	18	-2.82	-8.45	23.829
10	30	1.18	3.55	4.189
12	36	3.18	9.55	30.369
4	12	-4.82	-14.45	69.649
9	27	0.18	0.55	0.099
15	45	6.18	18.55	114.639
18	54	9.18	27.55	252.909
7	21	-1.82	-5.45	9.919
5	15	-3.82	-11.45	43.739
8	24	-0.82	-2.45	2.009
			Total	652.909

Hence ,

b) coefficient of correlation

  

= 0.9989

c) Hence correlation coefficient r is approximately equal to 1. Hence we conclude that there is perfect positive correlation between x and y.