Question

Here is a bivariate data set. х 94 94 81 67 у 98 -7 21 69 85 84 70 46 68 55 89 22 -65 10 -31 215 Find the correlation coefficient and report it accurate to four decimal places. r= Check Answer

Answer 1

Answer:

r = 0.6400

Solution:

The formula for correlation coefficient is given as below:

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

The calculation table is given as below:

No.	x	y	x^2	y^2	xy
1	94	98	8836	9604	9212
2	94	-7	8836	49	-658
3	81	21	6561	441	1701
4	67	69	4489	4761	4623
5	84	85	7056	7225	7140
6	70	22	4900	484	1540
7	46	-65	2116	4225	-2990
8	68	10	4624	100	680
9	55	-31	3025	961	-1705
10	89	215	7921	46225	19135
Total	748	417	58364	74075	38678

From above table, we have

n = 10

∑x = 748

∑y = 417

∑x^2 = 58364

∑y^2 = 74075

∑xy = 38678

r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

r = [10*38678 - 748*417]/sqrt((10*58364 - 748^2)*(10*74075 - 417^2))

r = 74864 / 116969

r = 0.640033

r = 0.6400

There is a moderate high positive linear relationship exists between two variables.