Question

Consider the follow set of ?=5 (?,?)(x,y) pairs:

?x	20	25	26	30	35
?y	21	30	35	31	40

NOTE: SXX = 126.8, SXY = 139.6, SYY = 197.2, ?¯x¯ = 27.2, and ?¯y¯ = 31.4.

Compute the sample correlation correct to three decimal places of accuracy.

Correlation = ?=

Answer 1

Answer:
The following table shows the calculations -

	x	y	x^2	y^2	xy
	20	21	400	441	420
	25	30	625	900	750
	26	35	676	1225	910
	30	31	900	961	930
	35	40	1225	1600	1400
Total	136	157	3826	5127	4410

Total number of observations, n = 5

Mean of x, = 136/5 = 27.2 (given)

T

Mean of y, $\bar{y}$ = 157/5 = 31.4 (given)

Sxx = $\sum$ (x^2) - (n x (^2)) = 3826 – (5 x (27.2^2)) = 126.8 (given)

T

Syy =  $\sum$(y^2) - (n x ($\bar{y}$^2)) = 5127 – (5 x (31.4^2)) = 197.2 (given)

Sxy =  $\sum$xy - (n x
T
x $\bar{y}$ ) = 4410 – (5 x 27.2 x 31.4) = 139.6 (given)

Therefore, Correlation Coefficient, r = Sxy / (Sxx . Syy)^0.5 = 139.6 / (126.8 x 197.2)^0.5 = 0.883