correlation

A computer while calculating correlation coefficient between two variables X and 7 from 25 pairs of observations obtained the following results:

N=25, ∑X=125, ∑X2 = 650,

∑Y=100, 272=460, ∑XY=508.

It was, however, discovered at the time of checking that two pairs of observation were not correctly copied. They were taken as (6, 14) and (8, 6) while the correct values were (8, 12) and (6. 8) prove that the correct value of the correlation coefficient should be 2/3. (I.C.W.A., Final, 1977)


Solution: Corrected ∑X = 125-6-8+8+6= 125

Corrected ∑Y = 100—14—6+12+8 = 100

Corrected ∑X2= 650—62— 82+82+ 62 = 950

Corrected ∑Y2 = 460—142—62+122+82 = 436

Corrected ∑XY= 508—(6 x 14)—(8 x 6) + (8 x 12) +(6 x 8)=520

Now the Corrected value of the Coefficient of Correlation or

Corrected r = (N∑XY-(∑X)(∑Y))/(√(N∑X2- (∑X)2 ) √(N∑X2- (∑X)2 ))

= ((25×520)- (125×100))/(√(25×650-(125)2 ) √(25×436-(100)2 ))

= 500/√(625×900) = 500/(25×30) = 500/750 = 2/3