Question

find the coefficient of correlation of following data taking new origin of x at 70 and y at 67. x: 67 68 64 68 72 70 69 70 y: 65 66 67 67 68 69 71 73​

Answer 1

Step-by-step explanation:

68,6972,53

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Answer 2

Answer:

Coefficient of correlation (r) between two variables x, y is given by;

r = Cov(x, y)/√(V(x)).√(V(y)), where Cov(x, y) = E{(x - x*)(y - y*)} is called co-variance between x, y & V(x) = E{(x-x*)² is called variance of x etc and E is Expected value operator with x* denoting the a.m. of x values and so on . Now, let u = (2x-4) & v = (3–2y) ==> u -u*= 2 (x - x*) and v -v* = - 2(y -y*) which in turn implies Cov(u, v) = E{(u -u*)(v -v*)}

= E{-4(x -x*)(y -y*)} = -4E{(x-x*)(y-y*)} = -4 Cov(x, y) and Var(u) = E{(u-u*)² = E{(2(x-x*))² = 4E{(x -x*)² = 4 Var(x) . Similarly Var(v) = 4 Var(y) . Therefore coefficient of correlation r’ between u, v is r’ = Cov(u, v)/{√(V(u))√V(v))}

= - 4 Cov(x, y)/{4 √(V(x))√(V(y)}

= (-4/4) r = - 1 .(1/2) = -1/2 (as r= 1/2).