Question

Q.2. The equations of the two lines of regressions are 3x+2y-26 = 0 and 6x+y-
31=0. Find a) Means of X and Y b) Var(X) if Var(Y) = 36

Answer 1

(i) Means x¯ and y¯ satisfy the equation of lines of regression.

∴3x¯+2y¯=266x¯+y¯=31

Solving, we get, x¯ = 4 and y¯ = 7

(ii) 6x+y=31x=−16y+316[bxy=−16]y=−32x+262y=−32x+13[byx=−32]

∴r2=byx×bxy=14r=12,−12⟹r=0.5,−0.5

Since bxy and byx are both negative, r is negative. Therefore, r = -0.5

(iii) byx=rσyσx−32=−12(σy3)σy=9