Question

The two regression lines are 3X+2Y=26 and 6X+3Y=31. Find the correlation coefficient.​

Answer 1

Answer:

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