For r denoting correlation coefficient and G.M as geometric mean. Which one of the following is true?
options:-
1) r>G.M
2)r<G.M
3)r=G.M
4)None of these
5)Other:_________________
Answers
Given : r denoting correlation coefficient and G.M as geometric mean
To find : Which one of the following is true?
Solution:
two regression coefficients a and b of the two regression lines can be stated as follows:
a = Sxy / (Sx)²
b = Sxy / (Sy)²
r = coefficient of correlation
r = Sxy / (Sx . Sy)
r² = ( Sxy / (Sx . Sy) )²
= (Sxy)²/ ( Sx² . Sy²)
= ( Sxy . Sxy )/ ( Sx² . Sy²)
= ( Sxy / Sx² ) . ( Sxy / Sy² )
= ab
r² = ab
=> r = √ab
=> r = GM of a & b
coefficient of correlation is the geometric mean of the two regression coefficients.
option 3 , r=G.M is correct option
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