Given that the regression equations of Y on X and of X on Y are respectively Y = X
and 4X − Y = 3, and the second moment of X about the origin is 2, find
i) the means of X and Y;
ii) the correlation coefficient between X and Y;
iii) the standard deviation of Y
1
Expert's answer
2019-03-25T15:32:41-0400
(i) Since two regression lines always intersect at a point representing mean values
(xˉ,yˉ)Y=X4X−Y=3
Then
xˉ=1,yˉ=1
(ii) To find the given regression equations in such a way that the coefficient of dependent variable is less than one at least in one equation. So
4X−Y=3⟹4X=3+Y⟹X=43+41Y
That is
bxy=41=0.25
Y=X
That is
byx=1
Hence coefficient of correlation r between x and y is given by:
r=bxy∗byx=0.25∗1=0.5
(iii) To determine the standard deviation of y , consider the formula:
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