Question #104710

Find coefficient of correlation, if variance of X series=2.25, standard deviation of Y series=4and regression equation of X on Y is X+0.3Y=1.8

Expert's answer

Sample regression coefficient x on y:

"\\rho"_{xy}=r*"\\sigma"_{x}/"\\sigma"_{y }

r - correlation coefficient between variables X and Y;

*σ*_{x, }*σ*_{y } - standard deviation calculated for the variables x b y

ρxy - coefficient in the equation

*σ*_{y} =4

σx= 1.5, if we extract the square root from the variance, we get the standard deviation

Transform the equation:

x+0.3y=1.8

0.3y=1.8-x, ρxy=0.3

Substitute in the first formula:

0.3=r*1.5/4

0.3=r*0.375

r=0.8

on a Cheddock scale

0.7 < r < 0.9: high.

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