If the regression equations of the variables x and y be x=19.13-0.83 y and y=11.64-0.50 x , then the correlation coefficient between x and y is:

Question

If the regression equations of the variables x and y be x=19.13-0.83 y and y=11.64-0.50 x , then the correlation coefficient between x and y is: (A)  0.66  (B)  -0.64  (C)  0.001  (D)  -0.001

Tardigrade Admin · Accepted Answer

If both regression coefficients are positive or negative,
then the correlation coefficient is positive or negative.
Given regression equations are

x = 19.13 - 0.83 y

and

y = 11.64 - 0.50 x

Their corresponding regression coefficients are

b_{x y} = - 0.83

and by

b_{y x} = - 0.50

∴

Correlation coefficient

= - b_{x y} \times b_{y x}

= - 0.83 \times 0.50

= - 0.64

If regression coefficients are of opposite sign, then correlation coefficient cannot be determined.

Q. If the regression equations of the variables $x$ and $y$ be $x = 19.13 - 0.83 y$ and $y = 11.64 - 0.50 x$ , then the correlation coefficient between $x$ and $y$ is:

$0.66$

$- 0.64$

$0.001$

$- 0.001$

Q. If the regression equations of the variables x and y be x=19.13−0.83y and y=11.64−0.50x , then the correlation coefficient between x and y is:

0.66

−0.64

0.001

−0.001

Q. If the regression equations of the variables $x$ and $y$ be $x = 19.13 - 0.83 y$ and $y = 11.64 - 0.50 x$ , then the correlation coefficient between $x$ and $y$ is:

$0.66$

$- 0.64$

$0.001$

$- 0.001$