Question

Find the mean of the variables X and Y and correlation coefficient given the following Regression

Equations 2y-x-50=0; 3y-2x-10=0​

Answer 1

Given:

2y - x - 50 = 0

3y - 2x - 10 = 0​

To find:

Mean of the variables X and Y

Correlation coefficient

Solution:

2y - x - 50 = 0

2y - x = 50                                  (i)

3y - 2x - 10 = 0​

3y - 2x = 10                                (ii)

Solving equation (i) and (ii) simultaneously

2y - x = 50         ×2

3y - 2x = 10  

So, we get

4y - 2x = 100

3y - 2x = 10  

(-)  (+)       (-)    

y = 90

Putting value of y in equation (i)

2y - x = 50

2(90) - x = 50

180 - x = 50

x = 180 - 50

x = 130

So, we get X' = 130 and Y' = 90

Assume equation (i), regression equation of Y on X

2y - x = 50

2y = x + 50

$y = \frac{1}{2} x + 25$

So, $b_y_x = \frac{1}{2}$

Consider equation (ii), regression equation of X on Y

3y - 2x = 10

2x = 3y - 10

$x = \frac{3}{2}y - 5$

So, $b_x_y = \frac{3}{2}$

$r = \sqrt{b_x_y * b_y_x} \\\\r = \sqrt{\frac{1}{2} * \frac{3}{2} }$

r = 0.866

So, correlation coefficient is 0.866