Question

in a bivariate data two regression equations are 3x+4y=1 and 3x+y=4 find the mean of x and y . also find r

Answer 1

Solution:

The two regression equations are:

1. 3 x + 4 y =1

2. 3 x + y=4

Equation (1) - Equation (2)

4 y - y = 1 -4

3 y = -3

Dividing both sides by ,3 we get

y=-1

Putting the value of y ,in equation (2)

3 x -1 = 4

3 x = 5

$x=\frac{5}{3}$

1. 3 x + 4 y =1

4 y = 1 - 3 x

$y= \frac{1}{4}-\frac{3 x}{4}\\\\ b_{y x}=\frac{-3}{4}$

2. 3 x + y=4

3 x = 4 - y

$x=\frac{4}{3}-\frac{y}{3}$

$b_{xy}=\frac{-1}{3}$

Coefficient of correlation, r =

       $\sqrt{b_{yx}\times b_{xy}} \\\\ =\sqrt{\frac{-1}{3} \times \frac{-3}{4}}\\\\ =\frac{1}{2}$ →→→Positive Correlation