Question

Given the 2 regression lines 3x+12y=19,3y+9x=46,find the coefficient of correlation between x and y?​

Answer 1

Step-by-step explanation:

Given lines of regression are:

3x+12y−19=0 .........(1)

9x+3y−46=0 ..........(2)

From equation (1), the regression line of y on x is.

12y=−3x+19

⇒y=−

12

3

x+

12

19

⇒y=−

4

1

x+

12

19

∴b

yx

=−

4

1

From equation (2), the regression line of x on y is.

9x=−3y+46

⇒x=−

9

3

y+

9

46

⇒x=−

3

1

y+

9

46

∴b

xy

=−

3

1

Now, r=

b

yx

⋅b

xy

r=

(−

4

1

)×(−

3

1

)

r=

12

1

r=0.288.