Question

If the regression equation of y on x is 2 x + 3 y = 1 then which of the following is the regression coefficient of y on x

Answer 1

Step-by-step explanation:

For regression equations, both coefficients both bxy and byx need to be of the same sign.

If 2x+3y=6 is Y on X and 5x+7y−12=0 is X on Y

then Y=

3

6

−

3

2

x then X=

5

12−7y

byx

1

=−

3

2

and bxy

1

=−

5

7

If 2x+3y=6 is X on Y and 5x+7y=12 is Y on X

Then x=

2

6−3y

and y=

7

12−5x

bxy

2

=−

2

3

and byx

1

=−

7

5

bxy

1

×byx

1

=

15

14

<1

byx

2

×bxy

2

=

4

15

<1

We know bxy×byx=r

2

which is always <1

So first assumption is correct

Regression equation of Y on X is 2x+3y=6

Regression equation of X on Y is 5x+7y−12=0