Question

If the regression line of y on x and x on y are given by 2x+3y=-1 and 5x+6y=-1 then the arithmetic means of x and y are given by​

Answer 1

Step-by-step explanation:

1. 2x+3y=-1___________(1)×2

5x+6y=-1___________(2)×1

2.4x+6y=-2_______(1)

5x+6y=-1________(2)

3. (1)-(2)

4x+6y=-2

-5x-6y= 1

_____________

-x+(0)y=-1

x=1

substitute in 1st Equation

2(1)+3y=-1

3y=-3

y=-1

x=1 and y=-1

Answer 2

The answer is x = 1 and y = -1.

Step-by-step explanation:

we use arithmetic mean to find the average of all given quantities by dividing them with the total number of those quantities. regression line is a line we can use to describe the trend of a data which can help us in it helps in forecasting and tells us about relationship between variables.

now, in this question we have to given, the regression line of y on x and x on y is given by 2x+3y= -1 and 5x+6y= -1. now to calculate arithmetic means of x and y follow the steps :-

lets take equation A = 2x+3y = -1 and equation B = 5x+6y = -1

now, multiply equation A by 2 and equation B by 1,

(2x+3y= -1) * 2   and  (5x+6y =-1) * 1

we got, A= 4x+6y= -1 and B = 5x+6y= -1

now subtract equation A from equation B,

 (4x+6y= -1 )

- (5x+6y= -1 )

= -x+(0)y = -1  or x = 1

here put the value of x in original equation A,

2(1) + 3y = -1

3y = -3

y = -1

and hence x=1 and y = -1