Question

Equations of two lines of regression are 4x+3y+7 = 0 and 3x+ 4y + 8 = 0, the mean of x and y are
(a) $\frac{5}{7}$ and $\frac{6}{7}$
(b) $\frac{-4}{7}$ and $\frac{-11}{7}$
(c) 2 and 4
(d) None of these

Answer 1

x-y =1
x= 1+y
4(1+y)+3y+7= 4+4y+3y+7 = 11+7y
7y = -11
y = -11/7
x = 1+y
x = 1- 11/7
x= -4/7

Answer 2

Answer:

The answer is Option (b)

The required mean values of x and y are -4/7 and -11/7 respectively.

Step by step Explanation:

Regression is the measure of average relationship between two or more variables in terms of original units of the data.

The mean values of x and y lie on the regression lines and are obtained by solving the given regression equations.

Given equations;

4x+3y+7=0      ——- (1)

3x+4y+8=0      ——- (2)

Solving equations (1) & (2)

4x+3y+7=0            Multiply by 3

3x+4y+8=0            Multiply by 4

  12x+ 9y+21=0

  12x+16y+32=0

(-)   (-)  (-)

  ————————-

      -7y-11y=0

           -7y=11

             

         y = -11/7

Substituting the value of y = -11/7 in equation (1)

4x+3(-11/7)+7=0

4x-(33/7)+7=0

Taking 7 as LCM

(28x-33+49)/7 = 0

Multiplying by 7 on both sides

28x-33+49=0

28x = -16

Dividing by 4 on both sides

7x = -4

x = -4/7

Therefore, the required mean values of x and y are -4/7 and -11/7 respectively.