Question

For a bivariate data, two times of regression are 40x-18y = 214 and 8x - 10y + 66 =0 then find the value of mean of x and mean of y (a) 17 and 13) 13 and 17(c) 13 and -17(d)-13 and 17​

Answer 1

Solution :

The first equation = 40x - 18y = 214

The second equation = 8x - 10y + 66 = 0 = 8x - 10y = -66

By applying elimination method,

Multiply first equation by -1 and multiply second equation by 5.

- 40x + 18y = - 214

40x - 50y = - 330

On adding these two equations together, we get

- 40x + 18y = - 214

+ 40x - 50y = - 330

- 32y = - 544

Now, for "y"

- 32y = - 544

=> y = - 544 / - 32

=> y = 17

Now, for "x"

Substitute the value of "y" in the first equation.

- 40x + (18)(17) = - 214

=> - 40x + 306 = - 214

=> - 40x = - 214 - 306

=> - 40x = - 520

=> x = - 520 / - 40

=> x = 13

.°. x = 13 and y = 17