Question

The regression equation are 16x - 9y+94 = 0 and x-y + 5 = 0 If the variance of y is 16, then the

standard deviation of x is​

Answer 1

9 is the correct answer

Step-by-step explanation:

we may write y =x  − 5 and 16x = 9y+ 94  where x and y are means of variables x and y.

16x= 9(x- 5 )+ 94= 9x + (94 -45)

or 7x= 49 or x = 7

Then y =x - 5 = 7-5 =2

So the means are x = 7 and y = 2.

Let y = x – 5 be the regression line of y on x and

16x = 9y + 94 be the regression line of x on y.

If the variance of y = 16,

Byx = 1, bxy = 9/16  

r² = Byx + bxy

r = √ 1 X 9/16 = ¾

bxy = r σ x/σ y

16 = 6/4 σ x/4√ 16

σ x = 3

Cov (X,Y)/ σ x.σ y = r

Cov (X,Y) = ¾ x 3 x 4 = 9

thus, standard deviation of x is​ 9

hence, 9 is the correct answer