Question

For two variables x and y, it is known that cov (x, y) = 8, r=0.4, variance of x is 16 and sum of
squares of deviation of y from its mean is 250. The number of observations for this bivariate
data is
(a) 7
(b) 8
(c) 9
(d) 10​

Answer 1

Answer:

10

Step-by-step explanation:

Given :

r = 0.8, Cov(x,y) = 8, Var(x) =16

r = Cov(x,y)/√{ Var(x)*Var(y)}

0.4 = 8/√{16* Var(y)}

0.4 = 8/ {4 * SD(y)}

(0.4*4)/8 = 1/ SD(y)

1.6/8 = 1/ SD(y)

0.2 = 1/ SD(y)

SD(y) = 1/ 0.2

= 5

SD(y) = √{Sigma(y - Mean(y)}^2/n

5 = √250/n

Squaring on both sides

25 = 250/n

n = 10