Question

If the regression line of Y on X is ŷ = 35 + 2x and Cov (x, y) = 50, find the standard deviation of X.

Answer 1

ŷ = 35 + 2x ∴ b = 2, Cov (x, y) = 50,
S_x = ?

Now, \(b=\frac{Cov(x,y)}{S^2_x}\)

∴ 2 = \(\frac{50}{S^2_x}\)

∴ 2S_x² = 50

∴ S_x² = \(\frac{50}{2}\) = 25

∴ S_x = 5

Hence, Standard deviation of X obtained is 5.