If the regression line of Y on X is ŷ = 11 + 3x and Sx: Sy = 3 : 10

1.	If the regression line of Y on X is ŷ = 11 + 3x and Sx: Sy = 3 : 10, find the coefficient of determination.
Answer» ŷ = 11 + 3x ∴ b = 3 S_x : S_y = 3 : 10, ∴ S_x = 3, S_y = 10. \(Now, b = r . \frac{S_y} {S_x}\) ∴ 3 = r × \(\frac{10}{3}\) ∴ r = 3 × \(\frac{3}{10}=\frac{9}{10}\)= 0.9 Now, coefficient of determination R² = (r)² ∴ R² = (0.9)² = 0.81

If the regression line of Y on X is ŷ = 11 + 3x and Sx: Sy = 3 : 10, find the coefficient of determination.

Answer»

ŷ = 11 + 3x

∴ b = 3

S_x : S_y = 3 : 10,

∴ S_x = 3, S_y = 10.

\(Now, b = r . \frac{S_y} {S_x}\)

∴ 3 = r × \(\frac{10}{3}\)

∴ r = 3 × \(\frac{3}{10}=\frac{9}{10}\)= 0.9

Now, coefficient of determination

R² = (r)²

∴ R² = (0.9)²

= 0.81