Question

find the coefficient of determination. Write a statement of interpretation for it;

X: 1, 2, 4, 8, 10, 12

Y: 8, 7, 5, 4, 2, 1

Answer 1

X Values
∑ = 37
Mean = 6.167
∑(X - M_x)² = SS_x = 100.833

Y Values
∑ = 27
Mean = 4.5
∑(Y - M_y)² = SS_y = 37.5

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = -60.5

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -60.5 / √((100.833)(37.5)) = -0.9839
So Coefficient of determination is

Hence 96.81% of variation of y is explained by x.