Question

Calculus A hard problem help please

The graph below plots the values of y for different values of x:

Plot the ordered pairs 1, 8 and 2, 3 and 3, 0 and 4, 1 and 5, 2 and 6,1

What is the correlation coefficient for the data plotted?

-0.9

-0.6

0.6

0.9

Answer 1

X Values

∑ = 21

Mean = 3.5

∑(X - Mx)2 = SSx = 17.5

Y Values

∑ = 15

Mean = 2.5

∑(Y - My)2 = SSy = 41.5

X and Y Combined

N = 6

∑(X - Mx)(Y - My) = -18.5

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -18.5 / √((17.5)(41.5)) = -0.6865

Meta Numerics (cross-check)

r = -0.6865

Answer 2

∑x = 1 + 2 + 3 + 4 + 5 + 6 = 21
∑y = 8 + 3 + 0 + 1 + 2 + 1 = 15
∑x^2 = 1 + 4 + 9 + 16 + 25 + 36 = 91
∑y^2 = 64 + 9 + 0 + 1 + 4 + 1 = 79
∑xy = 8 + 6 + 0 + 4 + 10 + 6 = 34

r = (n∑xy - ∑x∑y)/(sqrt(n∑x^2 - (∑x)^2)*sqrt(n∑y^2 - (∑y)^2)) = (6(34) - 21(15))/(sqrt(6(91) - (21)^2)*sqrt(6(79) - (15)^2)) = (204 - 315)/(sqrt(546 - 441)*sqrt(474 - 225)) = -111/(sqrt(105)*sqrt(249)) = -111/(10.25*15.78) = -111/161.7 = -0.68