Web Analytics
Answered

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

Verified Answer :

nobillionaireNobley

∑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

TheLegendaryJet

Answer:

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

Related Questions