Question

Given the following sample observations, draw a scatter diagram on a separate piece of paper.

X:	−9	−14	13	1	16
Y:	51	243	159	4	338

Compute the correlation coefficient. (Round your answer to 3 decimal places.)

Try squaring the x variable and then determine the correlation coefficient. (Round your answer to 3 decimal places.)

Answer 1

X Values
∑ = 30
Mean = 6
∑(X - M_x)² = SS_x = 246

Y Values
∑ = 795
Mean = 159
∑(Y - M_y)² = SS_y = 74786

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 2709

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

r = 2709 / √((246)(74786)) = 0.632

Now converting x to x^2 we get

X Values
∑ = 703
Mean = 140.6
∑(X - M_x)² = SS_x = 40233.2

Y Values
∑ = 795
Mean = 159
∑(Y - M_y)² = SS_y = 74786

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 53385

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

r = 53385 / √((40233.2)(74786)) = 0.973