Question

the following bivariate data set contains an outlier.

x	y
27.7	12.9
29	13.9
33.1	7.6
31.7	48.2
32.3	12.4
31.1	32.9
29	22.4
35.2	29.5
47.2	62.3
31.7	21.9
27.6	20.4
29.2	16.9
37.6	54.2
34.1	27.7
106	-156.5

What is the correlation coefficient with the outlier?
r_w =

What is the correlation coefficient without the outlier?
r_wo =

Answer 1

With outlier correlation coefficient is as below:

X Values
∑ = 562.5
Mean = 37.5
∑(X - M_x)² = SS_x = 5365.28

Y Values
∑ = 226.7
Mean = 15.113
∑(Y - M_y)² = SS_y = 35182.457

X and Y Combined
N = 15
∑(X - M_x)(Y - M_y) = -11764.81

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

r = -11764.81 / √((5365.28)(35182.457)) = -0.8563

Now without outlier correlation coefficient is as below:

X Values
∑ = 456.5
Mean = 32.607
∑(X - M_x)² = SS_x = 337.869

Y Values
∑ = 383.2
Mean = 27.371
∑(Y - M_y)² = SS_y = 3627.669

X and Y Combined
N = 14
∑(X - M_x)(Y - M_y) = 830.383

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

r = 830.383 / √((337.869)(3627.669)) = 0.7501