Question

Calculate the correlation coefficient​ r, letting Row 1 represent the​ x-values and Row 2 the​ y-values. Then calculate it​ again, letting Row 2 represent the​ x-values and Row 1 the​ y-values. What effect does switching the variables have on​ r?

Row 1

18

20

36

48

52

66

75

Row 2

118

110

206

200

141

171

202

Calculate the correlation coefficient​ r, letting Row 1 represent the​ x-values and Row 2 the​ y-values.

requals

Calculate the correlation coefficient​ r, letting Row 2 represent the​ x-values and Row 1 the​ y-values.

What effect does switching the variables have on the correlation​ coefficient?

The correlation coefficient

▼

remains unchanged

decreases

increases

changes sign

when the​ x-values and​ y-values are switched.

Answer 1

The correlation coefficient​ r, letting Row 1 represent the​ x-values and Row 2 the​ y-values

X Values
∑ = 315
Mean = 45
∑(X - M_x)² = SS_x = 2834

Y Values
∑ = 1148
Mean = 164
∑(Y - M_y)² = SS_y = 10114

X and Y Combined
N = 7
∑(X - M_x)(Y - M_y) = 3448

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

r = 3448 / √((2834)(10114)) = 0.644

The correlation coefficient​ r, letting Row 2 represent the​ x-values and Row 1 the​ y-values

X Values
∑ = 1148
Mean = 164
∑(X - M_x)² = SS_x = 10114

Y Values
∑ = 315
Mean = 45
∑(Y - M_y)² = SS_y = 2834

X and Y Combined
N = 7
∑(X - M_x)(Y - M_y) = 3448

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

r = 3448 / √((10114)(2834)) = 0.644

The correlation coefficient remains unchanged when the​ x-values and​ y-values are switched.