Question

# For each of the following data sets, choose the most appropriate response from the choices below...

 For each of the following data sets, choose the most appropriate response from the choices below the table. Data Set #1 Data Set #2 x y x y 10 18 -22 92 13 12 -19 85 18 8 -16 71 24 2 -13 75 27 0 -10 68 32 4 -7 69 21 7 -5 66 41 13 0 62 45 17 2 59 a. A strong positive linear relation exists a. A strong positive linear relation exists b. A strong negative linear relation exists b. A strong negative linear relation exists c. No linear relation exists c. No linear relation exists Determine the linear correlation coefficient for each dataset in problem #10. Linear Correlation for Data Set #1: Linear Correlation for Data Set #2:

Data Set 1 c. No linear relation exists X Values
∑ = 231
Mean = 25.667
∑(X - Mx)2 = SSx = 1140

Y Values
∑ = 81
Mean = 9
∑(Y - My)2 = SSy = 330

X and Y Combined
N = 9
∑(X - Mx)(Y - My) = 22

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

r = 22 / √((1140)(330)) = 0.0359

Data set 2 b. A strong negative linear relation exists X Values
∑ = -90
Mean = -10
∑(X - Mx)2 = SSx = 548

Y Values
∑ = 647
Mean = 71.889
∑(Y - My)2 = SSy = 908.889

X and Y Combined
N = 9
∑(X - Mx)(Y - My) = -655

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

r = -655 / √((548)(908.889)) = -0.9281