Question

Data from the U.S. Federal Reserve Board on the percentage of disposable personal income required to meet consumer loan payments and mortgage payments for selected years are shown in the following table. What is the value of the correlation coefficient for this data set? (Give the answer to four decimal places.) r = Consumer Debt Household Debt Consumer Debt Household Debt 7.89 6.22 6.23 5.72 7.90 6.14 6.08 5.95 7.64 5.95 6.33 6.09 7.62 5.83 6.98 6.28 7.49 5.83 7.38 6.07 7.48 5.86 7.52 5.80 7.37 5.82 7.84 5.81 6.57 5.80

Answer 1

X Values
∑ = 108.32
Mean = 7.221
∑(X - M_x)² = SS_x = 5.463

Y Values
∑ = 89.17
Mean = 5.945
∑(Y - M_y)² = SS_y = 0.423

X and Y Combined
N = 15
∑(X - M_x)(Y - M_y) = 0.196

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

r = 0.196 / √((5.463)(0.423)) = 0.1288