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.) Consumer Household Consumer Household Debt Debt Debt Debt 7.89 6.22 6.23 5.72 7.92 6.15 6.09 5.94 7.66 5.95 6.33 6.08 7.60 5.82 6.97 6.29 7.48 5.82 7.38 6.07 7.50 5.86 7.52 5.79 7.37 5.82 7.83 5.82 6.58 5.80

Answer 1

х Y X*Y X2 Y2 7.89 6.22 49.0758 62.2521 38.6884 7.92 6.15 48.708 62.7264 37.8225 7.66 5.95 45.577 58.6756 35.4025 7.6 5.82 44.232 57.76 33.8724 7.48 5.82 43.5336 55.9504 33.8724 7.5 5.86 43.95 56.25 34.3396 7.37 5.82 42.8934 54.3169 33.8724 6.58 5.8 38.164 43.2964 33.64 6.23 5.72 35.6356 38.8129 32.7184 6.09 5.94 36.1746 37.0881 35.2836 6.33 6.08 38.4864 40.0689 36.9664 6.97 6.29 43.8413 48.5809 39.5641 7.38 6.07 44.7966 54.4644 36.8449 7.52 5.79 43.5408 56.5504 33.5241 7.83 5.82 45.5706 61.3089 33.8724 Sum = 108.35 89.15 644.1797 788.1023 530.2841

ans:0.1427

SSxy = ΣΧΥ; Σκη - (Σκ) (ΣΥ) Σ» (Σκ)' SSxx 2 η 1 SSyy ΣΥ? Υ; m 1=1 i=1 In this case, based on the data provided, we get that SSXY = 644.18 1 (108.35 x 89.15) = 0.22 15 SSxx = 788.102 1 (108.35)2 = 5.454 15 SSγY = 530.284 1 (89.15)2 = 0.436 15 Therefore, based on this information, the sample correlation coefficient is computed as follows 1 SSXY SSXX SSyy 0.22 5.454 x 0.436 = 0.142