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 7.88 6.23 6.24 5.74 7.92 6.14 6.09 5.94 7.65 5.96 6.31 6.10 7.61 5.82 6.96 6.28 7.48 5.82 7.38 6.09 7.48 5.85 7.52 5.79 7.36 5.82 7.83 5.80 6.57 5.80

Answer 1

From given data we have Number of sample n = 15 1 XY Y^2 2 6.23 49.0924 38.8129 х 7.88 7.92 7.65 3 6.14 48.6288 37.6996 4 5.96 45.594 5 7.61 44.2902 5.82 5.82 35.5216 33.8724 33.8724 34.2225 6 7.48 43.5336 7 7.48 5.85 8 7.36 9 10 X^2 62.0944 62.7264 58.5225 57.9121 55.9504 55.9504 54.1696 43.1649 38.9376 37.0881 39.8161 48.4416 54.4644 56.5504 61.3089 SUM=787.0978 5.82 5.8 5.74 5.94 6.1 6.28 6.09 5.79 11 33.8724 33.64 32.9476 35.2836 37.21 43.758 42.8352 38.106 35.8176 36.1746 38.491 43.7088 44.9442 43.5408 45.414 SUM=643.9292 6.57 6.24 6.09 6.31 6.96 7.38 7.52 7.83 SUM = 108.28 12 13 14 15 16 39.4384 37.0881 33.5241 33.64 SUM=530.6456 5.8 17 SUM=89.18

Now we have to calculate the correlation coefficient r. Y = ηΣ sy-Σκ) Σy) (η Σα2 - Σκ)2)(ηΣv2 - Σy)2) 15*643.9292-(108.28)(29.18) (154787.0978- (108.28)?)+ (15+530.6456- (89.18)?) - 0.1086 :: correlation coefficient r = 0.1086

tnk u