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 = 0.0921 X Consumer Household Consumer Household Debt Debt Debt Debt 7.88 6.23 6.25 5.72 7.91 6.15 6.10 5.95 7.64 5.96 6.31 6.08 7.60 5.82 6.96 6.28 7.48 5.83 7.39 6.09 7.50 5.86 7.52 5.78 7.38 5.80 7.85 5.80 6.57 5.79

Answer 1

Solution,

X	Y	XY	X^2	Y^2
7.88	6.23	49.0924	62.0944	38.8129
7.91	6.15	48.6465	62.5681	37.8225
7.64	5.96	45.5344	58.3696	35.5216
7.6	5.82	44.232	57.76	33.8724
7.48	5.83	43.6084	55.9504	33.9889
7.5	5.86	43.95	56.25	34.3396
7.38	5.8	42.804	54.4644	33.64
6.57	5.79	38.0403	43.1649	33.5241
6.25	5.72	35.75	39.0625	32.7184
6.1	5.95	36.295	37.21	35.4025
6.31	6.08	38.3648	39.8161	36.9664
6.96	6.28	43.7088	48.4416	39.4384
7.39	6.09	45.0051	54.6121	37.0881
7.52	5.78	43.4656	56.5504	33.4084
7.85	5.8	45.53	61.6225	33.64

n	13
sum(XY)	555.03
sum(X)	92.97
sum(Y)	77.56
sum(X^2)	669.76
sum(Y^2)	463.14
Numerator	4.66
Denominator	18.19
r	0.2561
r square	0.0656
Xbar(mean)	7.1515
Ybar(mean)	5.9662
b	0.0734
a	5.4416

Σεν- (Σκ)(Σ) α 2

r = 0.2561