Here is a bivariate data set. x y 27.2 91.8 19 117 19.5 82.6 25.9 192.3...

Here is a bivariate data set.

x	y
27.2	91.8
19	117
19.5	82.6
25.9	192.3
47.7	95.2
15.7	18.6
4.6	34.7
24.1	34.3
24.7	-39
22.4	29.2
52.7	39.1
7.6	81.3
28.2	131.4
16.8	-42.6
25.4	70.6
24.9	65.9
11.1	5.7
5.7	-74.3
28.7	-20.3
-3.8	54.4

Find the correlation coefficient and report it accurate to three decimal places.
r =

Expert Solution

Solution :

X	Y	XY	X^2	Y^2
27.2	91.8	2496.96	739.84	8427.24
19	117	2223	361	13689
19.5	82.6	1610.7	380.25	6822.76
25.9	192.3	4980.57	670.81	36979.29
47.7	95.2	4541.04	2275.29	9063.04
15.7	18.6	292.02	246.49	345.96
4.6	34.7	159.62	21.16	1204.09
24.1	34.3	826.63	580.81	1176.49
24.7	-39	-963.3	610.09	1521
22.4	29.2	654.08	501.76	852.64
52.7	39.1	2060.57	2777.29	1528.81
7.6	81.3	617.88	57.76	6609.69
28.2	131.4	3705.48	795.24	17265.96
16.8	-42.6	-715.68	282.24	1814.76
25.4	70.6	1793.24	645.16	4984.36
24.9	65.9	1640.91	620.01	4342.81
11.1	5.7	63.27	123.21	32.49
5.7	-74.3	-423.51	32.49	5520.49
28.7	-20.3	-582.61	823.69	412.09
-3.8	54.4	-206.72	14.44	2959.36

n	20
sum(XY)	24774.15
sum(X)	428.10
sum(Y)	967.90
sum(X^2)	12559.03
sum(Y^2)	125552.33
Numerator	81125.01
Denominator	326965.72
r	0.2481

The correlation coefficient r ,

r = 0..2481

Answer : The correlation coefficient r is 0.248

orchestra answered 2 years ago

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