Question

ns Here is a bivariate data set. 49.3 155.2 6.7 32.3 47.6 $0.9 44.3 44.8 (0/10) (0/10) [10/10] 6 (0/10) 298 5.7 15.6 -30.2 33.2 -16.8 27.9 45.9 21 22.1 39.2 -3.1 46.4 -113.1 11 (2/10) 212 (2/10) 13 (0/10) 214 (0/10) Q15 (0/10) Q 16 (0/10) Find the correlation coefficient and report it accurate to three decimal places. 17 (0/10) Points possible: 10 Unlimited attempts. Q 19 (0/10) Submit t Version 川1 6

Answer 1

Correlation coefficient:

	X	Y	xy	x2	y2
	49.3	155.2	7651.36	2430.49	24087.04
	6.7	32.3	216.41	44.89	1043.29
	47.6	50.9	2422.84	2265.76	2590.81
	44.3	44.8	1984.64	1962.49	2007.04
	29.8	5.7	169.86	888.04	32.49
	15.6	-30.2	-471.12	243.36	912.04
	33.2	-16.8	-557.76	1102.24	282.24
	27.9	-45.9	-1280.61	778.41	2106.81
	21	-22.1	-464.1	441	488.41
	39.2	-3.1	-121.52	1536.64	9.61
	46.4	-113.1	-5247.84	2152.96	12791.61
total	361	57.7	4302.16	13846.28	46351.39
n	11

$r=11*4302.16-(361)(57.7)/\sqrt{[11*13846.28-(361)^{2}][11*46351.39-(57.7)^{2}]}$

$r=47323.76-20829.7/\sqrt{[152309.08-130321][509865.29-3329.29]}$

$r=26494.06/\sqrt{[21988.08][506536]}$

$r=26494.06/105535.5584$

$r=0.251$

Correlation coefficeint:

	X	Y	xy	x2	y2
	48.4	43.3	2095.72	2342.56	1874.89
	35.2	40.7	1432.64	1239.04	1656.49
	92.8	253.4	23515.52	8611.84	64211.56
	66.7	259.2	17288.64	4448.89	67184.64
	61.1	-69.2	-4228.12	3733.21	4788.64
	46.8	-68.5	-3205.8	2190.24	4692.25
	64.4	23.8	1532.72	4147.36	566.44
	62	217.7	13497.4	3844	47393.29
	74.9	24.8	1857.52	5610.01	615.04
	54.3	-26.1	-1417.23	2948.49	681.21
total	606.6	699.1	52369.01	39115.64	193664.45
n	10

$r=10*52369.01-(606.6)(699.1)/\sqrt{[10*39115.64-(606.6^{2}][10*193664.45-(699.1)^{2}]}$

$r=523690.1-424074.06\sqrt{[391156.4-367963.56][1936644.5-488740.81]}$

$r=99616.04/\sqrt{[23192.84][1447903.69]}$

$r=99616.04/183251.1899$

$r=0.543$

what proportion of the variation in y can be explained by the variation in the values of x?

r²=(0.543)2

=0.2948

=0.29

29%proportion of the variation in y can be explained by the variation in the values of x