Question

What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. x 12.1 26.3 32.2 38.3 51.3 20.5 22.7 y 2.78 1.98 1.48 1.03 0.75 2.38 2.20 (a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.) Σx = Correct: Your answer is correct. Σy = Correct: Your answer is correct. Σx2 = Correct: Your answer is correct. Σy2 = Correct: Your answer is correct. Σxy = Correct: Your answer is correct. r =

Answer 1

Let x = depth of dive in meters

Let y = optimal time in hours.

Sr.No	X	Y	X^2	Y^2	XY
1	12.1	2.78	146.41	7.73	33.64
2	26.3	1.98	691.69	3.92	52.07
3	32.2	1.48	1036.84	2.19	47.66
4	38.3	1.03	1466.89	1.06	39.45
5	51.3	0.75	2631.69	0.56	38.48
6	20.5	2.38	420.25	5.66	48.79
7	22.7	2.2	515.29	4.84	49.94
Total	203.40	12.60	6909.06	25.97	310.02

Σx = 203.40, Σy= 12.60, Σx2 = 6909.06, Σy2 = 25.97, Σxy=310.02

r = -0.979

depth of dive in meters & optimal time in hours are negatively correlated

as one increases other will get decreased.