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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 15.1 24.3 29.2 38.3 51.3 20.5 22.7 y 2.48 2.18 1.68 1.03 0.75 2.38 2.20 (a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (b) Use a 1% level of significance to test the claim that ρ < 0. (Round your answers to two decimal places.) t = critical t = (c) Find Se, a, and b. (Round your answers to five decimal places.) Se = a = b = Find the predicted optimal time in hours for a dive depth of x = 29 meters. (Round your answer to two decimal places.) hr

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 15.1 24.3 29.2 38.3 51.3 20.5 22.7 y 2.48 2.18 1.68 1.03 0.75 2.38 2.20 (a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (b) Use a 1% level of significance to test the claim that ρ < 0. (Round your answers to two decimal places.) t = critical t = (c) Find Se, a, and b. (Round your answers to five decimal places.) Se = a = b = Find the predicted optimal time in hours for a dive depth of x = 29 meters. (Round your answer to two decimal places.) hr

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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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 15.1 24.3 29.2 38.3 51.3 20.5 22.7
y 2.48 2.18 1.68 1.03 0.75 2.38 2.20
(a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.)
Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =

(b) Use a 1% level of significance to test the claim that ρ < 0. (Round your answers to two decimal places.)
t =
critical t =
(c) Find Se, a, and b. (Round your answers to five decimal places.)
Se =
a =
b =

Find the predicted optimal time in hours for a dive depth of x = 29 meters. (Round your answer to two decimal places.)
hr
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