Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter R, Problem 2.51RE
Penguins again In Chapter 8 we learned about the extraordinary depth and duration of the dives taken by penguins. In that chapter we modeled a re-expression of Heart rate with the Duration (min) of dives. The data also include the depth of each dive. Here is an analysis that incorporates both variables:
Response variable is: LogHeartRate
R squared = 79.5% s = 0.0869
| Variable | Coefficient |
| Intercept | 1.99213 |
| Duration(min) | –0.04510 |
| Depth(m) | 0.000887 |
- a) What is an appropriate interpretation of the coefficient of Duration in this regression?
Here is a partial regression plot for the coefficient of Duration:
- b) Based on this plot, do you think the coefficient of Duration is a good estimate of the relationship of Duration to (log) Heart rate in these penguins? Explain.
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Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.
x days
76
79
36
95
207
y km/100
14.2
19.6
5.4
11.2
35.9
(a) Verify that
Σx = 493,
Σy = 86.3,
Σx2 = 65,187,
Σy2 = 2029.21,
Σxy = 11317.3,
and
r ≈ 0.93885.
Σx
Σy
Σx2
Σy2
Σxy
r
(b) Use a 1% level of significance to test the claim
ρ > 0.
(Use 2 decimal places.)
t
critical t
(c) Verify that
Se ≈ 4.6183,
a ≈ 0.5575,
and
b ≈ 0.1694.
Se
a
b
Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2…
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.
x days
75
79
35
91
203
y km/100
14.2
19.1
5.8
11.2
35.4
(a) Verify that
Σx = 483,
Σy = 85.7,
Σx2 = 62,581,
Σy2 = 1978.69,
Σxy = 10982.3,
and
r ≈ 0.94895.
Σx
Σy
Σx2
Σy2
Σxy
r
(b) Use a 1% level of significance to test the claim
ρ > 0.
(Use 2 decimal places.)
t
critical t
(c) Verify that
Se ≈ 4.1118,
a ≈ 0.7378,
and
b ≈ 0.1698.
Se
a
b
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.
x days
75
79
35
91
203
y km/100
14.2
19.1
5.8
11.2
35.4
(d) Find the predicted distance (km/100) when a drift bottle has been floating for 80 days. (Use 2 decimal places.) km/100(e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)
lower limit
km/100
upper limit
km/100
(f) Use a 1% level of significance to test the claim that
β > 0.
(Use 2 decimal places.)
t
critical t
(g) Find a 95% confidence interval for β and interpret…
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