An accurate assessment of oxygen consumption provides important information for determining energy expenditure requirements for physically demanding tasks. The paper “Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation” (Ergo- nomics [1991]: 1469–1474) reported on a study in which x 5 oxygen consumption (in milliliters per kilogram per minute) during a treadmill test was determined for a sample of 10 fire fighters. Then y 5 oxygen consumption at a comparable heart rate was measured for each of the 10 individuals while they performed a fire-suppression simulation. This resulted in the following data and scatterplot:

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An accurate assessment of oxygen consumption
provides important information for determining energy
expenditure requirements for physically demanding
tasks. The paper “Oxygen Consumption During Fire
Suppression: Error of Heart Rate Estimation” (Ergo-
nomics [1991]: 1469–1474) reported on a study in which
x 5 oxygen consumption (in milliliters per kilogram per
minute) during a treadmill test was determined for a
sample of 10 fire fighters. Then y 5 oxygen consumption
at a comparable heart rate was measured for each of the
10 individuals while they performed a fire-suppression simulation. This resulted in the following data and
scatterplot:

simulation. This resulted in the following data and
scatterplot:
Firefighter
y
Firefighter 6
35.4
26.3
y
50
40
30
20
1
51.3
49.3
Fire-simulation
consumption
35
34.1
29.5
2
42
7
8
35.4 38.6
33.9 29.4
3
The regression equation is
firecon=-11.4 + 1.09 treadcon
Predictor
Coef
Constant -11.37
treadcon
1.0906
S = 4.70
R-sq = 59.5%
41.1
30.6
Stdev
12.46
0.3181
4
36.3
28.2
a. Does the scatterplot suggest an approximate linear
relationship?
Treadmill
49 consumption
b. The investigators fit a least-squares line. The result-
ing Minitab output is given in the following:
9
10
40.6
39.5
23.5 31.6
t-ratio
-0.91
5
36.5
28.0
0.388
3.43 0.009
R-sq(adj) = 54.4%
Predict fire-simulation consumption when treadmill
consumption is 40.
c.
How effectively does a straight line summarize the
relationship?
d. Delete the first observation, (51.3, 49.3), and calcu-
late the new equation of the least-squares line
and the value of r². What do you conclude? (Hint:
For the original data, Σx = 388.8, Σy = 310.3,
Ex² = 15,338.54, Σ xy = 12,306.58, and
2y = 10,072.41.)
Transcribed Image Text:simulation. This resulted in the following data and scatterplot: Firefighter y Firefighter 6 35.4 26.3 y 50 40 30 20 1 51.3 49.3 Fire-simulation consumption 35 34.1 29.5 2 42 7 8 35.4 38.6 33.9 29.4 3 The regression equation is firecon=-11.4 + 1.09 treadcon Predictor Coef Constant -11.37 treadcon 1.0906 S = 4.70 R-sq = 59.5% 41.1 30.6 Stdev 12.46 0.3181 4 36.3 28.2 a. Does the scatterplot suggest an approximate linear relationship? Treadmill 49 consumption b. The investigators fit a least-squares line. The result- ing Minitab output is given in the following: 9 10 40.6 39.5 23.5 31.6 t-ratio -0.91 5 36.5 28.0 0.388 3.43 0.009 R-sq(adj) = 54.4% Predict fire-simulation consumption when treadmill consumption is 40. c. How effectively does a straight line summarize the relationship? d. Delete the first observation, (51.3, 49.3), and calcu- late the new equation of the least-squares line and the value of r². What do you conclude? (Hint: For the original data, Σx = 388.8, Σy = 310.3, Ex² = 15,338.54, Σ xy = 12,306.58, and 2y = 10,072.41.)
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