5.66 ● 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”

(Ergonomics [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 firefighters.

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:

Firefighter 1 2 3 4 5 x 51.3 34.1 41.1 36.3 36.5 y 49.3 29.5 30.6 28.2 28.0 Firefighter 6 7 8 9 10 x 35.4 35.4 38.6 40.6 39.5 y 26.3 33.9 29.4 23.5 31.6 20 30 40 50 35 42 49 Treadmill consumption Fire-simulation consumption

a. Does the scatterplot suggest an approximate linear relationship?

b. The investigators fit a least-squares line. The resulting Minitab output is given in the following:

The regression equation is

firecon 5 211.4 1 1.09 treadcon Predictor Coef Stdev t-ratio p Constant 211.37 12.46 –0.91 0.388 treadcon 1.0906 0.3181 3.43 0.009 s 5 4.70 R-sq 5 59.5% R-sq(adj) 5 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 calculate the new equation of the least-squares line and the value of r2. What do you conclude? (Hint:

For the original data, ox 5 388.8, oy 5 310.3, ox2 5 15,338.54, oxy 5 12,306.58, and oy2 5 10,072.41.)