An accurate assessment of oxygen consumption provides

Chapter 0, Problem 5.82

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An accurate assessment of oxygen consumption provides important information for determining energy ex- 1 x 1 y a x2 62.600235 a xy 1114.5 a y2 57,939 n 12 a x 22.207 a y 793 penditure requirements for physically demanding tasks. The paper Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation (Ergonomics [1991]: 14691474) reported on a study in which x oxygen consumption (in milliliters per kilogram per minute) during a treadmill test was determined for a sample of 10 fire- fighters. Then y 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 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 = +11.4 + 1.09 treadcon Predictor Coef Stdev t-ratio p Constant 11.37 12.46 0.91 0.388 treadcon 1.0906 0.3181 3.43 0.009 s = 4.70 R-sq = 59.5% 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 calculate the new equation of the least-squares line and the value of r 2. What do you conclude? (Hint: For the original data g x 388.8 g y 310.3 g x2 15,338.54 g xy 12,306.58 2 10,072.41