Game performance of water polo players. The journal Biology of Sport (Vol. 31, 2014) published a study of the physiological performance of top-level water polo players.

Eight Olympic male water polo players participated in the study. Two variables were measured for each during competition: y = mean heart rate over the four quarters of the game (expressed as a percentage of maximum heart LO9 rate) and x = maximal oxygen uptake (VO2max). The data (simulated, based on information provided in the article)

are shown in the accompanying table. The researchers conducted a simple linear regression analysis of the data.

A MINITAB printout of the analysis follows.

POLO SAS Output for Exercise 11.23 Player HR% VO2Max 1 55 148 2 54 157 3 70 160 4 67 179 5 74 179 6 77 180 7 78 194 8 85 197

a. Give the equation of the least squares line.

b. Give a practical interpretation (if possible) of the y-intercept of the line.

c. Give a practical interpretation (if possible) of the slope of the line.

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The regression equation is HR = 27.2 + 0.558 VO2Max Predictor Coef SE Coef T P Constant V02Max -27.24 19.77 0.5580 0.1130 -1.38 0.217 4.94 0.003 S = 5.26859 R-Sq = 80.3% R-Sq (adj) = 77.0% Analysis of Variance Source DE SS MS F P Regression 1 677.45 677.45 24.41 0.003 Residual Error 6 166.55 27.76 Total 7 844.00