How do we estimate a regression relationship when each subject is measured multiple times over a series of X-values ? The easiest approach is to use a summary slope for each individual and then calculate the average slope. Green et al. (2001) dealt with exactly this type of problem in their study of macaroni penguins exercised on treadmills. Each penguin was exercised at a range of speeds, and its oxygen consumption was measured in relation to its heart rate (a proxy for metabolic rate). The graph provided shows the relationship for just two individual penguins.

a. Calculate the mean, standard deviation, and sample size of the slope for penguins in each of the three groups. Display your results in a table.

b. Test whether the means of the slopes are equal between the three groups.

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Mass-specific O₂2 consumption (ml/min/kg) 35 30 25 20 15 10 5- 100 120 140 160 180 200 220 Heart rate (beats/min)