SuperstarsIn the TV show Superstars the top athletes from various sports compete against one another in a variety of events. The athletes vary considerably in height and weight. To compensate for this in the weight-lifting competition, the body weight of the athlete is subtracted from his lift. What kind of relationship does this suggest? Use the following table, which displays the winning lifts at the 1996 Olympic Games, to show this relationship.

Physiological arguments have been proposed that suggest that the strength of a muscle is proportional to its cross-sectional area. Using this submodel for strength, construct a model relating lifting ability and body weight. List all assumptions. Do you have to assume that all weight lifters are geometrically similar? Test your model with the data provided.
Now consider a renement to the previous model. Suppose there is a certain amount of body weight that is independent of size in adults. Suggest a model that incorporates this renement, and test it against the data provided.
Criticize the use of the preceding data. What data would you really like to have to handicap the weight lifters? Who is the best weight lifter according to your models?
Suggest a rule of thumb for the Superstars show to handicap the weightlifters.

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Winning lifts from the 2000 Olympic Games Max participant weight (kg) Lift (kg) 185 225 <48 48-53 58-63 75 >75 56 62 69 77 85 94 105 > 105 242.50 245 300 305 325 357.50 376.50 390 405 425 472.5 Male (M) or female (F) F F F F F MMMMM M M M