A sports enthusiast wants to examine the factors that influence a quarterback's salary (Salary). In particular, he wants to assess the influence of the pass completion rate (PC), the total touchdowns scored (TD), and a quarterback's age (Age) on Salary. He uses 2009 data, a portion of which is shown in the accompanying table.

a. Estimate and interpret the model: Salary = β0 + β1 PC + β2 TD + β3 Age + ε. Show that this model is preferable to a model that uses log of salary as the response variable.
b. Consider the quadratic effect of Age by adding Age2 in the regression. Use a partial F test to determine the joint statistical significance of Age and Age2.

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Salary Name in $ millions)PC Philip Rivers Jay Cutler 25.5566 22.0441 TD Age 27 26 28 27 65.2 Tony Romo 0.6260 63.1 26 29