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; the complete data set can be found on the text website, labeled Quarterback Salaries.
a. Estimate and interpret the model: Salary = β0 + β1PC + β2TD + β3Age + 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.