University of Colorado sociologists investigated the impact of race on the value of professional football players' "rookie" cards (Electronic Journal of Sociology, 2007). The sample consisted of 148 rookie cards of National Football League (NFL) players who were inducted into the Football Hall of Fame. The price of the card (in dollars) was modeled as a function of several qualitative independent variables: race of player (black or white), card availability (high or low), and player position (quarterback, running back, wide receiver, tight end, defensive lineman, linebacker, defensive back, or offensive lineman).
a. Create the appropriate dummy variables for each of the qualitative independent variables.
b. Write a model for price (y) as a function of race. Interpret the β's in the model.
c. Write a model for price (y) as a function of card availability. Interpret the β's in the model.
d. Write a model for price (y) as a function of position. Interpret the β's in the model.