Refer to the Electronic Journal of Sociology (2007) study of the impact of race on the value of professional football players’ “rookie” cards, presented in Exercise. Recall that the sample consisted of 148 rookie cards of National Football League (NFL) players who were inducted into the Football Hall of Fame. The researchers modeled the natural logarithm of card price (y) as a function of the following independent variables:
Race: x1 = 1 if black, 0 if white
Card availability: x2 = 1 if high, 0 if low
Card vintage: x3 = year card printed
Finalist: x4 = natural logarithm of number of times player was on final Hall of Fame ballot
Position-QB: x5 = 1 if quarterback, 0 if not
Position-RB: x7 = 1 if running back, 0 if not
Position-WR: x8 = 1 if wide receiver, 0 if not
Position-TE: x9 = 1 if tight end, 0 if not
Position-DL: x10 = 1 if defensive lineman, 0 if not
Position-LB: x11 = 1 if linebacker, 0 if not
Position-DB: x12 = 1 if defensive back, 0 if not
a. The model E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + β6x6 + β7x7 + β8x8 + β9x9 + β10x10 + β11x11 + β11x11 + β12 x12 was fit to the data, with the following results: R2 = .705, adj- R2 = .681, F = 26.9. Interpret the results practically. Make an inference about the overall adequacy of the model.
b. Refer to part a. Statistics for the race variable were reported as follows: β1 = -147, sβ1 = .145, t = -1.014, p-value = .312. Use this information to make an inference about the impact of race on the value of professional football players’ rookie cards.
c. Refer to part a. Statistics for the card vintage variable were reported as follows: β3 = -.074, sβ2 = .007, t = -10.92, p-value = .000. Use this information to make an inference about the impact of card vintage on the value of professional football players’ rookie cards.
d. Write a first-order model for E (y) as a function of card vintage (x4) and position (x5 – x12) that allows for the relationship between price and vintage to vary with position.