Impact of race on football card values. 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 12.89 (p. 732).

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

[Note: For Position, offensive lineman is the base level]

a. The model E1y2 = b0 + b1 x1 + b2 x2 + b3 x3 + b4x4 +

b5 x5 + b6 x6 + b7 x7 + b8 x8 + b9 x9 + b10 x10 + b11x11

+ b11 x11 + b12 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: b n 1 = -147, sbn 1

= .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: b n 3 = -.074, sbn 2

= .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 1x42 and position 1x59x122 that allows for the relationship between price and vintage to vary with position.