Solution Found!
Impact of race on football card values. Refer to
Chapter 12, Problem 89E(choose chapter or problem)
Impact of race on football card values. Refer to theElectronic Journal of Sociology (2007) study of the impact of race on the value of professional football players’ “rookie” cards, Exercise 12.72 (p. 712). Recall that the sample consisted of 148 rookie cards of NFL players who were inducted into the Football Hall of Fame(HOF). The researchers modeled the natural logarithm of card price (y) as a function of the following independent variables:
a. The model \(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\beta_{4} x_{4}+\beta_{5} x_{5}+\beta_{6} x_{6}+\beta_{7} x_{7}+\beta_{8} x_{8}+\beta_{9} x_{9}+\beta_{10} x_{10}+\beta_{11} x_{11}+\beta_{12} x_{12}\) was fit to the data with the following results: \(R^2=.705,\ R_a^2\ =\ .681,\ F=26.9\) 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: \(\hat{\beta}_{1}=-.147,\ s_{\hat{\beta}_{1}}=.145,\ t=-1.014\), 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: \(\hat{\beta}_3=-.074,\ s_{\hat{\beta}_3}=.007,\ t=-10.92\), 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 (\(x_3\)) and position (\(x_5-x_{12}\)) that allows for the relationship between price and vintage to vary depending on position.
Questions & Answers
QUESTION:
Impact of race on football card values. Refer to theElectronic Journal of Sociology (2007) study of the impact of race on the value of professional football players’ “rookie” cards, Exercise 12.72 (p. 712). Recall that the sample consisted of 148 rookie cards of NFL players who were inducted into the Football Hall of Fame(HOF). The researchers modeled the natural logarithm of card price (y) as a function of the following independent variables:
a. The model \(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\beta_{4} x_{4}+\beta_{5} x_{5}+\beta_{6} x_{6}+\beta_{7} x_{7}+\beta_{8} x_{8}+\beta_{9} x_{9}+\beta_{10} x_{10}+\beta_{11} x_{11}+\beta_{12} x_{12}\) was fit to the data with the following results: \(R^2=.705,\ R_a^2\ =\ .681,\ F=26.9\) 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: \(\hat{\beta}_{1}=-.147,\ s_{\hat{\beta}_{1}}=.145,\ t=-1.014\), 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: \(\hat{\beta}_3=-.074,\ s_{\hat{\beta}_3}=.007,\ t=-10.92\), 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 (\(x_3\)) and position (\(x_5-x_{12}\)) that allows for the relationship between price and vintage to vary depending on position.
ANSWER:Step 1 of 4
The given model is
The following are the quantitative and qualitative variables.
