Attendance at sports events depends on various factors. Teams typically do not change ticket prices from game to game to attract more spectators to less attractive games. However, there are other marketing tools used, such as fireworks, free hats, etc., for this purpose. You work as a consultant for a sports team, the Brisbane Broncos, to help them forecast attendance, so that they can potentially devise strategies for price discrimination. After collecting data over two years for every one of its home games of the 2017 and 2018 seasons, you run the following regression: Attend = 15005 + 201 x Temperat + 465 x BroncNetWin
+82 x OppNetWin +9647 x DFSaSu
+1328 x Drain + 1609 x DQld-978 x D2018, R2 = 0.416, SER = 6983,
where Attend is the announced stadium attendance, Temperat it the average temperature on game day, BronNetWin are the net wins of the Broncos before the game (wins – losses), OppNetWin is the opposing team's net wins before the game, and DFSasu, Drain, DQld, and D2018 are binary variables, taking a value of 1 if the game was played on a weekend, it rained during that day, the opposing team is from Queensland, and the game was played during 2018, respectively.
a) What was the average attendance in 2017, on a sunny weekday with a temperature of 30C, when the Broncos had a Win-Loss record of 15-5 and facing an opponent from NSW with a record of 11-9? What would be the difference in attendance if the exact same game (e. g. under identical conditions) took place in 2018?
b) Interpret the R2. Do the coefficients on BroncNetWin, DFSaSu, and Drain have the expected signs?
c) Excluding the last three binary variables yields the following regression result: Attend = 14838 + 202 x Temperat + 435 x BroncNetWin +90 OppNetWin + 10472 x DFSasu, R2 = 0.410, SER = 6925, Why did the R2 decrease in this regression? Is it justified to remove these three explanatory variables from the regression?