"State University" is a medium-sized college with a football team. The athletics department wishes to better understand what factors are associated with attendance at home games. The data file "Football" is available on Canvas. The data records information for 16 randomly chosen (non-consecutive) home games played during the last 5 seasons before the pandemic. Attendance measures the number of people in attendance at the game. Home Team Win Percentage measures the percentage of previous games during the season that the home team won. Opponent Team Win Percentage measures the percentage of previous games during the season that the opponent won. Time is a qualitative variable indicating whether the game was played during the day or at night. (a) Estimate a multiple regression model where Attendance is the dependent variable and Home Team Win Percentage, Opponent Team Win Percentage, and Time are the independent variables. Use day games as the reference category. Write down your estimated regression equation(s). (b) Construct and conduct an appropriate hypothesis test for determining whether this model, as a whole, is useful. Use a 5% level of significance. (c) Identify the 95% confidence interval for the slope coefficient associated with the variable "Home Team Win Percentage." Interpret it within the context of this problem. (d) Using the results of your model, is attendance at night games significantly different from attendance at day games, all else equal? Justify your response with statistical reasoning