Your professor makes available to you one extra credit opportunity to possibly raise your total points in this class. This extra credit is a multiple regression that is similar to the one you completed for your mini report. Follow the directions below and determine what variables contribute to projecting the attendance at the Prescott Maples home games.
The Back Story
Bud Ford, the general manager and owner of the double A farm team, the Prescott Maples, has been talking to his staff about a better way of predicting attendance at the Maple's home games. Playing at ACE Stadium in west Prescott, the team averages about 2,000 people in attendance for each home game. The team sells season tickets, day of game tickets and gives away some tickets to sponsors, nonprofit organizations serving children, and for other good causes.
So while the team may sell over the average number of seats, this does not translate into people actually attending a game. Bud said, "I just don't understand it! They pay for a seat then don't come. It makes no sense to me." So his stadium manager and concession manager have been trying to figure out how they could better predict the attendance at five (5) typical Maple games.
The concession manager, Ralph Peanut, believes that part of this prediction could be the estimated number of hot dogs that would be sold at the game. Bud and the stadium manager aren't sure, but are willing to put this theory to the test. That's where you come into the picture. Your job is to investigate the historical data prepared by Bud, and then using that data create a multiple regression that helps to predict the attendance at these five typical games.
Table: Estimated number of Attendance at Five Typical Maple's Games
Game Attendance Regular Ticket Sales Advanced Ticket Sales Estimated Hot Dogs to be Sold
a 645 231 539
b 743 320 852
c 1,745 134 396
d 1,854 871 783
e 1,745 765 1,239
Your Tasks:
1. Complete a one variable summary for all 20 games over the four variables: 1) attendance; 2) regular ticket sales; 3) advanced ticket sales; and 4) Hot dogs sold at the game.
a. What do these statistics tell you about the group of games? Be specific and look at the range, standard deviation, the IQR, the mean versus the median and other statistics from this output.
2. Complete a correlation on the data (StatTools: Summary Statistics/Correlation and Covariance/Correlation/Entries below the diagonal only). What does this correlation show you about the data, which variables are correlated with attendance the most and the least? What do you think the regression will show about these variables?
3. Complete a single histogram on all four of these variables and analyze the results.
a. What do these histograms tell you about the relationship for each of these variables?
4. Complete 4 Q-Q plots for these variables.
a. What do these plots tell you about the data? Is it relatively normal or not and why?
5. Complete a single box and whisker plot with all four of the variables on it.
a. First explain in the paper what a box and whisker plot is, and how to understand it.
b. What do these box and whisker plots tell you about the individual variables and how do they compare to each other?
6. Complete a multiple regression using the attendance as the dependent variable, and the rest as the independent variables.
a. Do any of the variables t-score (p-value) exceed the alpha (.05) for this test? If so, remove that/those variables and rerun the regression.
b. What does the r-squared value tell you about this data?
c. What does the standard error of the estimate tell you about the data?
d. According to the f-ratio, is this regression significant or not and why?
e. Using the coefficients generate predict the attendance for the five "typical" games found in Table 1 above. (You are to complete the column found on the right in yellow and include this table in your mini report.) Remember to only use the variables that are significant to calculate this table.
7. What general things can you tell Bud Ford about projected attendance at these games? Does knowing the number of hot dogs that could be sold help or hurt the estimated attendance theory? Be specific in your answer.