## Tuesday, March 31, 2015

### Super Bowl

Background
There have been 48 Super Bowls.  Some have been close contests that have gone down to the last play of the game such as Super Bowl 34 between St Louis and Tennessee, while others have been blowouts like Super Bowl 20 between Chicago and New England.   What does it really take to win a Super Bowl?  During this activity you will explore the statistics behind winning and losing the game.  You will also be asked to make predictions and explain your data.
Procedure
1. Using the Excel document as your data source, enter the scores of the winning and losing teams into your calculator.  The winning teams’ scores will be entered into L1 and the losing teams’ scores should be entered in L2.  You should check to make sure that your data was entered correctly and check that you have 48 entries for both L1 and L2.
2. Determine the average score for the winners and the average score for the losers.  All scores should be rounded to the nearest integer.
Winner's Average: 30
Loser's Average: 16

3. Create a box and whisker chart for both the winners’ and losers’ scores.  How do the median scores compare?  Remember, in order to construct a box and whisker chart, you will need to find the minimum, median, maximum and the 1st and 3rd quartiles.  Make sure that the scales are accurate.

Winners: Minimum: 14 Losers: Minimum: 3
Median:  30.5                                         Median: 16.5
Maximum: 55                                           Maximum: 31
1st Quartile: 23                              1st Quartile: 10
3rd Quartile: 35                                        3rd Quartile: 20.5
The median score of the winners was almost twice as much as the loser's median score.

1. Compare the Standard Deviations between the winning and losing scores.  How are they similar?  How are they different?  What do they mean? The Loser's Standard Deviation was 6.8, and the Winner's Standard Deviation was 9.8.  Since the median of the winner is nearly twice the number of the loser's median, the same can be said about the standard deviation. Around 65% of the loser's scores are between 9.3 and 22.8, while for the winners, 65% of the scores are between 20.2 and 39.8. This is a logical outcome, because the larger the range of scores, the larger the standard deviation is.

1. Could there be a correlation between the Super Bowl number and the score of the game?  Calculate the linear regression between the Super Bowl number and the winning score.  What is the correlation coefficient?  What does that tell us?  Passing numbers have increased over the past few years due to changes in rules.  Has there been an increase in scores over the past few games?  How did you come to that conclusion? There is little to no correlation between the Super Bowl number and score of the game. This is because the correlation coefficient of the winners and the number of Super Bowls is .19. If the  correlation coefficient is below .25, it means it has weak correlation. In my personal opinion, there could be a chance that the scores are improving over time as the players learn new strategies and ways to play the game.

2. Calculate the linear regression between the winning team and the losing team.  What does the correlation coefficient tell us?  Based on your model, if the winning team scores 35 points, how many points will the losing team score?  If the losing team scores 12 points, how many will the winning team score? The correlation coefficient of the losers and winners is .21, which is below .25. This means there little to no correlation between the winning and losing score. However, they are more closely linked that the winning score and Super Bowl number. We know that if the winning team scores 35 points, the losing team will score 16 points. If the losing score scores 12 points, the winning scores 13.