Tuesday, March 31, 2015

SuperBowl Blog

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 score: 30
Loser’s average score: 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. Samuel Lashlee updated January 21, 2013 Page 1Super Bowl History.

Losing Team:
Median: 16.5
Minimum: 3
Maximum: 31
Q1: 10
Q3: 20.5

Winning Team:
Median:  30.5
Minimum: 14
Maximum: 55
Q1: 23
Q3: 35

Screen Shot 2015-03-31 at 11.01.19 AM.png

The losing team’s median score is lower than the winning team’s, and as you can see, it’s also almost double the amount.

4. Compare the Standard Deviations between the winning and losing scores.  How are they similar?  How are they different?  What do they mean?

Winning Standard Deviation: 9.8
Losing standard Deviation: 6.8

Standard Deviation is a measure that is used to quantify the amount of variation of a set of data values according to Google. Not only that, but a standard deviation close to 0 shows that the points tend to be very close to the mean. Due to that, you can see that the winning deviation has a wide variety of different scores. They both don’t have an outlier, and they are different since the loser’s scores are less spread out than the scores from the winning team’s.

5. 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 can be a correlation between the Super Bowl number and the score of the game. The linear regression equation is y = ax + b. From using the calculator, the a would be replaced as 0.2 (correlation coefficient) and the b as 11.2 (y = 0.2x + 11.2). This tells us that there is an increase in scores over the past few games since the slope is positive.

6. 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?

y = 0.15x + 11.21

The linear regression would be y = 0.2x + 11.21. The correlation coefficient tells us which direction it moves, so the positive relationship means that the two variables move into the same direction. Based on my equation, if the winning team scores 35 points, the losing team’s score would be 16.46. Not only that, but if they losing team scores 12 points, then the winning team will score 13.01 points.

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