The Monthly Flocculation of Gasoline Prices

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The Monthly Flocculationof Gasoline PricesDoes time of year affect the price of gas?

12/19/2008IB Math StudiesSarah Beck


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A. Statement of Task

The American Automobile Association (AAA) gives a daily American nationalaverage of the fuel prices that are derived from credit card transactions from more

than 85,000 stations across the nation. Daily averages are able to inform the

consumer superficially in decisions of getting gas today or tomorrow. Daily averages

do not give the consumer a yearly outlook, which is the purpose of this

investigation. Monthly averages could help families and businesses save money

when they are planning a trip, thats price is affected by the price of gasoline.

I plan to take national gasoline daily averages from a 10 year period, 1998-

2007, from the Energy Information Administration which has the official energy

statistics from the US government. From these daily averages, I plan to make

monthly averages. With the monthly averages, I will create a scatter plot,containing a best fit line. Then, I will use the correlation coefficient to measure the

strength and the direction of a linear relationship between tw (U.S. Retail Gasoline

Prices, Regular Grade)o variables. I will also use the coefficient of determination

because it gives the proportion the variance (fluctuation) of one variable that is

predictable from the other variable. Using the slope of the best fit lines from the 12

months, I will compare them to the slope of the best fit line of all of the average gas

prices from 1998-2007 by their percentage differences. The comparison will show if

there is any correlation between gasoline and the month of year.

B. Data Collection

arJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Aver

ges

198

1.131

1.082

1.041

1.052

1.092

1.094

1.079

1.052

1.033

1.042

1.028

0.986

1.059

199

0.972

0.955

0.991

1.177

1.178

1.148

1.189

1.255

1.28 1.274

1.264

1.298

1.165

2

00

1.30

1

1.36

9

1.54

1

1.50

6

1.49

8

1.61

7

1.59

3

1.51 1.58

2

1.55

9

1.55

5

1.48

9

1

201

1.472

1.484

1.447

1.564

1.729

1.64 1.482

1.427

1.531

1.362

1.263

1.131

1.4

202

1.139

1.13 1.241

1.407

1.421

1.404

1.412

1.423

1.422

1.449

1.448

1.394

1.35

203

1.473

1.641

1.748

1.659

1.542

1.514

1.524

1.628

1.728

1.603

1.535

1.494

1.590

2 1.59 1.67 1.76 1.83 2.00 2.04 1.93 1.89 1.89 2.02 2.01 1.88 1.880


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Slope:

y = mx + b

Formula forlinear regression

(best fit line)

04 2 2 6 3 9 1 9 8 1 9 22

051.82

31.91

82.06

52.28

32.21

62.17

62.31

62.50

62.92

72.78

52.34

32.18

62.295

206

2.315

2.31 2.401

2.757

2.947

2.917

2.999

2.985

2.589

2.272

2.241

2.334

2.588

207

2.274

2.285

2.592

2.86 3.13 3.052

2.961

2.782

2.789

2.793

3.069

3.02 2.800

ta

v.

1.5492

1.5846

1.6833

1.8098

1.8762

1.8603

1.8494

1.8466

1.8772

1.8168

1.7756

1.7214

1.770

C. Analysis

This section contains a short review of the type of math used during the

analysis portion of this investigation. Also included are a few definitions in order to

demonstrate a clear and understandable experiment.

slope =m

=

n( xy) - ( x)(y)

n( x2) - ( x)2

intercept= b

=

y - m(x)

n

Here, means "the sum of." Therefore, I created a chart to organize my

variables. Below is an example of Januarys data.


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rms; therefore, n=101393454545 ? 0.139= .0.7828 ? 0.783

Key:

x as to the year

y as to the average monthly price

Therefore:

intercept= b

=

y - m(x)

n

Therefore the slope of the line is: y= 0.139x + 0.783

x y xy x2

1 1.131 1.131 12 0.972 1.944 4

3 1.301 3.903 9

4 1.472 5.888 16

5 1.139 5.695 256 1.473 8.838 36

7 1.592 11.144

49

8 1.823 14.584

64

9 2.315 20.835

81

10 2.274 22.74 100

5515.49

2

96.702

385

slope =m

=114.96

825

10(96.702) -(55)(15.492)=10(385) - (55)2

15.492 -0.139345454(55)=

10


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First, I pressed the STAT button.

t, I scrolled down to edit, then hit ENTER.

Once in edit, I entered my x variables into L1. I then scrolled over to L2 and entered my y vassed enter, I had my correlation coefficient (r) and coefficient of determination (r2) for the m

Then, I used my calculator to calculate the correlation coefficient and

coefficient of determination.


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X 100 = 13.4%1.770867 1.5492

Meaning, 1.5492 is 13.4% below 1.770867; therefore, -13

((1.770867 + 1.5492)/2)

I then used the percentage difference equation to figure each months average

to the 10 year average.

Graphs:


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Percentage Difference between the 10 Year Average and the 10 Year

MonthlyAverage

Month PercentageDifference

January -13.4%February -11.1%March -5%

April +2.17%

May +5.78%

June +4.93%July +4.34%

August +4.19%

September +5.83%October +2.56%

November +2.67%

December +2.83%

D. Evaluation

The mathematical applications applied to this experiment illustrated thatthere is some significant relation between the price of gasoline per gallon and the

time of year.

When looking at the percentage differences between the 10 year average

and the 10 year monthly average, it seems that there is a pattern to the price of

gas. For example, if we start from April, we can see a sharp increase of price in May,then a slow decrease that lasts through August. Then, prices shoot up again, and

then decrease steadily until March of the next year.

I have hypothesized about why gas prices seem to have this cycle of price

fluctuation, which can be seen below.

Month PercentageDifference

Possible Reason For Fluctuation

April +2.17% Price s possibly because spring break (generally occurs in April) isa large driving season.

May +5.78% Memorial day is a large driving holiday (approx 1/3 of Americans

travel to celebrate it). Increase of Demand=Increase in PriceJune +4.93% Price s from May, but is still relativity high, possibly because June

is the first month of Hurricane Season

July +4.34% Price s from June, but remains above 4%, possibly because Fourthof July is a large driving holiday.

August +4.19% Price s from July, but is still over 4%. This is possibly becauseAugust is one of (if not the last) month of summer for students i.e.

Last minute travel.

Septemb +5.83% Price s possibly because all schools are back by this time, meaning


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er that school busses are in operation for the first time since May. Theprice is high, but will adjust over time. Also, The first day of

September is Labor Day, which is a large driving day.

October +2.56% Price s from September, possibly because October does not haveany large vacation and travel days.

Novembe

r

+2.67% Price s possibly because families are traveling to other homes for

Thanksgiving. Therefore, with a larger demand, a larger price.Decembe

r+2.83% Price s possibly because families are traveling to other homes for

Christmas. Therefore, with a larger demand, a larger price.

January -13.4% Price s from December, possibly because people must pay backChristmas spending, therefore, cut back on gas.

February -11.1% Price s from January, possibly because there are not any significanttraveling holidays in February.

March -5% Price s from January, possibly because there are not any significanttraveling holidays in February.

My data in graphical form shows that year after year, there was a steady

increase in fuel prices per gallon. I also included the coefficient of determination (r2)in order to show how well the measure of the regression line represents the data.

Because all of my coefficients of determination follow this value: 0.75 r2 < 0.90;

there is a strong correlation between my data and the best fit line. Having a strong

correlation is good because it shows that there was only a small room for error in

the best fit line.

There were, although, places in my experiment in where I possibly could have

improved. For example, my gasoline averages do not factor in inflation. Therefore,

the percent change between the 10 year average and the 10 year monthly average

could have been lower. Also, the averages were very geographically general.

Different regions of the United States will have different gasoline price averages. If

one was planning a trip, it would be more beneficial or them to use the gasoline

price averages, specific to the region they are traveling to, or regions they are

traveling through.

E. Sources

Affairs, Bureau of Consular. Hurricane Season - Know Before You Go. 3 December

2008

.

U.S. Retail Gasoline Prices, Regular Grade. 3 November 2008

.

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The Monthly Flocculation of Gasoline Prices