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Oil: A Statistical Analysis of West Texas Intermediate and Brent

Crude

Adam Jarolimek | Joseph Lorusso | Thomas Walsh Philip Yudin

Financial Markets & Instruments Professor Goldstein 12/9/13

“The authors of this paper hereby give permission to Professor Michael Goldstein to distribute this

paper by hard copy, to put it on reserve at Horn Library at Babson College, or to post a PDF

version of this paper on the internet.”

“I pledge my honor that I have neither received nor provided any unauthorized assistance during

the completion of this work.”

Phil Yudin Joseph Lorusso Thomas Walsh Adam Jarolimek

_____________________________________________________________________________________

1

Table of Contents

Executive Summary 3

Overview 4

Determinants of Price 5

United States Petroleum Reserves 5

NYMEX Natural Gas Price 6

Treasury Note 6

LIBOR 6

S&P500 7

USD/GBP Exchange Rate 7

OPEC Oil Production 8

Analysis of Spot Prices of WTI and BRENT 8

Hypotheses 8

Hypotheses Testing Methods 9

R-Squared 11

P-Value of Coefficients 11

Predictions Using Regression Models 12

Conclusion 15

References 16

Regression Data 17

2

Executive Summary:

Crude oil is one of the most fundamental and influential commodities in modern society. At home

and abroad, it is the underlying fuel for the vast majority of anything that requires power, and for this

reason, its geopolitical importance is unparalleled. With advances in refining and fracking techniques, and

the ever-increasing usage of natural gas in conjunction with it, crude oil will continue to be the primary

driver of the energy market for the foreseeable future.

By examining the effects of various industrial, economic and financial factors related to the

industry, this paper will deliver an implicit as well as statistical analysis of price movement within two of

the biggest oil extraction pricing benchmarks, the Brent Crude and the West Texas Intermediate. The

paper will give an overview of the industry and the role of the WTI and Brent within it and will identify a

cross-section of factors that are involved in the day-to-day valuation and trading of the different

benchmarks. The paper will inspect and break down what each individual factor is and its importance to

the industry. By exposing how each factor acts in relation to the others and to the benchmarks, their

importance and functionality within the larger context of the oil industry can be observed. After the

factors are analyzed, they will be quantified and used in a regression attempting to establish a relationship

between the two benchmarks and their underlying factors. By observing and manipulating the data

outputs, the paper will show a model that predicts the prices of each benchmark as a function of the

different variables.

The examination of the two benchmarks from a holistic as well as quantitative standpoint will

provide a much larger breadth of information than basic research could. The paper hopes to give readers

not only an understanding of the primary American and European oil pricing benchmarks, but an

understanding of how they react to vibrations in other industries and entities throughout the global

economy.

3

Overview of the Oil Market

Brent Crude and the West Texas Intermediate are two types of oil that serve as benchmarks in

current oil pricing. Both are considered “sweet” oils, a term which is derived from the percentage of

sulfur in the fuel. A value below 0.5% signals that the oil is “sweet”, while any greater than 0.5%

indicates that the oil is “sour”. Sour and sweet oils are both useful, however users of oil prefer sweet oil

because it takes moderately less refining in order to remove the impurities.1 Each oil commodity varies in

price based on a plethora of different factors that include the state of the global economy, geopolitical

tensions, emerging market demand, and price of substitutes.

Brent Crude comes from a variety of drilling sites in the North Sea in Europe and is the primary

global price benchmark for crude oils.2 This crude oil had its name derived from the a shared project

between ExxonMobil and Royal Dutch Shell that named each of the drilling locations after birds, with

this specific project named after the Brent goose. Brent is also an acronym for the different layers of an

1 "What Is Brent Oil?" Commodity HQ. 2 "Brent vs. WTI." Energy and Capital.

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WTI vs. Brent Spot Price

Cushing, OK WTI Spot Price FOB Europe Brent Spot Price FOB (Dollars per Barrel)

4

oil field. Brent is used to price a majority of the global crude oil supply market.3 This commodity trades

on the InterContinental Exchange, or ICE, as well as the New York Mercantile Exchange. West Texas

Intermediate is a crude oil that is sourced mainly from the Permian Basin in West Texas. It also trades on

the InterContinental Exchange and the New York Mercantile Exchange.

Currently, the two crude oils are the basis for a comparison known simply as the Brent – WTI

Spread, which indicates the difference in price between equal volumes of the two commodity prices. This

information is important to energy traders and is a useful piece of information as an indicator of current

financial performance for each respective market.4 At the time of writing, WTI Crude Oil is trading at

$97.65 per barrel and Brent Crude Oil is trading at $111.61. 5 The reasons for the difference in these

prices will be further examined in a later section of this report, but first it will be important to understand

the different factors that influence each commodity’s price.

Determinants of Price

United States Petroleum Reserves

The existing inventory of crude oil in the United States is a major determinant in the current

commodity price. The United States maintains a Strategic Petroleum Reserve that has a capacity of 727

million barrels and inventory of almost 700 million barrels at the end of 2012.6 This reserve affects the

price of oil based on the availability of oil, as a sudden release of thirty million barrels would inflate the

supply of crude oil and could devalue it, or conversely a large purchase of oil to add to the reserves could

decrease the price of the oil. The likelihood of the government to make a purchase is the firm basis for

consumer speculation, thereby causing the futures market for crude oil to sometimes shift unexpectedly in

addition to the spot price for each commodity.

3 "What Is Brent Oil?" Commodity HQ. 4 Why the WTI Vs. Brent Crude Spread Is Shrinking." Minyanville. 5 "Crude Oil Price Forecast." OilPricenet. 6 "How Crude Oil Inventories Impact The Market." Energy Select Sector SPDR (ETF)

5

NYMEX Natural Gas Price

Natural Gas prices can be directly linked to the price of oil commodities, particularly in Europe

due to the proximity of the Brent mining fields. Some analysts argue that Natural Gas is now more closely

following the pricing of Coal, however the widely accepted opinion is that the entire energy market has

some correlation that can be analyzed statistically.7 Natural Gas is arguably one of the primary substitutes

for oil and therefore it can be expected that if the price of Natural Gas commodities changes, the price for

other energy alternatives would be affected in turn, either inversely or directly.

Treasury Note

Treasury Notes are debt instruments backed by the United States government. These instruments

are sold on auction, meaning that the value of the note is derived from overall perception of the market

and faith in the United States government. The 10 Year Treasury note specifically is a factor that can

influence the spread of West Texas Intermediate to Brent Crude because of the geographic location of

these commodities.8 Brent is based out of the North Sea while WTI comes from the Permian Basin in

Texas, meaning that tension or conflict in the United States that influences the Treasury Note could also

be a factor that impacts the ability for consumers to import or export crude oil, thereby affecting the price

of the oil due to a change in the supply or demand thereof, though the magnitude of such a shift will need

to be evaluated through statistical analysis.

LIBOR

LIBOR, or the London Interbank Offered Rate, is a calculated average interest rate that reflects

how much interest the primary banks in London would be charged for borrowing from other banks.

LIBOR is currently calculated for ten different currencies and fifteen time periods with the shortest being

an overnight rate and the longest being a one year rate. This rate is a large determinant in borrowing

7 Farzad, Roben. "High Oil Prices Cut The Cost Of Natural Gas." BusinessWeek. 8 "What Are Treasury Bills, Notes and Bonds?" US Economy.

6

activity and has a large effect on various financial markets.9 It does not directly interact with the oil

commodities, but a large enough change in LIBOR could create a financial ripple effect that is ultimately

felt by the crude oil market due to the nature of lending and borrowing.

S&P 500

Standard and Poor’s 500 is an index that is calculated using information from 500 publicly traded

company stocks that is chosen specifically for market size, liquidity, and industry grouping. The intent of

the index is to demonstrate the risk and return of the United States equity environment and the index

components are weighted based on each firm’s market capitalization. This index likely has a correlation

with the price of oil commodities due to the fact that it is a representation of the current economic

situation within the United States.10 Some analysts choose S&P as a more valid representation as opposed

to the Dow Jones because of the difference in number of firms considered, and therefore the spot price for

oil, which is based on how much a consumer would be willing to pay for a barrel of oil at the current

moment, would fluctuate directly with a shift in S&P 500 because of the better economic situation.

United States Dollar to British Pound Sterling Exchange Rate

As the value of the dollar changes in the global environment, there are rippling effects throughout

the economic system that are tied directly to oil. Specifically, due to the fact that many currencies tie their

value to the value of the United States Dollar, studies have found that the effect of increasing oil prices

are not felt quite as dramatically internationally as they are felt domestically, with the example of WTI

price tripling in the United States while only doubling in countries such as Britain.11 Due to these linkages

across geographic boundaries, the expectation is that a stronger dollar will cause a narrowing of the Brent

to West Texas Intermediate spread based on the increased price of each barrel internationally.

9 "Back to Basics: What Is LIBOR?" Finance & Development. 10 "Standard & Poor's 500 Index” Investopedia. 11 Oil and Gas Prices: The Exchange Rate Impact. Rep. KPMG.

7

OPEC Crude Oil Production

OPEC, or the Organization of Petroleum Exporting Countries, is an association of middle-eastern

countries that has unified to ensure stability of the oil markets as well as a steady supply of oil to

consumers.12 The price of the West Texas Intermediate and Brent Crude depends greatly on the

production levels of OPEC due to the microeconomic principle of supply and demand. OPEC regulates its

member countries and has attempted to keep the price and market stables, however if this mission

changes, WTI and Brent will see their respective spot rate fall as consumers have more options in the

crude oil market, despite the “sour” or sulfurous nature of these oils.

Analysis of the Spot Prices of WTI and Brent Crude Oil Hypotheses: WTI Hypothesis:

H1. US Total Petroleum stocks have a positive relationship with price H2. Natural Gas Price has a positive relationship with price H3. 10 YR T-Bill Rate has a positive relationship with price H4. LIBOR 1 Month Rate has a positive relationship with price H5. S&P500 Index level has a negative relationship with price H6. USD/GBP exchange rate has a positive relationship with price H7. OPEC Production has a negative relationship with price

BRENT Hypothesis:

H1. European Total Petroleum stocks have a positive relationship with price H2. Natural Gas Price has a positive relationship with price H3. 10 YR T-Bill Rate has a positive relationship with price H4. LIBOR 1 Month Rate has a positive relationship with price H5. FTSE100 Index level has an negative relationship with price H6. USD/GBP exchange rate has a positive relationship with price H7. OPEC Production has a negative relationship with price

12 "Our Mission." OPEC

8

Hypotheses Testing Methods

First, multiple regression analysis was performed to test the correlation between the spot

price of WTI Crude Oil and the seven explanatory variables listed below. Then, a similar

multiple regression was performed to test the correlation between the spot price of Brent Crude

Oil. Two variables were exclusive to each regression: Total U.S. Petroleum stocks (millions of

barrels) and the S&P500 Index for the WTI regression and Total European Petroleum stocks

(millions of barrels) and the FTSE 100 Index for the Brent regression. The other five

explanatory variables were used in both regressions. These two analyses were run based on

monthly data from April, 1990 to June 2013, resulting in 279 data points.

A log linear regression was also performed on this data series in order to examine a

possible difference in data distribution. In order to run such a regression, the natural log of each

data point is taken and then a regression is performed. Not all data is in a standard distribution,

commonly seen as a bell curve, and if data is in a Poisson distribution, a log linear regression

may produce more accurate results. The resulting regression model explains the variation in the

natural log of the dependent variable based on the natural logs of the independent variables. Each

coefficient in a log-linear regression represents the elasticity of the price of oil with respect to its

corresponding variable. So for example, a 1% increase in X1 will result in a “α1” percent change

in price.

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The two linear regression models used are as follows: Ywti=α0 +α1wti X1wti +α2 X2+α3 X3 +α4 X4 +α5 X5wti+ α6 X6 + α7 X7 + êi

• Ywti = Spot Prices of WTI Crude Oil • X1wti = U.S. Total Petroleum Stocks, Millions of barrels • X2= NYMEX Natural Gas Price in U.S. Dollars • X3 = 10-Year Treasury Note Rate • X4= LIBOR 1 Month Rate • X5wti = S&P500 Index • X6= U.S. Dollars per Pound Sterling • X7= OPEC Crude Oil production, thousands of barrels per day • α 0= differential effects of factors other than these seven factors • α1wti= differential effect of U.S. Total Petroleum Stocks, Millions of barrels • α2= differential effect of the NYMEX Natural Gas Price in U.S. Dollars • α3= differential effect of the 10-Year Treasury Note Rate • α4= differential effect of LIBOR 1 Month Rate • α5wti= differential effect of the S&P500 Index • α6= differential effect of U.S. Dollars per British Pound Sterling • α7= differential effect of OPEC Crude Oil production, thousands of barrels per day

YBrent=α0 +α1Brent X1Brent +α2 X2+α3 X3 +α4 X4 +α5 X5Brent+ α6 X6 + α7 X7 + êi

• YBrent = Spot Prices of Brent Crude Oil • X1Brent= Total European Petroleum stocks, millions of barrels • X2= NYMEX Natural Gas Price in U.S. Dollars • X3 = 10-Year Treasury Note Rate • X4= LIBOR 1 Month Rate • X5Brent = FTSE 100 Index • X6= U.S. Dollars per Pound Sterling • X7= OPEC Crude Oil production, thousands of barrels per day • α 0= differential effects of factors other than these seven factors • α1Brent= differential effect of Total European Petroleum stocks, millions of barrels • α2= differential effect of the NYMEX Natural Gas Price in U.S. Dollars • α3= differential effect of the 10-Year Treasury Note Rate • α4= differential effect of LIBOR 1 Month Rate • α5Brent= differential effect of the FTSE 100 Index • α6= differential effect of U.S. Dollars per Pound Sterling • α7= differential effect of OPEC Crude Oil production, thousands of barrels per day

The two log-linear regression models are as follows, with the same variables and data set: Ln(YWTI)=α0 +α1wti ln(X1wti) +α2 ln(X2)+α3 ln(X3 )+α4 ln( X4) +α5 ln(X5wti)+ α6 ln(X6) + α7 ln(X7) + êi

Ln(YBrent )=α0 +α1Brent ln(X1Brent) +α2 ln(X2)+α3 ln( X3) +α4 ln(X4) +α5 ln(X5Brent)+ α6 ln( X6) + α7 ln(X7) + êi

10

R-squared:

The “R Squared” value will be used to explain the percent of variation in the spot prices

by the explanatory variables. The R-squared values we discovered are 81.826% and 87.757%

for the WTI linear and the WTI log linear respective regressions (Exhibits 1 and 2). The R-

squared values were 72.804% and 82.703% for the Brent linear and log-linear respective

regressions (Exhibits 4 and 5). These percentages represent what proportion of the spot price (the

natural log of the spot price for the log linear regressions) can be explained by our explanatory

variables. The remaining percent cannot be significantly accounted for by our model as we left

out variables such as GDP, number of active rigs, and government policies. There are many

reasons we did not include these data points as they are either hard to measure, difficult to attain,

or not calculated frequently enough.

P-Value and Coefficients:

The p-value is a measure of a variable’s significance in a regression model. The variables

with p-values greater than .05 will be rejected based on our hypothesis, using a 95% confidence

interval. The coefficient output explains how the spot price will increase by the coefficient

amount if the variable that corresponds with that coefficient increases by 1. Our results show that

for Brent, the p values for the 10 Year Treasury rate, the OECD Petroleum stocks, and the

FTSE100 Level, .1268, .08465, and .357872 respectively, variables are greater than .05 so we

deem them statistically insignificant (Exhibit 4). When we ran the Brent log-linear regression the

OECD petroleum stocks became a lot less significant (Exhibit 5). For WTI, the NYMEX

Natural Gas Price, the 10Year Treasury rate, and the S&P500, with p-values of .138, .06, and .28

respectively, variables are greater than .05 so we deem them statistically insignificant (Exhibit

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1). When we ran the WTI log-linear regression we found that the NYMEX p-value became

statistically significant (Exhibit 2).

The 10 year rate is less significant than LIBOR because it is a long term rate and the

nature of these oil spot prices are more short term and coincide with the LIBOR rate. The market

levels are likely insignificant because oil price is more likely to affect market rates rather than

vice versa. The Natural Gas price proves to be insignificant likely to the current inability for

substitution. For Hypotheses H1- H7, we investigate the influence of the seven independent

variables. As expected, the U.S. Petroleum stocks and the USD/GBP exchange rate had a

statistically significant positive correlation with the spot prices of WTI and Brent. Unexpectedly,

the Libor rate had a statistically significant negative correlation with price, so as the Libor rate

increases, oil price seems to decrease. OPEC production unexpectedly had a significant positive

correlation with oil price. As OPEC production increased, the price under all four regressions

increased. This may be due to the fact that, as a cartel, OPEC works to keep oil prices high. So,

OPEC output and the worldwide price of oil are necessarily linked. As oil prices rise, OPEC

countries are allowed to produce more crude oil without depressing prices. The other variables

were deemed insignificant and went against our initial hypothesis. This might be because many

of these variables are affected by and dependent on oil price and not vice versa.

Prediction Using Regression Models With R-squared values of 81.826% for and 72.804% for WTI and Brent linear regression

models and 87.757% and 82.703% for the corresponding log-linear models, the correlation

between our explanatory variables and the actual spot prices seemed relatively high. However, in

order to further test the hypotheses, it is necessary to analyze the accuracy of each regression

model’s predictions. The four regression models were used to predict the spot price every month;

12

this value was then compared with the actual spot price of WTI and Brent crude oil. First, the

absolute value of the difference between the predicted and actual price is calculated; these values

are averaged to calculate the mean absolute error (MAE). Taking the absolute differences and

dividing them by the actual price results in the absolute percentage difference. The average of all

of the absolute percentage differences calculates the mean absolute percentage error (MAPE).

Finally, the last measure to compare our prediction is the root mean square error (RMSE), which

is the average of all the squared difference between the predicted and actual spot prices.

The analysis of the three measures of the predictions’ error shows that the regression

models were not as appropriate as the R-squared values suggest. The WTI and Brent linear

regressions had MAPEs of 32.22% and 44.85% respectively, indicating that the two models were

unable to adequately predict the spot price at a given time. The mean absolute error values

indicate that, on average, the predictions were off by 9.927079 and 13.04058 dollars for the WTI

and Brent regressions (exhibits 1 and 4). Again, this shows that the two linear regression models

are inaccurate at predicting crude oil spot price in either market. The log-linear models seem to

predict the natural log of the spot prices better than the linear models could predict the exact spot

prices. With mean absolute percentage errors of 5.76% and 6.81%, the WTI and Brent log-linear

regressions can somewhat accurately predict the natural log of the spot prices (exhibits 2 and 5).

However, these error values do not represent the accuracy of predicting the spot price, only the

logarithm of the spot price; thus, even average errors of 5.76% and 6.81% are relatively high for

predicting the natural log of the spot price. So, even with the aforementioned error variables, the

log-linear models could not be used to accurately predict WTI or Brent spot prices.

As was discovered by analyzing the linear regression models’ p-values, certain variables

were determined to be statistically insignificant to the price of WTI and Brent crude oil. So,

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another regression was performed after removing certain variables from the equation. Then, the

previously detailed methodology for analyzing the models’ predictions and error values was used

again to assess the accuracy of the ‘corrected’ models. For the new WTI linear regression, the

NYMEX natural gas price, ten-year U.S. Treasury note rate, and the S&P500 index were

removed from the model. For the new Brent linear regression, the ten-year U.S. Treasury note

rate, and the FTSE 100 index were removed from the model. Although the OECD European

petroleum stocks had a slightly high P-value of 0.085 for the first Brent linear regression, in the

‘corrected’ regression, it was statistically significant, so it was not removed from the regression

model. Unfortunately, the removal of statistically insignificant factors did not demonstrably

increase the accuracy of the two predictive regression models. With mean absolute percentage

errors of 32.52% and 45.20% respectively, the WTI and Brent linear regression models remain

extremely inaccurate at predicting the spot price of either crude oil type.

Table 1

Error Analysis

WTI Linear

Regression

WTI Log Linear

Regression

Brent Linear

Regression

Brent Log-

Linear Regression

‘Corrected’ WTI

Linear Regression

‘Corrected Brent Linear

Regression

MAE (Mean

Absolute Error)

9.927079 0.194161 13.04058 0.228052 9.893613 13.09084

MAPE (Mean

Absolute Percentage

Error)

32.22% 5.76% 44.85% 6.81% 32.52% 45.20%

RMSE (Root Mean

Square Error)

12.73707 0.246218 17.45641 0.296151 12.8981 17.55145

14

Conclusion:

We attempted to analyze the relationships between both the spot price of WTI Crude oil and a

group of variables and the spot price of Brent and a group of similar variables. We looked at the prices of

natural gas, the value of the 10-Year Treasury Note, the 1 month LIBOR rate, the exchange rates between

the dollar and the pound, and OPEC crude oil production in relation to both benchmarks, while WTI was

looked at in relation to U.S. oil stockpiles and the S&P 500 and the Brent was looked at in relation to

European oil stockpiles and the FTSE 100. Across the four main regressions run (2 linear and 2 log

linear), the R-squared values ranged from 72.8% to 87.75%. This suggests relatively high correlation

between our explanatory variables and the spot price of WTI and Brent. In particular, the 10-Year

Treasury and the respective stock indexes of the two regions were not statistically significant in

estimating to the spot prices of the two benchmarks. The other explanatory variables had a noticeable

impact in our regression models, especially the exchange rate between the dollar and pound and OPEC

production. Unfortunately, our attempts to use our regression models to predict the spot prices at a given

time were unsuccessful. This is most likely due to our failure to identify and include better determinants

of the spot price. Interestingly enough, while our R-squared values suggested a strong relationship

between the determinants and the price throughout the models, the lack of these other determinants

hindered the model’s ability to predict price with a high degree of accuracy. In future iterations of the

models, the addition of more variables will likely increase its predictive ability, as oil prices are affected

by both economic and geopolitical factors on a global scale.

15

References

"Back to Basics: What Is LIBOR?" Finance & Development. Web. 08 Dec. 2013.

"The Basics of Oil Investing: The WTI-Brent Spread." Investment U. Web. 08 Dec. 2013.

"Brent vs. WTI." Energy and Capital. Web. 08 Dec. 2013.

"Crude Oil Price Forecast." OilPricenet. Web. 07 Dec. 2013.

"Crude Oil Prices: Seven Driving Factors." Investment U. Web. 08 Dec. 2013.

Farzad, Roben. "High Oil Prices Cut The Cost Of Natural Gas." BusinessWeek. Web. 8 Dec. 2013.

"Flashpoint: Crude Oil Inventories and Price Reactions." TradeStation Labs. Web. 08 Dec. 2013.

"How Crude Oil Inventories Impact The Market." Energy Select Sector SPDR (ETF). Web. 08 Dec. 2013.

"How Does the Weak Dollar Affect Oil Prices?" Project Syndicate. Web. 08 Dec. 2013.

Macroeconomic Impact of the WCS/WTI/Brent Crude Oil Price Differentials. Rep. RBC Economics.

Web. 8 Dec. 2013.

Oil and Gas Prices: The Exchange Rate Impact. Rep. KPMG. Web. 8 Dec. 2013.

"Our Mission." OPEC. Web. 07 Dec. 2013.

"Standard & Poor's 500 Index” Investopedia. Web. 08 Dec. 2013.

"What Are Treasury Bills, Notes and Bonds?" US Economy. Web. 08 Dec. 2013.

"What Is Brent Oil?" Commodity HQ. Web. 08 Dec. 2013.

"Why the WTI Vs. Brent Crude Spread Is Shrinking." Minyanville. Web. 08 Dec. 2013.

Data Retrieved from www.eia.gov and Bloomberg Terminal Database

16

http://www.eia.gov/

Exhibits

Exhibit 1

WTI Linear Regression

Regression Statistics Multiple R 0.904575341 R Square 0.818256548 Adjusted R Square 0.813562068 Standard Error 12.92370556 Observations 279

ANOVA df SS MS F

Regression 7 203785.8931 29112.27044 174.3018382 Residual 271 45263.0068 167.0221653

Total 278 249048.8999

Coefficients

Standard Error t Stat P-value

Intercept -358.40218 29.07911 -12.32507 5.1963E-28 U.S. Total Petroleum Stocks, Millions of barrels 0.11414 0.01103 10.34775 2.29319E-21 NYMEX Natural Gas 0.73355 0.49328 1.48709 0.138154844 10-Year Treasury Note Rate 2.87157 1.51846 1.89111 0.059675913 LIBOR 1 Month Rate -3.50816 0.82235 -4.26601 2.75246E-05 S&P500 0.00415 0.00383 1.08148 0.280445385 USD/GBP 22.33105 6.31747 3.53481 0.000479704 OPEC Production (000s per day) 0.00604 0.00082 7.32224 2.78781E-12

Error Analysis MAE (Mean Absolute Error)

9.927078876

MAPE (Mean Absolute Percentage Error)

32.22% RMSE (Root Mean Square Error)

12.73707185

WTI Log-Linear Regression

Regression Statistics Multiple R 0.926049417 R Square 0.857567523 Adjusted R Square 0.853888455 Standard Error 0.249825724

17

Observations 279

ANOVA df SS MS F


Total 278 118.7502611

Coefficients


Intercept -36.40993 4.65877 -7.81536 1.2160E-13 U.S. Total Petroleum Stocks, Millions of barrels 2.20233 0.39238 5.61278 4.9192E-08 NYMEX Natural Gas 0.33669 0.04416 7.62489 4.1385E-13 10-Year Treasury Note Rate 0.07727 0.12002 0.64384 5.2023E-01 LIBOR 1 Month Rate -0.22258 0.03330 -6.68385 1.3213E-10 S&P500 -0.08344 0.06420 -1.29983 1.9477E-01 USD/GBP 1.31867 0.20401 6.46381 4.7285E-10 OPEC Production (000s per day) 2.27123 0.43773 5.18860 4.1573E-07


0.194161172



0.246217943

WTI Linear Regression, Corrected


ANOVA df SS MS F


Total 278 249048.8999

Coefficients


Intercept -331.47327 17.04627 -19.44551 1.6149E-53

18

U.S. Total Petroleum Stocks, Millions of barrels 0.10226 0.01011 10.11053 1.2513E-20 LIBOR 1 Month Rate -2.28844 0.45669 -5.01091 9.7289E-07 USD/GBP 28.84572 5.50795 5.23711 3.2545E-07 OPEC Production (000s per day) 0.00605 0.00038 15.98213 4.4615E-41


9.893612924



12.89809969

Brent Linear Regression


ANOVA df SS MS F


Total 278 312622.8615

Coefficients


Intercept -259.50997 49.77350 -5.21382 3.675E-07 OECD European Petroleum Stocks, Millions of barrels 0.05120 0.02958 1.73117 8.456E-02 NYMEX Natural Gas -2.05548 0.66855 -3.07455 2.323E-03 10-Year Treasury Note Rate -3.14979 2.05660 -1.53155 1.268E-01 LIBOR 1 Month Rate -3.08481 1.16893 -2.63900 8.796E-03 FTSE 100 Level -0.00134 0.00146 -0.92099 3.579E-01 US$/GBP 45.14746 8.65443 5.21669 3.624E-07 OPEC Production (000s per day) 0.00743 0.00112 6.62605 1.852E-10


13.04058051

19



17.45641321

Brent Log-Linear Regression


ANOVA df SS MS F


Total 278 141.4661188

Coefficients


Intercept -25.68808 6.59238 -3.89663 1.2297E-04 OECD European Petroleum Stocks, Millions of barrels 0.55136 0.67570 0.81599 4.1523E-01 NYMEX Natural Gas 0.24221 0.05284 4.58391 6.9740E-06 10-Year Treasury Note Rate -0.10259 0.14401 -0.71237 4.7685E-01 LIBOR 1 Month Rate -0.28766 0.03977 -7.23302 4.8462E-12 FTSE 100 Level -0.13156 0.10947 -1.20186 2.3047E-01 US$/GBP 1.90524 0.24550 7.76065 1.7318E-13 OPEC Production (000s per day) 2.49738 0.53635 4.65626 5.0481E-06


0.228052079



0.296150864

Brent Linear Regression, "Corrected"


20

ANOVA df SS MS F


Total 278 312622.8615

Coefficients


Intercept -296.03294 32.09852 -9.22263 8.17307E-18 OECD European Petroleum Stocks, Millions of barrels 0.05321 0.02675 1.98906 0.047692194 NYMEX Natural Gas -2.23029 0.65632 -3.39819 0.000779448 LIBOR 1 Month Rate -4.80131 0.58509 -8.20607 9.10407E-15 US$/GBP 45.87246 8.03525 5.70890 2.96166E-08 OPEC Production (000s per day) 0.00801 0.00072 11.16142 4.43836E-24


13.09084179



17.55144854

Exhibit 2

WTI Log-Linear Regression Regression Statistics Multiple R 0.926049417 R Square 0.857567523 Adjusted R Square 0.853888455 Standard Error 0.249825724 Observations 279

ANOVA

21

df SS MS F Regression 7 101.8363673 14.54805247 233.0937071 Residual 271 16.91389385 0.062412892

Total 278 118.7502611

Coefficients


Intercept -36.40993 4.65877 -7.81536 1.2160E-13 U.S. Total Petroleum Stocks, Millions of barrels 2.20233 0.39238 5.61278 4.9192E-08 NYMEX Natural Gas 0.33669 0.04416 7.62489 4.1385E-13 10-Year Treasury Note Rate 0.07727 0.12002 0.64384 5.2023E-01 LIBOR 1 Month Rate -0.22258 0.03330 -6.68385 1.3213E-10 S&P500 -0.08344 0.06420 -1.29983 1.9477E-01 USD/GBP 1.31867 0.20401 6.46381 4.7285E-10 OPEC Production (000s per day) 2.27123 0.43773 5.18860 4.1573E-07


0.194161172



0.246217943

Exhibit 3

WTI Linear Regression, Corrected Regression Statistics Multiple R 0.902015595 R Square 0.813632133 Adjusted R Square 0.810911434 Standard Error 13.01525105 Observations 279

ANOVA

22

df SS MS F Regression 4 202634.1877 50658.54692 299.0526321 Residual 274 46414.71221 169.3967599

Total 278 249048.8999

Coefficients Standard Error t Stat P-value Intercept -331.47327 17.04627 -19.44551 1.6149E-53 U.S. Total Petroleum Stocks, Millions of barrels 0.10226 0.01011 10.11053 1.2513E-20 LIBOR 1 Month Rate -2.28844 0.45669 -5.01091 9.7289E-07 USD/GBP 28.84572 5.50795 5.23711 3.2545E-07 OPEC Production (000s per day) 0.00605 0.00038 15.98213 4.4615E-41

Exhibit 4

Brent Linear Regression Regression Statistics Multiple R 0.853256834 R Square 0.728047224 Adjusted R Square 0.721022614 Standard Error 17.71219846 Observations 279

23

ANOVA df SS MS F


Total 278 312622.8615

Coefficients


Intercept -259.50997 49.77350 -5.21382 3.675E-07 OECD European Petroleum Stocks, Millions of barrels 0.05120 0.02958 1.73117 8.456E-02 NYMEX Natural Gas -2.05548 0.66855 -3.07455 2.323E-03 10-Year Treasury Note Rate -3.14979 2.05660 -1.53155 1.268E-01 LIBOR 1 Month Rate -3.08481 1.16893 -2.63900 8.796E-03 FTSE 100 Level -0.00134 0.00146 -0.92099 3.579E-01 US$/GBP 45.14746 8.65443 5.21669 3.624E-07 OPEC Production (000s per day) 0.00743 0.00112 6.62605 1.852E-10


13.04058051



17.45641321

Exhibit 5

Brent Log-Linear Regression Regression Statistics Multiple R 0.909410368 R Square 0.827027217 Adjusted R Square 0.822559285 Standard Error 0.300490302 Observations 279

24

ANOVA df SS MS F


Total 278 141.4661188

Coefficients


Intercept -25.68808 6.59238 -3.89663 1.2297E-04 OECD European Petroleum Stocks, Millions of barrels 0.55136 0.67570 0.81599 4.1523E-01 NYMEX Natural Gas 0.24221 0.05284 4.58391 6.9740E-06 10-Year Treasury Note Rate -0.10259 0.14401 -0.71237 4.7685E-01 LIBOR 1 Month Rate -0.28766 0.03977 -7.23302 4.8462E-12 FTSE 100 Level -0.13156 0.10947 -1.20186 2.3047E-01 US$/GBP 1.90524 0.24550 7.76065 1.7318E-13 OPEC Production (000s per day) 2.49738 0.53635 4.65626 5.0481E-06


0.228052079



0.296150864

Exhibit 6

Brent Linear Regression, "Corrected" Regression Statistics Multiple R 0.851515156 R Square 0.72507806 Adjusted R Square 0.72004286 Standard Error 17.74327335

25

Observations 279

ANOVA df SS MS F


Total 278 312622.8615

Coefficients


Intercept -296.03294 32.09852 -9.22263 8.17307E-18 OECD European Petroleum Stocks, Millions of barrels 0.05321 0.02675 1.98906 0.047692194 NYMEX Natural Gas -2.23029 0.65632 -3.39819 0.000779448 LIBOR 1 Month Rate -4.80131 0.58509 -8.20607 9.10407E-15 US$/GBP 45.87246 8.03525 5.70890 2.96166E-08 OPEC Production (000s per day) 0.00801 0.00072 11.16142 4.43836E-24


13.09084179



17.55144854

26

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