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IB Math AA SL IA on Multiple Linear Regression CA$6.15   Add to cart
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IB Math AA SL IA on Multiple Linear Regression

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  • Course
  • Math AA SL
  • Institution
  • Sixth Year / 12th Grade

This Math AA IA is trying to look into "Multiple Regression Analysis between Crude Oil Price and Geopolitics" as its subject of investigation. This IA has scored full marks in the 2021 year's session

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Document information

  • July 24, 2023
  • 27
  • 2022/2023
  • Exam (elaborations)
  • Questions & answers

Subjects

  • mathematics
  • math aa sl
  • applications and analysis
  • multiple regression
  • regression
  • prediction
  • statistics
  • math ia
  • ib
  • ia

Written for

  • Secondary school
  • Math AA SL
  • 5
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Mathematics Analysis and Approach Standard Level Internal Assessment:

Multiple Regression Analysis between Crude Oil Price and Geopolitics

Introduction

7 years ago, my native country Ukraine engaged in war. Before we used to keep away from

politics, however when geopolitical events affect you personally, it is hard to be apolitical.

Since then, I have developed a big interest in international relations, especially conflicts and

economics, and hope to pursue it in my future. Throughout IB I explored this area, and once

stumbled upon an article about how Geopolitical Tensions influence Oil Prices. While

reading the article, it was hard for me to comprehend that such things as terrorism can

influence Oil Prices. Therefore, I started to wonder What is the level of relationship between

Geopolitical Tension and Crude Oil Price, and how can we estimate future oil prices’ shifts

depending on geopolitical factors? Since Oil is the most important source of energy, it is

crucial to know what factors affect its price change. I want to know how the sphere of my

interest – geopolitics – can influence the economy of Oil. The use of mathematics through

Multiple Linear Regression plays a pivotal role in understanding the relationship and project

possible oil changes.

Background information

Crude Oil Prices and influential factors

Crude Oil has been the most essential commodity in the world during the last half-century, as

the majority of our energy comes from the oil supply. Its production, storage, import, and

export create a multi-trillion-dollar industry. However, the prices of Crude Oil are a

complicated puzzle that is influenced by multiple factors. In this exploration, I am focusing

on geopolitical factors - Number of Terrorist Attacks Worldwide and OPEC’s Oil Production

,in Barrels. OPEC is a major oil-related intergovernmental organization, as its members own

the biggest amount of oil (in barrels) in the world.1

Historically, the relationship between geopolitics and fuel prices is a sensitive one and, it is

based on principles of supply and demand. As some of the biggest oil-producing countries

suffer from high political instability, the oil market is threatened by the rising number of

terrorist attacks that change physical supply or the sheer threat of production instability which

decreases demand. These geopolitical metrics thus allow capturing hidden structure in the

dynamics of the Crude Oil market.2

Econometrics

To understand the relationship between the oil market and geopolitical changes and to

explain consistently occurring correlation, econometrics is used. In general, the application of

econometrics serves to develop theories or test existing hypotheses and forecast future trends

from historical data in economics. It is useful for the investigation as it subjects real-world

data, as well as provides models to analyze the complex relationship between many variables.

This exploration will rely on multiple regression analysis techniques and null-hypothesis

testing. 3

Multiple Linear Regression

In statistics, linear regression is a model of a relationship between one independent variable

and a dependent variable. However, in reality, multiple factors predict the outcome of an

1
Mostert, Wolfgang. “Factors Influencing the International Price of Oil in the Medium to Long-Term.”
Mostert.dk. Accessed January 15, 2021. https://mostert.dk/pdf/Factors%20influencing%20price%20of
%20oil.pdf.


Niemi, Jaradd. “T-Distribution Critical Value.” Accessed March 19, 2021.
https://www.jarad.me/courses/stat226/tables/t-table.pdf.

2
Bariviera, Aurelio. “Crude Oil Market and Geopolitical Events: an Analysis Based on Information-Theory-
Based Quantifiers.” Https://Arxiv.org/. Accessed January 5, 2021. https://arxiv.org/pdf/1704.04442.pdf.

3
Hayes, Adam. “Econometrics: What It Means, and How It's Used.” Investopedia. Investopedia,
December 14, 2020. https://www.investopedia.com/terms/e/econometrics.asp.

,event. A dependent variable is rarely explained by only one independent variable. The crude

oil price depends on more than just the amount of oil produced or just the demand for it. To

assess the strength of a relationship, in which more than two independent variables are

present, which is often the case in social science, multiple linear regression is used. In causal

analysis, it also separates the effects of independent variables on the dependent variable so

that you can examine the unique contribution of each variable. The model assumes that there

are no major correlations between the independent variables, and often the effect of other

predictors statistically eliminated.

The formula for predicting the value of a dependent variable by multiple independent

variables:4

y=β 0 + β 1∗x 1 + β 2∗x 2+ … β p∗x p+ ϵ where,

y=dependent variable

x=independent variables

β 0= y −intercept (constant term)

β p=slope coefficients for each ∈dependent variable

ϵ=themodel ’ s error t erm(residuals)

Aim of Exploration

The study aims to “Detect whether two independent variables (Number of Terrorist Attacks

Worldwide and OPEC’ Oil Production in barrels) affect the dependent variable (Price of

Crude Oil), to estimate the magnitude of this effect, if any, and to create forecast formula

through Multiple Regression Analysis”.

Results Expected




4
Bevans, Rebecca. “Multiple Linear Regression: A Quick and Simple Guide.” Scribbr, October 26, 2020.
https://www.scribbr.com/statistics/multiple-linear-regression/.

, Moderate correlation between the independent variables and the dependent variable is

expected, as the variables are produced by human-behavior. In the exploration, independent

variables are Number of Terrorist Attacks ( x 1 ¿ and OPEC’s Oil Production in barrels ( x 2 ¿ ,

the dependent variable is Price of Crude oil ( y ) .

Alternative hypothesis (H A ) anticipated to be accepted.

H 0 :there is no relationship between the independent variables∧thedependent variable ( y ) ,

¿ the independent variables should not remain∈themodel .

H A :there is a significant relationship between theindependent variables ( x 1 , x 2 )∧the

dependent variable ( y ) ,∧theindependent variables should remain∈the model .

Raw Data

To conduct the multiple regression analysis, quantitative data for the two independent

variables ¿ ¿) number of terrorist attacks worldwide5 and number of barrels of crude oil

produced by OPEC between 1989-20196, and data for dependent variable ( y ¿Price of Crude

between 1989-20197 was found. In total, every variable includes 30 independently selected

observations that can be observed in Table 1. First 10 observations are presented below.



Table 1. Data on number of terrorist attacks worldwide ( x 1 ¿ ; OPEC’s production of oil barrels ( x ¿ ¿ 2 and Price of Crude

Oil ( y ) between 1989-2019



Raw Data (sample)

Year Number of Terrorist OPEC’s Crude Oil Price of Crude Oil addjusted


5
Hayes, Adam. “How Multiple Linear Regression Works.” Investopedia. Investopedia, March 17, 2021.
https://www.investopedia.com/terms/m/mlr.asp.

6
Global Terrorism Database. “Terrorism. Number of Terrorist Attacks, 1970-2019.” Accessed March 13,
2021. https://ourworldindata.org/terrorism.

7
Sönichsen, N. “OPEC's Crude Oil Production in Barrels from 1989 to 2019.” Accessed March 10, 2020.
https://www.statista.com/statistics/292590/global-crude-oil-production-opec-share/.

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