Final Project
Introduction
In this paper we will describe and demonstrate the application of statistics and probability theory to a real world problem. Our goal is to examine the relationship between historical gold and crude oil prices. In order to do this, we access the historical data of oil and gold prices on a yearly basis and use statistical tools to examine the data. We start from descriptive statistics and scatterplot and then perform correlation and regression analysis to find out the relationship between the two given prices. The summary of the project is given in conclusion section.
There is a relationship between commodity resources and gold. For example, if we look at the long-term chart of oil in gold prices, we find that their relationship was much more constant and unchanging than prices in fiat currencies. In 1965, gold was $ 35 per ounce and oil was $ 2.90 per barrel. In other words, a barrel of oil was 0.083 ounces of gold. In 2013, gold was $ 1,250, while oil price was $ 95. Hence, a barrel of oil was worth 0.076 ounces. However, the crude oil price varies greatly. Before the world financial crisis of 2008, oil reached a peak of $ 140 per barrel, and then by the end of the year it fell to $ 40 or 0.14 to 0.05 ounces in gold terms. It shows that there is no great accuracy in this relationship. As we know, during 2015 the price of oil fell again and reached a value of less than $ 30 per barrel. However, the price of gold has also lowered recently. In this regard, it is important to analyze the relationship between oil and gold prices over a long period of time. We want to find the answer on the following research question: “Is there a relationship between gold and oil prices?”
Methodology
In order to make analysis, we have accessed the data of oil and gold prices from 1946 to 2014 on a yearly basis. The data was retrieved from Inflationdata.com. The nominal values of oil prices and gold prices are given in the table below:
We analyze using the following statistical tools: descriptive statistics, frequency histograms, scatterplots and correlation analysis. Descriptive statistics is the most common technique of numerical data analysis. With the use of descriptive statistics we can evaluate random values that are calculated and collected in the data set. Frequency histogram is used to examine the shape of the frequency distribution. If the form of histogram is bell-shaped, then variable is approximately normally distributed. If the histogram is skewed, then the sample variable is not retrieved from a normally distributed population. Scatterplot visually represents the association between two variables. It shows the overall trend and characteristic of the relationship. Finally, correlation and regression analysis is a statistic tool of analytical examination of the relationship between the variables.
Analysis of the data
We begin with descriptive statistics. The basic indicators are given below in the table:
The average oil price during 1946-2014 was $21.60 per barrel with a standard deviation of $25.04 per barrel. The middle value of prices is median value - it is reported at the level of $14.87. The lowest price was $1.63 and the highest price was $95.2.
The average gold price during 1946-2014 was $322.49 per ounce with a standard deviation of $380.88 per ounce. The middle value of prices is median value - it is reported at the level of $278.98. The lowest price was $31.69 and the highest price was $1,668.98.
Since median and mean values are significantly different, the distributions of variables are skewed. Moreover, standard deviations are relatively high, compared to the mean values of the variables. This means that oil and gold prices significantly vary over the time period we consider.
Frequency histograms indicate that both variables are significantly skewed to the right. This means that the data is not normally distributed and we cannot use Pearson’s correlation coefficient and linear regression analysis. However, we assume the data is normal and proceed with regression analysis. The relationship between the prices of gold by oil is visualized on the following scatterplot:
It seems that there is a positive association between the data variables. The association was extremely strong when the price of oil was lower than $40 per barrel. The relationship between the variables, when oil price is above $40 is not that strong.
In order to describe the relationship, we use regression analysis. The following equation represents the linear relationship between gold price (Y) and oil price (X):
Y = 14.374X + 12.051
Conclusions and Implications
In this paper we have examined the association between gold and oil prices. It is appeared that the gold and oil prices are significantly associated. There is a strong linear positive relationship between the variables. We have developed a simple regression model to make a forecast of the gold price by the given oil price and verse versa.
Works Cited
"Comparing Oil vs. Gold." InflationData.com. Web. 06 Feb. 2016. (http://inflationdata.com/articles/comparing-oil-gold/)
