Our picture on this page shows the plotted data, with the Canadian-American exchange rate on the Y-axis and oil prices on the X-axis. We can clearly see a positive relationship between the two sets of data, though it is not a perfect linear one, as shown by the many points which are off of the line of best fit.
We have modelled the relationship between oil prices and the Canadian-American exchange rate as a linear one, and run a linear regression to achieve a line of best fit. There are a couple of important statistics generated by this.
The first important statistic is the R2, known as the "R-squared". The Glossary of Economics Terms defines R-squared as:
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R-squared is usually written R2. Is the square of the correlation coefficient between the dependent variable and the estimate of it produced by the regressors, or equivalently defined as the ratio of regression variance to total variance.
Secondly, we've estimated the following linear relationship between the exchange rate and oil prices:
y = 0.54 + 0.005x
Since the exchange rate is on the y axis and oil prices are on the x axis, this gives us the relationship:
Exchange Rate = 0.54 + 0.005 Oil Prices
We can interpret the two numerical figures as follows:
0.54 is the Y-intercept. In this case it is the value of the Canadian-American exchange rate if X (oil prices) goes to 0.
0.005 indicates the relationship between changes in oil prices and changes in the exchange rate. Here it means that whenever oil prices go up a dollar, the Canadian dollar gains half a cent on the U.S. one.
There's all kinds of useful information we can gather from this data. We can find out when the Canadian dollar will be equal to the U.S. dollar, if we believe this relationship is to continue into the future. We simply substitute "$1.00" into the value for the exchange rate then re-arrange:
1.00 = 0.54 + 0.005 Oil Prices
0.46 = 0.005 Oil Prices
Oil Prices = $92
Thus if we believe this trend to continue then the Canadian dollar will hit "par" when oil reaches $92 a barrel. I've heard from economic analysts who have far more sophisticated models that par should be achieved when oil reaches around $100 a barrel, which is quite close to the results in our simple statistical model.
By gathering publicly available data, we've been able to confirm a fact that has been in the news quite a bit recently - the fact that the Canadian dollar and oil prices are moving in tandem. If you were doing this as an econometrics project, you would likely want to go further than we have here. You could see if this relationship holds for other periods, such as during the oil crisis of the 1970s. Has there always been this 0.005 relationship between oil prices and the Canadian dollar? Do other factors, such as interest rates and inflation also impact the Canadian dollar?
If you have a question or an idea for an econometrics project feel free to send it to me using the feedback form.
