Analysis of Fuel Prices and Relationships: Melbourne, Victoria

Task 2: Written Report
Question 1
There is an empirical observation that fuel prices in capital tends to be lesser than
elsewhere in the state. The objective is to ascertain if this is true for the sample data provided.
This implies that the task is to ascertain if the Unleaded 91 price in Melbourne (Capital City
of Victoria) on average is lower than elsewhere in the state on the given date i.e. August 22,
2018.
In order to ascertain the same, hypothesis testing has been performed which has
resulted in the following result obtained using Excel.
From the above output, the conclusion can be drawn that the claim regarding fuel
prices being lower in capital city is not true for Victoria on August 22, 2018 with regards to
Unleaded 91.
Question 2
The objective is to explore the relationship between Unleaded 91 prices and Diesel
prices based on the sample data. Since the fuel of choice is Unleaded 91, hence this serves as
the independent variable while the Diesel price serves as the dependent variable. The
requisite scatter plot is indicated as follows.

From the above scatter plot, it is evident that the line of best fit is upward sloping
which implies that the relationship between the two variables is positive. Also, considering
that the deviation of the scatter plots from the best fit is not very high, hence the strength of
relationship is moderately strong. This is also supported by the coefficient of correlation
which is close of 0.6. Besides, it is expected that the change in Unleaded 91 price by 1 cent
would bring about change in Diesel price by 0.712 cents in the state of Victoria on August
22, 2018.
Question 3
In this particular case, there is addition of one more independent variable in the form
of location which has not been included in the above analysis. As a result, the analysis in this
case would be through multiple regression line. This model has been derived from Excel and
illustrated below.

In the above regression model, while one independent variable (i.e. Unleaded 91) has
been found to be significant, the other independent variable (i.e. Location) does not have
statistical significance. As a result, this multiple regression model is inferior to the simple
regression model predicted using Unleaded 91 as the sole independent variable.