Analysis of Fuel Prices and Relationships: Melbourne, Victoria

In this assignment we will discuss about written report and below are the summaries point:- Fuel prices in the capital city of Victoria on August 22, 2018, were not lower than elsewhere in the state. There is a positive relationship between Unleaded 91 prices and Diesel prices in Victoria on that date. Adding the independent variable of location did not yield a statistically significant result in the multiple regression analysis.

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.

Task 1: Statistical Appendix
Question 1
With regards to this, since claim needs to be tested for the population based on the
sample data provided, hence inferential statistical technique of hypothesis testing has been
used. The requisite hypotheses for the test are listed below.
Null Hypothesis: The average Unleaded 91 price in Melbourne on August 22, 2019 is greater
than or equal to the corresponding average Unleaded 91 price in regional cities of Victoria
state.
Alternate Hypothesis: The average Unleaded 91 price in Melbourne on August 22, 2019 is
less the corresponding average Unleaded 91 price in regional cities of Victoria state.
The significance level has been chosen as 5%.
The relevant test statistic for the hypothesis test has been chosen as T and not Z as for the two
variables, the population standard deviation is unknown. Besides, the relevant statistical test
is two sample independent t test. Also, this would be a one tail test (left tail) based on the
alternate hypothesis. The requisite test output obtained from Excel is indicated below.
The p value approach has been used for the given testy. The one tail p value is 0.3392.
As the p value is greater than the significance level (0.05), hence the available evidence is not
sufficient to reject the null hypothesis. Hence, the alternate hypothesis would not be accepted.
Therefore, it can be concluded that average Unleaded 91 price in Melbourne on August 22,

2019 is greater than or equal to the corresponding average Unleaded 91 price in regional
cities of Victoria state.
Question 2
The requisite variables for the scatter plot are defined below.
Independent Variable – Unleaded 91 Prices in Victoria on August 22, 2018
Dependent Variable – Diesel Prices in Victoria on August 22, 2018
The required scatter plot is indicated below.
There is positive relationship between the two variables. This is supported by the
positive value of the correlation coefficient and also the positive slope of the trendline. The
correlation coefficient is 0.6 which implies that the relationship between the two variable is
moderately strong. The coefficient of determination or R2 is 0.358 which implies that 35.8%
of the variation in the diesel prices on August 22, 2018 in Victoria can be explained by
variation in Unleaded 91 prices on the same date in Victoria.
The requisite simple regression model is obtained using Excel and highlighted below.

The regression equation is indicated below.
Diesel prices (Cent per litre) = 44.876 + 0.713Unleaded 91 prices (Cent per litre)
The slope value is 0.713 which implies that an increase in unleaded 91 price by 1 cent
on August 22, 2018 in Victoria would have led to increase in diesel prices by 0.713 cent on
the same date. Further, the slope coefficient in this case is significant as the p value is 0.000
which is lower than the significance value (5% assumed).
Question 3
In this case, another independent variable in the form of location has been added and
hence the multiple regression model is appropriate which has been obtained from Excel.

The multiple regression equation is indicated below.
Diesel prices (Cent per litre) = 44.731 -0.286*Location + 0.715*Unleaded 91 prices (Cent
per litre)
The multiple R is 0.60 and has not increased from the previous model. The coefficient of
determination is 0.3601 which implies that 36.01% of the variation in diesel prices on August
22, 2018 in Victoria can be jointly explained by the variation in unleaded 91 prices and
location.
The significance of the two slope can be tested as shown below.
Null Hypothesis: Slope can be assumed as 0 and hence not significant.
Alternate Hypothesis: Slope cannot be assumed as 0 and hence significant.
The significance level has been taken as 5%
The relevant output to test the above hypothesis is indicated below.
The p value approach is used here. The p value corresponding to the location variable is
0.710 and greater than the significance level. As a result, null hypothesis cannot be rejected
which implies that this slope is not significant. However, this is not the case for Unleaded 91
where the p value is lower than significance level and hence the slope significance is
established.
Despite having a slightly higher coefficient of determination, the multiple regression is not
the superior model. This is because adjusted R square value is higher in case of simple
regression (0.3507) as compared to multiple regression (0.3434). This value tends to adjust
for the difference in the number of predictor variables in the two models and hence provides a
more accurate comparison.