MAT10251- Sample Questions on Statistical Analysis

In this document we will discuss about statistical analysis and below are the summary points of this document:- A study conducted by Oz-Fuel-Watch to determine whether the mean price of Diesel fuel in the capital city of Victoria (Melbourne) was lower than the mean price elsewhere in the state on July 1, 2018. The study used a paired sample t-test, assuming that the variables were continuous and dependent. The vertical intercept is -2.48, indicating that the price of Unleaded 91 is dependent on the surplus of Diesel available. There is a fairly strong positive relationship between Unleaded 91 and Diesel, with 28% of the variability in the model accounted for by factors in the model and 62% of the variability accounted for by factors not in the model. The Unleaded 91 price at Capital-Melbourne is cheaper than at Regional areas of Victoria by 1.5 units. The variable that makes a significant contribution to the multiple regression model is Diesel (p<0.05) only since the Location coefficient is greater than 0.05. There is no best model to determine the association between Unleaded 91 and Diesel since both models have equal adjusted R squared.

RUNNING HEADER: MAT10251 STATISTICAL ANALYSIS 1
MAT10251 STATISTICAL ANALYSIS
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MAT10251 statistical analysis 2
Question 1
Capital city fuel prices are often less than elsewhere in the state. Oz-Fuel-Watch wishes to
know if on the 1th of July 2018 and in the state of Victoria the mean price of Diesel, was less
in the capital city than elsewhere in the state. A paired sample t-test was carried out to
determine this. The method was chosen since it compares the means between two distinct
groups1. The assumptions made was that the variables were continuous and dependent.
It was found out that the p-value of the difference in mean of Diesel fuel prices between the
capital city and elsewhere in the state of Victoria was less than 0.05 for the one-tail level of
significance only. The decision is to reject the null hypothesis. Thus, on the 17th of July 2018,
it was found out that the mean price of Diesel in the capital-Melbourne had a statistically
significant difference with the mean price of Diesel elsewhere in the state of Victoria.
Question 2
Oz-Fuel-Watch is interested in exploring the relationship between Unleaded 91 and Diesel
prices. A linear regression model was adopted since it is used in determine if there is any
relationship between two variables2. The assumption was that Unleaded 91 was the dependent
variable while Diesel was the independent variable.
The least squares regression equation derived is as shown below:
y = 0.9791x - 2.4812
Consequently, the correlation of coefficient was 0.53 with a coefficient of determination of
0.28.
The gradient of the regression is 0.28. Thus, holding all other factors constant a unit increase
in the price of Diesel leads to a 0.98 unit increase in the price of Unleaded 91 fuel. The
vertical intercept was observed is -2.48. Thus, holding all other factors constant, the price of
Unleaded 91 is dependent on the surplus of Diesel to be available.
The correlation coefficient of the Unleaded 91 and Diesel was found to be 0.53. Hence, there
is a fairly strong positive relationship between Unleaded 91 and Diesel. On the other hand,
the coefficient of determination was 0.28. Thus, 28% of the variability in the model is
accounted by factors in the model while 62% of the variability is accounted for by factors
which are not in the model.
Question 3
The location was plugged into the regression to determine of location influences the
relationship between Unleaded 91 and Diesel prices. The new multiple regression equation
was:
y = 1.01*Diesel – 1.5*Location – 6.28
The multiple correlation coefficient was 0.54 while the coefficient of multiple determination
was 0.27.
1 Doe John. The Student's t-test with extremely small sample sizes. (Guardiola, 2015)
2 Jackie B. Lee. Analysis of linear regression. (Klop Anfiele, 2012).

MAT10251 statistical analysis 3
From the multiple regression coefficients, all factors kept constant, the price of Unleaded 91
is -6.28. Moreover, it is evident that a unit increase in Diesel price leads to a 1.01 unit
increase in Unleaded 91 price. Consequently, the Unleaded 91 price at Capital -Melbourne is
cheaper than Unleaded 91 at the Regional areas of Victoria by 1.5 units.
The multiple correlation coefficient shows that there is a fairly strong positive association
between the three variables. Conversely, from the coefficient of multiple determination of
0.27, 27% of the variation in the model is accounted by factors within the model while 63%
is accounted by other factors which are not in the model.
The variable that makes a significant contribution in the multiple regression model is Diesel
(p<0.05) only since the Location coefficient is greater than 0.05.
From the two regression, it is evident that there is no best model to determine association
between Unleaded 91 and Diesel since both models have equal adjusted R squared.

MAT10251 statistical analysis 4
Appendix
Hypothesis:
H0: There is no difference in means between the price of Unleaded 91 and Diesel
Ha: There is a difference in means between the price of Unleaded 91 and Diesel
Table 1: Diesel t-test: Two-Sample Assuming Unequal Variances
135.0 140.0 145.0 150.0 155.0 160.0 165.0
120.0
125.0
130.0
135.0
140.0
145.0
150.0
155.0
160.0
165.0
f(x) = 0.979055609006103 x − 2.48115792009182
R² = 0.279723534378634
Scatterplot
Figure 1: Linear regression
Table 2: Correlation
Table 3: Multiple regression model

MAT10251 statistical analysis 5