Statistical Inference and Regression and Correlation Task

In this assignment we will discuss about statistical Inference and below are the summaries point:- Aim: determine if Capital city fuel prices were often less than elsewhere in the state Statistical test used: independent sample t-test Hypotheses: H0 = Capital city mean fuel prices were not significantly less elsewhere in the state; H1 = Capital city mean fuel prices were significantly less elsewhere in the state Result: Null hypothesis is accepted, meaning Capital city fuel prices were often not less than elsewhere in the state. Aim: determine the relationship between unleaded 91 and diesel prices Methods used: scatter plot and simple regression Scatter plot used to visualize the relationship between variables Simple regression used to find the least square regression equation, which is Diesel = 0.7147 * (Unleaded 91) + 44.876 Coefficient of correlation (Multiple R) = 0.599 and coefficient of determination (R square) = 0.3589, indicating a moderate positive relationship between the two variables and that 35.89% of the variability in diesel prices can be explained by the variability in unleaded 91 prices.  

Price Determination 1
Statistical Inference and Regression and Correlation Tasks
Name
Institution
Course
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Price Determination 2
Introduction
The aim of this assignment is conduct statistical inference and regression analysis using the
given data sample. Hypothesis will formulated and tested using the results obtained. After
conducting the analyses, insight is going to be given.
Question 1
Introduction
The aim of this part is to determine whether Capital city fuel prices were often less than
elsewhere in the state. To achieve this, Independent sample t-test will be used. The hypothesis
will be formulated, and the output will be used to test the result
Formulation of the assumptions
1. Capital city mean fuel prices were not significantly less elsewhere in the state– H0
2. Capital city mean fuel prices were significantly less elsewhere in the state– H1
Below is the output of the result
Table 1: Independent sample t-test
Testing the hypothesis
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Price Determination 3
While testing the hypothesis, the focus will be on the one tail p-value. Since it is greater than the
0.05, the null hypothesis is accepted, and therefore it is deduced that Capital city fuel prices
were often not less than elsewhere in the state (Miada and Ryan, 2016).
Question 2
Introduction
The aim of this assignment is to determine the relationship between unleaded 91 and Diesel
prices. To achieve this, Price Determination techniques are going to be applied. This can be
accomplished using two methods:
1) Using Scatter Plot
2) Using Simple regression
Scatter Plot
Before plotting the scatter plot, dependent and independent variable need to be selected. Diesel
price is chosen as the dependent variable and Unleaded 91 price as the independent variable.
Below is the scatter plot for the above:
130.0 135.0 140.0 145.0 150.0 155.0 160.0
125.0
130.0
135.0
140.0
145.0
150.0
155.0
160.0
165.0
f(x) = 0.712749041249649 x + 44.8763193340193
R² = 0.358905384490964
Scatter Plot Diesel VS Unleaded 91
Unleaded 91 (Cents per Litre)
Diesel (Cents
per Litre)
Plot 1: Scatter diagram showing the relationship between Diesel and Unleaded 91
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Price Determination 4
Simple Regression
Table 1: Simple linear regression coefficient
Table 2: Simple linear regression statistics
Interpretation
The least square regression formula is given by:
Y = mx + c, where y is the dependent variable, x is the independent variable, m is the
gradient and c is the y-intercept (Montana, Maxwell and Vincent, 2012).
Plot 1 and Table 1 gives the equation of the model to be:
Diesel = 0.7147 * (Unleaded 91) + 44.876
From this equation, it can be deduced that 44.876 cents per litre of diesel are not affected by the
price of Unleaded 91. Furthermore, it can be deduced that every 1 cent per litre of Unleaded 91
increases the price of diesel by 0.7147 cents per litre.
Table 2 gives the value of the coefficient of correlation, i.e., Multiple R to be 0.599 and the
coefficient of determination, i.e., R square to be 0.3589. Correlation coefficient explains the
association of the given variables. In this case, it can be deduced that the association or the
relationship between the price of diesel and unleaded 91 is 59.9 %. The coefficient of
determination determines how much variability of one variable can be explained using the
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Price Determination 5
variation of another variable. In this case, it can be deduced that 35.89 % of the price of diesel
can be explained using the price of unleaded 91 (Davis, 2017). Both the scatter plot and
regression statistics give the same value for R square (0.3589). Table 2 gives the value for
Multiple R but the scatter plot doesn’t give but it can be calculated using the value of R squared
from the plot.
Multiple R = √R2
=√ 0 .599
= 0.3589
Therefore, the values of R and R square are consistent with that of the scatter plot.
Question 3
Introduction
The aim of this part of the assignment is to determine the influence of location on the price of
diesel and unleaded 91. To achieve this, multiple regression analysis needs to be conducted using
location as one of the independent variables. The location data is transformed into binary, i.e.,
Capital – Melbourne is assigned the value of 0 and Regional the value of 1.Below is the output
of the regression.
Table 3: Multiple regression coefficient
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Price Determination 6
Table 4: Multiple regression statistics
The multiple regression equation can be summarized as (Steve, West and Alex, 2014):
Diesel = 0.2861 * (Location) + 0.7149 * (Unleaded 91) + 44.44
This means that 44.44 cents of diesel are not affected by both the location and the price of
unleaded 91. Furthermore, 1 unit of unleaded 91 increases the price of diesel by 0.7149 cents per
litre and the location increases the price of diesel by 0.2861 cents per litre. The multiple
regression correlation is given by 0.600, and this means that the relationship between the price of
diesel with both the price of unleaded and location is 60 %. The coefficient of multiple
regression analysis is given by 0.366, and this means that 36.6 % of the price of diesel is
explained by both the location and the price of unleaded 91. It can be noticed that the value of R
squared and Multiple R in multiple regression and simple correlation are almost equal.
Formulation of hypothesis
1.
a) The price of unleaded 91 does not have a significant influence on the price of diesel – H0
b) The price of unleaded 91 has a significant influence on the price of diesel – H1
2.
a) The location does not have a significant influence on the price of diesel
b) The location has a significant influence on the price of the diesel
Testing the hypothesis
The significance level selected during the multiple regression analysis is 0.05. The p-value
obtained after conducting the regression analysis is compared to the selected p-value.
To test hypothesis 1, the p-value from Table 3 is used. If the p-value obtained is higher than the
0.05, the null hypothesis is accepted, and when the p-value is less than 0.05, the alternate
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Price Determination 7
hypothesis is accepted. In this case, the p-value obtained is 5.08207E-09 and therefore, the null
hypothesis is rejected. Thus, it is deduced that there is some statistical evidence showing that the
price of unleaded 91 influence the price of the diesel. To prove the second hypothesis, the p-
value of the location is used. The p-value for the location is obtained to be 0.7095 which is
greater than 0.05. Therefore the null hypothesis is accepted, and thus, it can be deduced that there
is no statistical evidence to show that the local influence the price of the diesel (Seth, 2014.).
Therefore, the simple regression was the best model to determine the price of the diesel. This is
because the location used in conducting multiple regression analysis didn't influence the price of
the diesel.
Conclusion
It is evident from the analysis that the price of the unleaded 91 and diesel were correlated. It is
also evident that the price of unleaded 91 had an influence on the price of diesel. Meanwhile,
location had no influence on the price of diesel.
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Price Determination 8
Reference
Steve, P., West, S.G. and Alex, L.S., 2014. Applied multiple regression/correlation analysis for
the behavioral sciences. Psychology Press.
Seth, T.Z., 2014. Multiple regression and beyond: An introduction to multiple regression and
structural equation modeling. New York:Routledge.
Davis, M.A., 2017. Tests based on regression and correlation. In Goodness-of-Fit-Techniques
(pp. 195-234).New York:Routledge.
Miada, C.A. and Ryan, R.V., 2016. Advanced and multivariate statistical methods: Practical
application and interpretation.New York:Routledge.
Montana, D.C., Maxwell, E.A. and Vincent, G.G., 2012. Introduction to linear regression
analysis (Vol. 821). John Wiley & Sons.
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Price Determination 9
Appendix
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Price Determination 10
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Price Determination 11
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Price Determination 12
130.0 135.0 140.0 145.0 150.0 155.0 160.0
125.0
130.0
135.0
140.0
145.0
150.0
155.0
160.0
165.0
f(x) = 0.712749041249649 x + 44.8763193340193
R² = 0.358905384490964
Scatter Plot Diesel VS Unleased 91
Unleased 91 (Cents per Litre)
Diesel (Cents
per Litre)
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