Holmes Institute HI6007 Statistics and Research Methods Assignment

This assignment solution for HI6007 Statistics and Research Methods for Business Decision Making presents a comprehensive analysis of statistical concepts and techniques. The solution addresses three key problems: the application of graphical techniques (bar graphs) to compare carbon dioxide emissions across countries; the creation of frequency distribution tables, histograms, and ogives, alongside proportion calculations; and the use of time series plots, scatter plots, and regression analysis to explore the relationship between inflation rate and all-ordinaries index. The assignment includes detailed explanations, calculations, and interpretations of the statistical results, including correlation coefficients, regression equations, and significance testing. The solution utilizes Excel for data analysis and presents the findings with relevant graphical representations and numerical summaries, demonstrating a solid understanding of statistical methods and their application in a business context. The document concludes with a list of cited references.

University
Statistics and Research Method for Business Decision Making
By
Student Name
Date
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Question 1
Problem Statement
The objective of the question is to apply the apply the appropriate graphical techniques
to compare the amount of carbon dioxide emissions in millions of metric tons and
percentage for the top 15 carbon(iv)oxide emitting countries.
Part A
The graphical technique used to compare the amount of C02 emissions in millions of
metric tons in 2009 and 2013 broken down by the producer country is the bar graph and
is as shown below:
The highest emitting nation is China followed by the United States of America. The least
emitting nations are Italy, Iran, South Africa, France, Saudi Arabia and Australia.
Part B
The appropriate graphical technique to compare the percentage value of the amount of
C02 emissions (in %) in 2009 and 2013, broken down by the producer countries is the
bar graph of percentage shown below:
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The highest emitting countries in terms of percentage is China followed by USA, the
least are Italy, Iran, South Africa, France, Saudi Arabia, Australia.
Part 3
The bar graphs above resemble each other, the difference is that the first bar graph
indicates the emission in millions of metric tons while the second shows the emissions
as a percentage of the total emission in any given year. China is the greatest emitter of
C02 followed by China, the least emitters are Italy, Iran, South Africa, France, Saudi
Arabia and Australia.
Question 2
Problem Statement
The purpose of the question is to use the data provided to create frequency distribution
table, related histograms, ogives and to find proportions.
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Solution
Part A
The frequency and relative frequency distribution table is as shown below.
Part B
The cumulative frequency distribution and cumulative relative frequency distribution
table is as shown below:
Part C
The relative frequency histogram for the data is shown below. It is a plot of relative
frequency (Y axis) against the various classes.
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Part D
The ogive for the data is shown below. It a plot of cumulative frequency against the
upper limits of the various classes.
Part E
Proportion of data less than 65% is 0.4. It is determined in excel using the formula
(count below 65% divided by total count). The excel output is as below.
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Part F
Proportion of data more than 75 is determined by dividing the count of data above 75
with total count. The result is that 0.125 proportion of the data is above 75 as shown in
table on Part E.
Question 3
Problem Statement
The purpose of this question is to use the provided data to determine the appropriate
graphical technique to explain the variation of variables over time. Additionally, the
appropriate statistical techniques will be applied to determine the relationship between
the variables, regression and the test the significance of the relationship.
Part A
Time series plots are used to describe the inflation rate and all-ordinaries index through
the years 1995 to 2015. The time series plots are shown below.
It can be said that the inflation was averagely between 2.0 and 5.0 through the years
except for 1998 where it was minimum at less than and 2001 where it was peak at
above 5.0.
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All ordinaries index can be observed to have been increasing linearly through the years.
Part B
The appropriate plot to show the relationship between rate of inflation and all ordinaries
index is the scatter plot. It is shown below.
All ordinaries index is chosen to be the variable on the y-axis while the inflation rate is
chosen as the variable on the x-axis. This is because the relationship under
examination is how all ordinaries index is affected by change in the inflation rate. It can
be observed that there is a very weak positive linear relationship between the variables
(Newbold, Carlson, and Thorne, 2013).
Part C
The numerical summary
report about the data on
the two variables is shown
in the table below.
Part D
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The coefficient of correlation (r) between inflation rate and all ordinaries index is
r = √r2
r = √0.0015
r =0.039
The r value indicates that there is a positive but very weak relationship between the two
variables.
Part E
From the excel output below we can determine the regression linear equation.
The simple linear regression equation is:
Y =40.31 X1+3874.29
The coefficient of X1 (Rate of Inflation) indicate the value of the dependent variable (All
ordinaries index) the intercept was zero. The intercept shows the values of the
dependent variables if the independent variable was zero (Evans and Basu, 2013).
Part F
The coefficient of determination is shown in the excel output below:
The coefficient of determination is 0.0015 it indicates that only 0.15% of the variability
can be explained by the model.
Part G
To test the significance at 5% significance level, we look at the significance F in the
excel output below.
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Since the value of significance F (0.8671) is greater than the test significance level
(0.05), the relationship is not statistically significant (Linoff, 2012).
Part H
The standard error is 1268.43 as shown in the excel output below.
The regression model is not fit enough to describe the relationship between the
variables, there is a huge standard error, the relationship is not statistically significant
and only 3.8% of the relationship can be explained by the model (Croucher, 2016).
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References
Croucher, J. S. 2016. Introductory mathematics & statistics.6th ed. Australia: North
Ryde, N.S.W. McGraw-Hill Education.
Evans, J. R., and Basu, A. 2013. Statistics, data analysis, and decision modeling.5th ed.
Boston: Pearson.
Linoff, G. 2012. Data analysis using SQL and Excel. Indianapolis, Ind.: Wiley Pub.
Newbold, P., Carlson, W. and Thorne, B. 2013. Statistics for business and economics.
Harlow, Essex: Pearson Education.
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