Holmes Institute HI6007 Statistics Group Assignment

This document presents a comprehensive solution to a statistics assignment, likely for a business or research methods course. The assignment covers various statistical concepts and techniques, including the analysis of CO2 emissions, frequency distributions, and regression models. The solution includes graphical representations such as graphs and histograms, along with tables presenting data and statistical calculations. The analysis involves comparing CO2 emissions across different countries, determining proportions of data within specified ranges, and exploring the relationship between inflation rates and an All-Ordinaries Index. The document provides detailed answers to specific questions, interpreting statistical results, and drawing conclusions based on the data analysis. The assignment demonstrates an understanding of statistical methods and their application in a business context, including the use of correlation and regression to analyze relationships between variables and assess the significance of findings.

Running head: STATISTICS
Statistics
Name of the Student
Name of the University
Student ID

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Table of Contents
Answer 1.....................................................................................................................................2
Answer a..................................................................................................................................2
Answer b..................................................................................................................................2
Answer c..................................................................................................................................3
Answer 2.....................................................................................................................................3
Answer a..................................................................................................................................3
Answer b..................................................................................................................................3
Answer c..................................................................................................................................4
Answer d..................................................................................................................................4
Answer e..................................................................................................................................4
Answer f...................................................................................................................................5
Answer 3.....................................................................................................................................5
Answer a..................................................................................................................................5
Answer b..................................................................................................................................6
Answer c..................................................................................................................................6
Answer d..................................................................................................................................7
Answer e..................................................................................................................................7
Answer f...................................................................................................................................8
Answer g..................................................................................................................................8
Answer h..................................................................................................................................8
References list............................................................................................................................9

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Answer 1
Answer a
Graph 1: CO2 emission in 2009 and 2013 (broken down by countries)
Answer b
Graph 2: Percentage value of CO2 emission in 2009 and 2013 (broken down by
countries)

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Answer c
The comparison of CO2 emission signifies that in nations like United State, Canada,
Germany, United Kingdom, Italy, Iran, Australia, South Africa and France emission has
lowered in 2013 with United State making the largest reduction in emission. The trend is
reversed for some nation like China, Japan, Russia, India, South Korea and Saudi Arabia
accounting an increase in emission. Largest percentage increase has been observed in case
of China.
Answer 2
Answer a
Table No 1: Frequency distribution and relative frequency distribution
Answer b
Table No 2: Cumulative frequency distribution and cumulative relative frequency
distribution

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Answer c
Graph 3: Relative frequency histogram
Answer d
Graph 4: Ogive for cumulative frequency distribution
Answer e
The proportion of data less than 65 can be obtained as
Observation less than 65
Total number of observation

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¿ 16
40
¿ 0.4
Answer f
The proportion of data that is more than 75 can be obtained as
Observation greater than7 5
Total number of observation
¿ 6
40
¿ 0. 15
Answer 3
Answer a
Graph 5: Graphical descriptive measure for Rate of Inflation and All-Ordinaries Index
The trend line graph for the two variable shows that inflation rate has a fluctuating but
gradual declining trend. For All-Ordinaries index the trend however rising overtime.

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Answer b
Graph 5: Scatter diagram of Rate of Inflation and All-Ordinaries Index
Movement of All-Ordinaries Index is likely to depend on movement of inflation rate.
Therefore, inflation rate is the independent variable and plotted on the X axis (Carroll 2017).
All-Ordinaries Index is the dependent variable and plotted on Y axis.
Answer c
Table No 3: Summary statistics for Rate of Inflation and All-ordinaries Index

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Answer d
Table No 4: Correlation Coefficient
Correlation coefficient between Rate of Inflation and All-Ordinaries Index is 0.0388.
From the positive correlation coefficient a positive association can be comprehended between
the two variables (Yao and Li 2014). Computed value of correlation coefficient is close to zero
implying a weak relation.
Answer e
Table No 5: Simple linear regression model

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AllOrdinaries Index=3874.286+(40.308 × Rate of inflation)
The estimated coefficient of the linear regression model is 40.308. The coefficient
suggests rate of inflation has a positive impact on All-ordinaries index (Carroll 2017). In other
words, value of the index increases with increase in inflation and value of the index decreases
with a fall in inflation rate.
Answer f
The coefficient of determination or R2 from the regression model is determined as
0.0015. It can be interpreted as Rate of Inflation accounts for only 0.15 percent variation in
All-Ordinaries Index.
Answer g
Significance of the relation depends on statistical significance of the regression
coefficient. For the coefficient ‘Rate of Inflation’ the p value is 0.867. Computed p value is
higher than 5% significance value implying acceptance of null hypothesis of non-significance
of the coefficient.
Answer h
The value of standard error estimate is 237.690. The considerably larger standard
error suggests a large variation of fitted value from the actual value (Yao and Li 2014). The
linear regression model therefore is a not a good fit model.

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References list
Carroll, R.J., 2017. Transformation and weighting in regression. Routledge.
Yao, W. and Li, L., 2014. A new regression model: modal linear regression. Scandinavian
Journal of Statistics, 41(3), pp.656-671.