HI6007 Statistics and Research Methods Assignment T2 2019

This statistics assignment analyzes data related to CO2 emissions, welding times, inflation rates, and the All Ordinaries index. The assignment includes graphical representations of CO2 emissions across different countries and years, along with a frequency distribution analysis of welding times. Furthermore, it explores the relationship between inflation rates and the All Ordinaries index through scatter plots, descriptive statistics, and regression analysis. The analysis includes calculating coefficients of determination and correlation, interpreting regression outputs, and drawing conclusions about the relationships between the variables. The assignment demonstrates the application of statistical techniques to real-world data and provides insights into business decision-making.

Running head: STATISTICS
Statistics
Name of the Student:
Name of the university:
Authors Note:

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Table of Contents
Q1...............................................................................................................................................3
Q2...............................................................................................................................................4
Q3...............................................................................................................................................6
References:...............................................................................................................................11

2STATISTICS

3STATISTICS
Q1.
a)
United States
China
Russia
Japan
India
Germany
Canada
United Kingdom
South Korea
Italy
Iran
South Africa
France
Saudi Arabia
Australia
0
2000
4000
6000
8000
10000
12000
CO2 Emissions
Series1 Series2
Countries with their fuel emissions in 2009(blue) and 2013(red)
Fuel Emisssions(million metric tonn)
b)
United States
China
Russia
Japan
India
Germany
Canada
United Kingdom
South Korea
Italy
Iran
South Africa
France
Saudi Arabia
Australia
0
2000
4000
6000
8000
10000
12000
CO2 Emissions
Series1 Series2
Countries with their fuel emissions in 2009(blue) and 2013(red)
Fuel Emisssions(million metric tonn)

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Fig 1: Graphical representation showing the emission of CO2 in the year 2009( blue)
and 2013 (red).
c)
The emission of CO2 is represented graphically for the countries in two different
years (2009 and 2013) and it is seen that United States, China and Russia are the
countries with the highest CO2 emissions in year 2009. And for the countries the
emission of CO2 decreases in 2013 compared to 2009 only for United States. For
China and Russia the emission increases in 2013 compared to 2009.
And for the countries with the lowest emissions, France, Saudi Arabia and Australia
the emission is higher in 2013 only for Saudi Arabia.
Q2.
a) and b)
Classes Frequency Rel. Freq. Cum. Freq.
Cum. Rel.
Freq
35-44 3 8% 3 8%
45-54 4 10% 7 18%
55-64 9 23% 16 40%
65-74 18 45% 34 85%
75-84 4 10% 38 95%
85-94 1 3% 39 98%
95-104 1 3% 40 100%

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The data given is of time required for welding and the 40 data are grouped into the
relevant class intervals with frequency, relative frequency, cumulative frequency, and
cumulative relative frequency.
c)
Relative Frequency Histogram:
44 54 64 74 84 94 104 More
0
5
10
15
20
Histogram
Time to weld
Frequency
d)
35-44 45-54 55-64 65-74 75-84 85-94 95-104
0
5
10
15
20
25
30
35
40
45
Ogive of welding time
e)
Arranging the data set is ascending order we get:
Proportion of data below 65 : 4 %
Proportion of data above 75 : 12.5%

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Q3.
The data for inflation rates and All ordinaries index are given from year 1995 to 2015.
The analysis here investigates the relationship, if any, between all ordinaries index
and the rate of inflation.
a)
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
7000.0
All-Ordinaries index
The graph between all ordinaries index and time in years shows that the price index
rises with years with sharp peak between the years 2006 to 2009. And there does
not seem to be any repetitive pattern in the data.
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Rate of inflation (%)

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The rate of inflation is plotted against the years from 1995 to year 2015. There are
sharp peaks around the years 1996, 2001, 2008, 2011 and 2014. And sharp falls are
seen around the years 1998, 2009,2012 and 2002.
b)
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
7000.0
f(x) = 40.3077051702228 x + 3874.28641228011
R² = 0.00151127464405965
All-Ordinaries index
A scatter plot is drawn between the two variables and as the relation is wanted to be
known for how the change in inflation changes the All ordinaries index, the inflation
rates are plotted in the x axis and the all ordinaries index are plotted in y axis.
The coefficient of determination is found to be 0.0015 which indicates a very weak
positive relationship between the two variables(Stine and Foster 2014).
It means only 1.5% of the variation of the All ordinaries index can be explained by
the variation of the inflation rate.

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c)
Rate of inflation (%)
Mean 2.69047619
Standard Error
0.26039391
1
Median 2.5
Mode 2.4
Standard
Deviation
1.19327480
6
Sample
Variance
1.42390476
2
Kurtosis
2.03828159
8
Skewness
0.79840767
4
Range 5.6
Minimum 0.3
Maximum 5.9
Sum 56.5
Count 21
All-Ordinaries index
Mean 3982.7333
Standard Error 269.9897
Median 4127.6
Mode #N/A
Standard
Deviation 1237.2482
Sample
Variance 1530783.2
Kurtosis
-
1.0100094
Skewness 0.182747
Range 4336.8
Minimum 2000.8
Maximum 6337.6
Sum 83637.4
Count 21
The descriptive statistics for the All Ordinaries Index is calculated and for the
Inflation rate is observed that the mean is 2.69 and the median is 2.5 so the

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distribution is slightly right skewed. The maximum inflation rate was 5.9 and the
minimum was 0.3. The distribution had a Std Deviation of 1.19. The first, second and
third quartiles are at 2.15, 2.5 and 2.95 respectively.
For the All Ordinaries Index it is found that, the mean of the distribution is 3982.74
and the median 4127.6. Hence, the distribution is significantly left skewed. The
maximum All Ordinaries Index was 6337.6 and the minimum was 2000.8. The
standard deviation of the distribution is 1237.24.
The first, second and third quartiles for All Ordinaries Index are at 2997.5, 4127.6
and 5022 respectively.
3(d) The coefficient of correlation is a statistical value that measures the strength of
the relationship between the relative variation between the two variables.
The Correlation is found from excel data analysis tools and is found to be 0.038
which indicates that the two variables have a weak positive relationship.
Rate of
inflation
(%)
All-Ordinaries
index
Rate of inflation (%) 1
All-Ordinaries index
0.0388751
2 1
3(e)
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.038875116
R Square 0.001511275
Adjusted R Square -0.051040764
Standard Error 1268.430355
Observations 21
ANOVA
df SS MS F Significance F
Regression 1 46268.67733
46268.677
3
0.02875
8 0.867132273
Residual 19 30569395.73
1608915.5
6
Total 20 30615664.41

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Coefficie
nts
Standar
d Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercep
t
3874.28
6412
696.831
9943
5.55985
725
2.31E-
05
2415.80
0286
5332.77
2538
2415.80
0286
5332.77
2538
Rate of
inflation
(%)
40.3077
0517
237.690
1351
0.16958
089
0.867
132
-
457.183
4651
537.798
8754
-
457.183
465
537.798
8754
3 (e)
From the regression summary, the estimated linear equation is found to be:
y = 40.31x+3874.29
y is the All Ordinaries Index and x is the inflation rate.
The coefficients suggest that with every 1% rise in inflation rate the all ordinaries
price index rises by 40.31.
3(f)
The coefficient of determination from the regression summary is found to be 0.0015
the same as from our scatter plot. Coefficient of determination indicates how much of
the variability of one variable can be explained by the variability of the other( Siegel
2016) . The value obtained from the regression summary indicates that only 1.5% of
the variability between the variables can be explained by the model.
3(g)
If the significance level is set at 5% the value of alpha for the whole model is 0.05.
From the regression summary the P value is seen to be 0.87 and hence the null
hypothesis can’t be rejected and we cannot conclude that the inflation rate can be
used to successfully predict the All Ordinaries Index for the whole sample
3(h)
The Standard Error of the regression indicates the mean distance that the observed
values fall from the regression line. In other words, it represents how much error
creeps up in the regression model using the units of the target variable.
Standard Error for the model is 1268.43.

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References:
Siegel, A., 2016. Practical business statistics. Academic Press.
Stine, R. and Foster, D., 2014. Statistics for Business: Decision Making and.
Addison-Wesley SOFTWARE-JMP.