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HI6007 Statistics and Research Methods for Business Decision Making Assessment 2 Answer

Assessment Details and Submission Guidelines
Trimester
T1 2019
Unit Code
HI6007
Unit Title
Statistics and Research Methods for Business Decision Making
Assessment Type
Assessment 2
Assessment Title
Group Assignment
Purposeofthe assessment (with ULO
Mapping)
Students are required to show the understanding of the principles and techniques of business research and statistical analysis taught in the course.
Weight
30 % of the total assessments
Total Marks
30
Word limit
N/A
Submission Guidelines
  • All work must be submitted on Blackboard by the due date along with a completed Assignment Cover Page.
  • The assignment must be in MS Word format, no spacing, 12-pt Arial font and 2 cm margins on all four sides of your page with appropriate section headings and page numbers.
  • Reference sources must be cited in the text of the report, and listed appropriately at the end in a reference list using Harvard referencing styl

Assignment Specifications

Purpose:

This assignment aims at Understand various qualitative and quantitative research methodologies and techniques, and other general purposes are:

  1. Explain how statistical techniques can solve business problems
  2. Identify and evaluate valid statistical techniques in a given scenario to solve business problems
  3. Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving
  4. Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package
  5. Justify and interpret statistical/analytical scenarios that best fits business solution

Assignment Structure should be as the following:

This is an applied assignment. Students have to show that they understand the principles and techniques taught in this course. Therefore students are expected to show all the workings, and all problems must be completed in the format taught in class, the lecture notes or prescribed text book. Any problems not done in the prescribed format will not be marked, regardless of the ultimate correctness of the answer.

(Note: The questions and the necessary data are provided under “Assignment and Due date” in the Blackboard.)

Instructions:

  • Your assignment must be submitted in WORD format only.
  • When answering questions, wherever required, you should copy/cut and paste the Excel output (e.g., plots, regression output etc.) to show your working/output.
  • Submit your assignment through Safe-Assign in the course website, under the Assignments and due dates, Assignment Final Submission before the due date.
  • You are required to keep an electronic copy of your submitted assignment to re-submit, in case the original submission is failed and/or you are asked to resubmit.
  • Please check your Holmes email prior to reporting your assignment mark regularly for possible communications due to failure in your submission.


Important Notice:

All assignments submitted undergo plagiarism checking; if found to have cheated, all involving submissions would receive a mark of zero for this assessment item.

Please read below information carefully and respond all questions listed.

Question 1

Australian exports (goods and services) along with its top 8 export markets in 2004-05 and 2014-15 are shown in the table stored in file EXPORTS.XLSX (in the course website). Using this data, answer the questions below.

  1. Use an appropriate graphical technique to compare the value of Australian exports (in A$ bn) in 2004-05 and 2014-15, broken down by country of export destination.
  2. Use an appropriate graphical technique to compare the percentage value of Australian exports (in %) in 2004-05 and 2014-15, broken down by country of export destination.
  3. Comment your observations in parts (a) and (b).(2 marks)

Question 2.

The following data are the 40 days umbrella sales from a store.(8 Marks)

63
74
42
65
51
54
36
56
68
57
62
64
76
67
79
61
81
77
59
38
84
68
71
94
71
86
69
75
91
55
48
82
83
54
79
62
68
58
41
47


4. Construct a frequency distribution and a relative frequency distribution for the data.

5. Construct a cumulative frequency distribution and a cumulative relative frequency distribution for the data.

6. Plot a relative frequency histogram for the data.

7. Construct an ogive for the data.(1 mark)

8. What proportion of the grades is less than 60?(1 mark)

9. What proportion of the grades is more than 70?(1mark) Use following class intervals to answer the above questions

Question 3.(18 Marks)

Assume you are a research analyst in an economic consultancy firm. Your team leader has given you a research task to investigate whether the per capita retail turnover in Australia is a good predictor of the final consumption expenditure of the country.

Relevant Variables:

FINAL CONSUMPTION EXPENDITURE: (Trend) in $ Millions; - quarterly data from September 1983 to March 2016.

RETAIL TURNOVER PER CAPITA - (Trend) Total (State) in $;- quarterly data from September 1983 to March 2016.

[Quarterly time series data (for the period September 1983 to March 2016) are from the Australian Bureau of Statistics (ABS)]

The data are stored in the file named “ASSIGNMENTDATA.XLSX” in the course website. Using EXCEL, answer below questions:

  1. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables.
  2. Use an appropriate plot to investigate the relationship between FINAL CONSUMPTION EXPENDITURE and RETAIL TURNOVER PER CAPITA. Briefly explain the selection of each variable on the X and Y axes and why?
  3. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, coefficient of variation, smallest and largest values, and the three quartiles, for each variable.
  4. Calculate the coefficient of correlation(r) between FINAL CONSUMPTION EXPENDITURE and RETAIL TURNOVER PER CAPITA. Then, interpret it.
  5. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.
  6. Determine the coefficient of determination R2 and interpret it.
  7. Test whether FINAL CONSUMPTION EXPENDITURE positively and significantly increases with

RETAIL TURNOVER PER CAPITA at the 5% significance level.

8. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model?

Answer

Solution 1a: Stacked Column graph was used to represent the given data as follows:

Stacked Column graph

Solution 1b: 100% Stacked Column graph was used to represent the given data as follows:

100% Stacked Column graph

Solution 1c: It can be seen that while Stacked Column graph in part (a) represents absolute numbers, 100% Stacked Column graph in part (b) represents percentages was used to represent the given data. The first graph gives absolute export numbers for Top 8 countries while the second graph gives percentage share of 8 countries in given exports total. 

For example, while the first graph does not indicate decrease in proportion of United Kingdom’s share in Top 8 countries’ exports numbers from 2004-05 to 2014-15, it is evident in the second graph where pink bar reduces in width. Similarly, China’s drastic jump in percentage terms normalises.

Solution 2 a & b: Following table presents the information required:

ClassesFrequencyRelative FrequencyCumulative FrequencyCumulative Relative Frequency
LowerUpper
304000.0%00.0%
405025.0%25.0%
5060410.0%615.0%
6070820.0%1435.0%
70801127.5%2562.5%
8090820.0%3382.5%
90100512.5%3895.0%
10011025.0%40100.0%
  40100.0%  


Frequency was calculated using Frequency’ formula and relative frequency is frequency divided by total sales. Cumulative numbers present total from first Class interval till the Corresponding Class interval.

Solution 2c: Relative Frequency Histogram was made using column chart on Relative Frequency Data:

Relative Frequency Histogram

Solution 2d: Ogive was made using line chart on Cumulative Relative Frequency data:

 Ogive was made using line chart on Cumulative Relative Frequency data

Solution 2e: This was calculated by counting all the data points that are less than 60. The arrived at number was divided by total number of data points as follows:

 CountProportion
<601435.0%


It can be seen that 35% of the grades are less than 60.

Solution 2f: This was calculated by counting all the data points that are greater than 70. The arrived at number was divided by total number of data points as follows:

 CountProportion
>701537.5%


It can be seen that 37.5% of the grades are greater than 70.

Solution 3a: Line charts were used to present the two variables. It can be seen that both the variables indicate an increasing trend over the quarters as follows:

retail turnover per capita

Solution 3b: Scatter Plot chart was used to present the two variables. Independent variable, Retail Turnover per Capita ($) is on x-axis while the dependent variable, Final Consumption expenditure ($Mn) is on y-axis. It can be seen that both the variables indicate a positive linear trend:

scatter plot

Solution 3c: Descriptive Statistics tool was used to generate following output:

Retail Turnover per Capita ($) Final Consumption expenditure ($Mn) 




Mean         2,205.76 Mean              1,46,019.85 
Standard Error               47.46 Standard Error                    4,098.05 
Median         2,180.20 Median              1,39,137.00 
Mode         2,852.80 Mode#N/A
Standard Deviation             543.19 Standard Deviation                  46,904.33 
Sample Variance   2,95,059.60 Sample Variance     22000,16,261.88 
Kurtosis                -1.61 Kurtosis                           -1.30 
Skewness                  0.07 Skewness                            0.31 
Range         1,558.70 Range              1,51,259.00 
Minimum         1,455.90 Minimum                  81,889.00 
Maximum         3,014.60 Maximum              2,33,148.00 
Sum   2,88,954.80 Sum         191,28,601.00 
Count131Count131

The above present required summary of mean, median, mode, range, standard deviation, variance, etc.

Solution 3d: Correlation tool was used as follows:

 Retail Turnover per Capita ($)Final Consumption expenditure ($Mn)
Retail Turnover per Capita ($)1
Final Consumption expenditure ($Mn)                             0.99 1


It can be seen that degree of correlation is very high at 0.99 which indicates a positive linear relationship such that an increase of one unit in retail turnover per capita causes an increase of 0.99 units in final consumption expenditure (Rumsey, 2016).

Solution 3e: Regression tool was used as follows:

regression tool

From above, the linear regression equation can be interpreted as:

y = -42,102.53 + 85.29 x

where, 

  • Independent variable: x is Retail Turnover per Capita ($), 
  • Dependent Variable: y is predicted variable and is Final Consumption Expenditure
  • Constant: -42,103.53 is the y-intercept coefficient. It is also known as ‘β0’ or ‘constant’. 

Solution 3f: The values of R and R2 help in determining the degree of relationship between independent and dependent variables. These are also called as Coefficients of Determination (Jackson, 2009).

In the given case, R value is 0.99 which indicates that there is high degree of correlation between the variables in consideration. R2 is at 0.98 with adjusted R2 being 0.98. The value of R2 is nothing but the proportion of change in dependent variable that can be explained through the independent variables (Lang et al., 2013). As can be seen, at 98.0%, a high proportion of change in value of ‘Final Consumption Expenditure ($Mn)’ can be attributed to change in Retail Turnover per Capita ($).

Solution 3g: From above table, we can see that the p-value for variable, Retail Turnover per Capita ($) is 0.0000 which is less than the assumed significance level of α = 0.05. Hence, we can conclude that the FINAL CONSUMPTION EXPENDITURE positively and significantly increases with RETAIL TURNOVER PER CAPITA at the 5% significance level.

Solution 3h: From above table, we can see that the Standard error of estimate is 2700.17 for the constant and 1.19 for the x variable. 

We can see that the Significance value is 0.0000 which is less than the assumed significance level of α = 0.05. Hence, we can conclude that the regression model is a good linear fit. This is further supported by value of R and R2

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