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HI6007 Statistics and Research Methods for Business Decision Making: Group Assignment 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

Due Date

Lecture 10

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 style.


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:

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.

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.(4 Marks)

  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.(1 mark)
  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


  1. Construct a frequency distribution and a relative frequency distribution for the data.
  2. Construct a cumulative frequency distribution and a cumulative relative frequency distribution for the data.(2 marks)
  3. Plot a relative frequency histogram for the data.(1 mark)
  4. Construct an ogive for the data.(1 mark)
  5. What proportion of the grades is less than 60?(1 mark)
  6. What proportion of the grades is more than 70?(1mark) Use following class intervals to answer the above questions
Classes
Frequency
Relative Frequency
Cumulative Frequency
Cumulative
Relative
Frequency
30 - 40




40 - 50




50 - 60




60 - 70




70 - 80




80 - 90




90 - 100



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.(1 mark)
  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. Calculatethecoefficientofcorrelation(r)betweenFINAL 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.(4 marks)
  6. Determine the coefficient of determination R2 and interpret it.(2 marks)
  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?(1 mark)

Answer

Q1

Clustered Column graph was made in MS-Excel:

clustered column graph- top 8 export markets for goods and services

The graph indicates change in export value from 2004-05 to 2014-15 for the Top 8 countries. China registered a tremendous growth while United Kingdom reported a slight decrease.

100% Stacked Column graph was made in MS-Excel:

 Stacked Column graph- top 8 export market for good and services

The data labels indicate absolute values while the width of the bars indicates percentage change for respective countries. The highest percentage growth was registered by China. The percentage change for United Kingdom is clearly evident in the width of the bars.

From above discussion, we can see that the clustered column only present absolute value numbers while the 100% stacked column assist with the absolute numbers through data labels and percentage changes through the graph. Hence, 100% Stacked Column graph presents much more information.

Q2

  1. (b)
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%  


(c) & (d) Histogram tool was used in MS-Excel:

Histogram of Umbrella sales

The blue bars represent frequency at various intervals while the orange line chart represents the ogive.

  1. (f): This was done by counting all the data points through ‘Countif’ function. The proportion was arrived at by dividing result by total data points (40):
 CountProportion
<601435.0%
>701537.5%


It can be seen that 35% of the grades are less than 60 and 37.5% of the grades are greater than 70.

Q3

(a) MS-Excel Line charts were used to present the time series for each of the two variables and both indicate an increasing trend over the time period:

Quarterly retail turnover per capita

quarterly consumption expenditure

MS-Excel Scatter plot was used to present the two variable relationships that show a positive linear trend as indicated by the black line and regression equation on the chart below. Blue dots indicate various data points over the period:

relationship between retail turnover per capita and consumption expensiture

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

Mode is N/A as no value is repeated for the data and hence, Mode can’t be calculated.

Correlation is at 0.988 between the two variables indicating a very high degree positive relationship. In other words, a one unit increase in retail turnover per capita causes an increase of 0.988 units in final consumption expenditure.

  Unit   $$ Millions
 Unit   $1
$ Millions                  0.988 1


Regression was done by using Data Analysis option in MS-Excel:

Linear Regression Equation is: y = -42,102.53 + 85.29 x

where, y is the dependent variable which will be predicted through the above equation (in this case, Consumption expenditure). X is the independent variable (in this case, Retail Turnover per Capita). The y-intercept coefficient is -42,102.53.

  1. Coefficients of Determination are 0.99 and 0.98 which is a very high value and indicates a good fit of the regression model. In other words, 98% of change in variable y can be attributed to variable x.
  2. In order to test the significance of variable x, we will check the p-value against the row for variable. We can see from above table that this value is p-value = 0.000 which is less than significance level of 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.
  3. Standard error of estimate is measure of accuracy of prediction through regression line. We can see that the Standard error of estimate is 2700.17 for the constant and 1.19 for the x variable. 

Similar to what we did in Part (g), we can check the fit of the regression model through significance value in ANOVA table which is 0.000 in this case. As this value is less than the assumed significance level of α = 0.05, we can conclude that the regression model is a good linear fit. 

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