|Assessment Details and Submission Guidelines|
|Unit Title||Statistics and Research Methods for Business Decision Making|
|Assessment Type||Assessment 2|
|Assessment Title||Group Assignment|
|Purposeofthe assessment (with ULO|
|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|
|Due Date||Lecture 10|
This assignment aims at Understand various qualitative and quantitative research methodologies and techniques, and other general purposes are:
Assignment Structure should be as the following:
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)
The following data are the 40 days umbrella sales from a store.(8 Marks)
|Classes||Frequency||Relative Frequency||Cumulative Frequency||Cumulative|
|30 - 40|
|40 - 50|
|50 - 60|
|60 - 70|
|70 - 80|
|80 - 90|
|90 - 100|
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.
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:
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)
Clustered Column graph was made in MS-Excel:
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:
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.
|Classes||Frequency||Relative Frequency||Cumulative Frequency||Cumulative Relative Frequency|
(c) & (d) Histogram tool was used in MS-Excel:
The blue bars represent frequency at various intervals while the orange line chart represents the ogive.
It can be seen that 35% of the grades are less than 60 and 37.5% of the grades are greater than 70.
(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:
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:
Descriptive Statistics tool was used to generate following output:
|Retail Turnover per Capita ($)||Final Consumption expenditure ($Mn)|
|Standard Error||47.46||Standard Error||4,098.05|
|Standard Deviation||543.19||Standard Deviation||46,904.33|
|Sample Variance||2,95,059.60||Sample Variance||22000,16,261.88|
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|
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.
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.