HI6007 Statistics and Research Methods for Business Decision Making: Group Assignment 2 Answer
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.
- & (b)
|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.
- & (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):
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.
- 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.
- 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.
- 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.