HI6007 Statistics: Retail Turnover and Final Consumption Analysis

This assignment delves into the statistical analysis of retail turnover per capita and its relationship with final consumption expenditure. It uses percentage analysis, graphical representation, and numerical summaries to understand the connection between these two variables. The analysis includes calculating means, standard deviations, and correlation coefficients. A simple regression model is employed to predict final consumption expenditure based on retail turnover, with the coefficient of determination and t-tests used to assess the model's validity and significance. The assignment concludes that retail turnover positively and significantly impacts final consumption expenditure.

Name
Institution
Course
Date

a)
Sep-1983
Jan-1985
May-1986
Sep-1987
Jan-1989
May-1990
Sep-1991
Jan-1993
May-1994
Sep-1995
Jan-1997
May-1998
Sep-1999
Jan-2001
May-2002
Sep-2003
Jan-2005
May-2006
Sep-2007
Jan-2009
May-2010
Sep-2011
Jan-2013
May-2014
Sep-2015
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
Relationship between final consumption expenditure
and retail turn over per capita
per capita (%) final consumption (%)
quarter
percentage
b)
1200.0 1400.0 1600.0 1800.0 2000.0 2200.0 2400.0 2600.0 2800.0 3000.0 3200.0
0
50000
100000
150000
200000
250000
Retail Turnover-Final Consumption Expenditure
relationship
Retail Turnover
Final Consumption Expenditure
Final consumption expenditure is used in the y-axis while the retail turnover per capita is
used in the x-axis. This is because the final consumption depends on the retail turnover
c)
The following output represents the numerical summary of the two variables.

Retail turnover per
capita;
FINAL CONSUMPTION
EXPENDITURE ;
Mean 2205.76 Mean 146019.85
Standard Error 47.46 Standard Error 4098.05
Median/QR2 2180.20 Median 139137.00
Standard Deviation 543.19 Standard Deviation 46904.33
Sample Variance 295059.60 Sample Variance
2200016261.8
8
Minimum 1455.90 Minimum 81889.00
Maximum 3014.60 Maximum 233148.00
coefficient of
variation 0.25 coefficient of variation 0.32
QR1 1652.95 QR1 103558.5
QR3 2793.4 QR3 192800.5
The average shows that the final expenditure was higher than the turnover per capita.
The standard deviations indicated that there was greater variability in final expenditure
than in the turnover per capita. The quartile range indicates that most of the
observations for the two variables were in the third quartile. The coefficient of variation
indicates that the ratio between standard deviation and mean was higher for the final
consumption expenditure than that of the turnover per capita (Taylor, 2011).
d)
a)
Retail turnover per capita;FINAL CONSUMPTION EXPENDITURE ;
Retail turnover per capita; 1
FINAL CONSUMPTION EXPENDITURE ;0.98769713 1
The correlation coefficient indicated that an increase in retail turnover led to an increase
in the final consumption (Taylor, 2011).
a)
Simple regression model
Coefficien
ts
Standar
d Error t Stat
P-
value
Intercept -42102.53 2700.17 -15.59 0.00
Retail turnover per
capita; 85.29 1.19 71.74 0.00

The model indicated that for one unit increase in the retail turnover per capita the final
consumption expenditure increased by 85.29 units.
b)
The coefficient of determination for the model was 97.56% this indicated that 97.56% of
the model was explained by retail turnover per capita which implied that the model was
perfect for the data (Brown, 2013).
c)
A t-test to investigate whether retail turnover led to a positive increase for the final
expenditure.
Coefficient
s
Standar
d Error t Stat
P-
value
Retail turnover per
capita; 85.29 1.19 71.74 0.00
The test had a p-value of 0.00 which was less than 0.05 level of significance thus the
retail turnover lead to a positive and significant increase in the final consumption
expenditure.
d)
The standard error for the predictor variable was 1.19 which indicated that there was no
greater variability in the model and hence the model was fit for the data.

References
Taylor, R. (2011). Interpretation of the correlation coefficient: a basic review. Journal of
diagnostic medical sonography, 6(1), 35-39.
Brown, J. D. (2013). The coefficient of determination. Available at:
https://files.eric.ed.gov/fulltext/EJ1134515.pdf