STATISTICS FOR BUSINESS DECISIONS
UNIT NO: HI6007
SUBMITTED TO: SUBMITTED BY:
ANNE BEADNOK MANPREET SINGH (EMV3847)
AVNEET SINGH (DY31651
SARABJIT KAUR (AZZ3789)
RENUKA MEHTA (SEI3053)
Table of Contents
TOC o “1-3” h z u Question 12Question a2Question b2Question c3Question 23Question a3Question b4Question c4Question d5Question e5Question f5Question 36Question a6Question b7Question c8Question d8Question e9Question f PAGEREF _Toc8161002 h 10Question g PAGEREF _Toc8161003 h 10Question h10References PAGEREF _Toc8161005 h 11
Question 1Answer 1 (a)
Figure 1: Values of Australian export by export
Answer 1 (b)
Figure 2: Percentage values of Australian export by country
Answer 1 (c)
The values of Australian export to China increased significantly between 2004-05 and 2014-2015 with values of export increased from 15.9 billion dollars in 2004-05 to 90.3 billion dollar in 2014-15. For other countries like Japan, United States, Republic of Korea and Singapore values of export though increase but not as much as China. In case of New Zealand and United Kingdom values of export remain almost same between the two periods.
In absolute terms value of export to the selected destination though have increased in 2014-15 but the percentage share of Australian export to these destination has declined. The only omission has been discovered or China with percentage share of export has enlarged from 15.4 percent in 2004-05 to 40.4 percent in 2014-15.
Question 2Answer 2 (a)
Table 1: Frequency and relative frequency distribution
Classes Frequency Relative Frequency
30-40 2 0.05
40-50 4 0.1
50-60 8 0.2
60-70 11 0.275
70-80 8 0.2
80-90 5 0.125
90-100 2 0.05
Total 40 1
Answer 2 (b)
Table 2: Cumulative frequency distribution and cumulative relative frequency distribution
Classes Cumulative Frequency (less than) Cumulative Frequency (more than) Cumulative Relative Frequency (less than) Cumulative Relative Frequency (more than than)
30-40 2 40 5 100
40-50 6 38 15 95
50-60 14 34 35 85
60-70 25 26 62.5 65
70-80 33 15 82.5 37.5
80-90 38 7 95 17.5
90-100 40 2 100 5
Answer 2 (c)
Figure 3: Relative frequency histogram
Answer 2 (d)
Figure 4: Ogive
Answer 2 (e)
Proportion of grades less than 60
1440=0.35Answer 2 (f)
Proportion of grades more than 70
Answer 3 (a)
Figure 5: Trend in retail turnover per capita
Figure 6: Trend in final consumption expenditure
The trend analysis of retail turnover per capita discloses that the series has expanded adequately overtime. In case of final consumption expenditure, the series has constituted a sharply increasing trend.
Answer 3 (b)
Figure 7: Scatter plot between final consumption expenditure and retail turnover per capita
Scatter plot lends a hand to distinguish the connection between a dependent and an independent variable graphically (Chatterjee and Hadi 2015). The above scatter plot wishes to determine the relation between final consumption expenditure and retail turnover per capita over time. The increase in retail turnover per capita likely to increase income of retailers who then can spend more on their consumption expenditure. Retail turnover per capita can strikes the final consumption expenditure in a positive way. For this reason, retail turnover per capita is taken as independent or X variable and final consumption expenditure is taken as dependent or Y variable.
Answer 3 (c)
Table 1: Numerical summary report of retail turnover per capita and final consumption expenditure
Retail turnover per capita Final consumption expenditure
Mean 2205.76 Mean 146019.85
Standard Error 47.46 Standard Error 4098.05
Median 2180.20 Median 139137.00
Mode 2852.80 Mode #N/A
Standard Deviation 543.19 Standard Deviation 46904.33
Sample Variance 295059.60 Sample Variance 2200016261.88
Kurtosis -1.61 Kurtosis -1.30
Skewness 0.07 Skewness 0.31
Range 1558.70 Range 151259.00
Minimum 1455.90 Minimum 81889.00
Maximum 3014.60 Maximum 233148.00
Sum 288954.80 Sum 19128601.00
Count 131.00 Count 131.00
Largest(1) 3014.60 Largest(1) 233148.00
Smallest(1) 1455.90 Smallest(1) 81889.00
CV 24.63 CV 32.12
First Quartile 1652.95 First Quartile 103558.50
Second Quartile 2180.20 Second Quartile 139137.00
Third Quartile 2793.40 Third Quartile 192800.50
Answer 3 (d)
Table 2: Correlation coefficient between final consumption expenditure and retail turnover per capita
Retail turnover per capita Final consumption expenditure
Retail turnover per capita 1
Final consumption expenditure 0.98769713 1
The correlative coefficient between retail turnover and final consumption expenditure is acquired as 0.9877. The positive correlation coefficient indicates a supportive relationship between the two variables. That means an increase in one of the variables likely to increase the other. The value of correlation coefficient is close to 1 meaning a strong association exists between the two variables (Fox 2015).
Answer 3 (e)
Table 3: Result of estimated regression
Multiple R 0.98769713
R Square 0.975545621
Adjusted R Square 0.975356052
Standard Error 7363.225229
df SS MS F Significance F
Regression 1 2.8E+11 2.8E+11 5.1E+03 7.9E-106
Residual 129 7.0E+09 5.4E+07
Total 130 2.9E+11
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -42102.5334 2700.1650 -15.5926 0.0000 -47444.8760 -36760.1907
Retail turnover per capita 85.2868 1.1889 71.7365 0.0000 82.9346 87.6391
From the regression result, the estimated regression equation is obtained as
Final consumption expenditure= -42102.5334+( 85.2868 ?Retail turnover per capita)Estimated co-efficient of the linear model is 85.2868. The positive coefficient implies a positive relation between retail turnover per capita and that of final consumption expenditure (Schroeder, Sjoquist and Stephan 2016). That simply directs an increase of retail turnover per capita increases final consumption expenditure and vice-versa.
Answer 3 (f)
The coefficient of determination from the regression model is obtained as 0.9755. This implies retail turnover per capita explains nearly 98 percent variation in final consumption expenditure (Darlington and Hayes 2016).
Answer 3 (g)
The regression coefficient for retail turnover per capita is 85.2868. The positive coefficient per capita retail turnover has a positive impact on final consumption expenditure. That final consumption increases with increase in retail turnover per capita. Statistical significance of the estimated coefficient can be tested from the associated p value of the coefficient (Brook 2018). The obtained p value for the coefficient is 0.0000. The p value is less than 5% significance level indicating rejection of null hypothesis of no statistically significant relation between retail turnover per capita and final consumption expenditure. Therefore, final consumption expenditure favorably and remarkably goes up with rise in retail turn over at the 5% significant level. Answer 3 (h)
Standard error of an estimate measures the average distance between observed value and that of the fitted value. In other words, it gives an estimate of how good the regression model is in explaining the dependent variable (Hox 2017). Smaller values indicate a good fit since then observed values are closer to the fitted line. The obtained standard error of the estimate is 1.1889. This means the average distance between the fitted line and observed data point is 1.18 percent. The relatively small value of standard error indicates that the model is a good fit model.
Brook, R.J., 2018. Applied regression analysis and experimental design. Routledge.
Chatterjee, S. and Hadi, A.S., 2015. Regression analysis by example. John Wiley & Sons.
Darlington, R.B. and Hayes, A.F., 2016. Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.
Fox, J., 2015. Applied regression analysis and generalized linear models. Sage Publications.
Hox, J.J., Moerbeek, M. and Van de Schoot, R., 2017. Multilevel analysis: Techniques and applications. Routledge.
Schroeder, L.D., Sjoquist, D.L. and Stephan, P.E., 2016. Understanding regression analysis: An introductory guide (Vol. 57). Sage Publications.