Analysis and Interpretation of Simple Linear Regression Model

The provided content discusses a simple linear regression analysis between retail turnover per capita and consumption expenditure. The results show a strong positive correlation between the two variables, with an R-squared value of 0.975545621, indicating that approximately 97.5% of the variation in consumption expenditure can be explained by retail turnover per capita. The slope coefficient is 85.287, suggesting that for every $1 increase in retail turnover per capita, there is a corresponding $85.2 million increase in consumption expenditure. The intercept is -42102.5, indicating that when retail turnover per capita is zero, the initial value of consumption expenditure is -$42102.5 million. The analysis also rejects the null hypothesis that final consumption expenditure has no effect on retail turnover per capita, suggesting a positive and significant relationship between the two variables.

Question NO: 1 A.
Australia: Direction of exports
Top 8 export markets for goods and services
A$ bn
Country
1
2
3
4
5
6
7
8
2004-
05
2014-
15
Subtotal 103.3 223.5
source: DFAT and Austrade
services
Australia: Direction of exports
Top 8 export markets for goods and
China 15.9 90.3
Japan 28.2 46.6
United States 13.9 20.5
Republic of Korea 11 20.5
India 7.1 12.7
New Zealand 12.2 12.3
Singapore 5.8 12
United Kingdom 9.2 8.6

B.
Top 8 export markets for goods and services
A$ bn
Country 2004-0
5
2014-1
5
China 15.9 90.3
Japan 28.2 46.6
United States 13.9 20.5
Republic of Korea 11 20.5
India 7.1 12.7
New Zealand 12.2 12.3
Singapore 5.8 12
United Kingdom 9.2 8.6
Subtotal 103.3 223.5
source: DFAT and Austrade
Changing into Percentage table
Top 8 export markets for goods and services
A$ bn
Country 2004-05 2014-15
China 15.39% 40.40%
Japan 27.30% 20.85%
United States 13.46% 9.17%
Republic of Korea 10.65% 9.17%
India 6.87% 5.68%
New Zealand 11.81% 5.50%

Singapore
United Kingdom
5.61%
8.91%
5.37%
3.85%
Subtotal 100.00% 100.00%
source: DFAT and Austrade

2004-05
China Japan United States Republic of Korea
India New Zealand Singapore
United Kingdom
C. Observation from Question (A) and (B)
In the diagram A, it is clearly seen that the export market for the goods and services in 2014-15 has
increased as compared to that of the 2004-05 excluding UK which has fallen by 0.6 billion. Among
the 8 countries, China has the highest number of exports comparing to that of other countries.
Likewise, the next figure shows the percentage change in the exports of goods and services.
This figure shows that the exports during the 2004-05 was high as compared to the year
2014-15. It means that the exports market of these 8 top countries has fallen down than in the
year 2004-05.
Analyzing both the figure, although in the first figure it shows that the export market for the
year 2014-15 was higher in comparison to that of previous year but in actual the percentage
change in the export market was fallen down certain percentage excluding China market whose
exports market remains higher throughout the two given years.
0.134
0.106
0.270.068
0.118
0.153
0.089
1

Question 2:
(A) and (B)
Classe
s
Frequenc
y
Relative
frequenc
y
Cumulativ
e
frequency
Cumulativ
e relative
frequency
Lower
bound
Upper
bound
Mid-
point
30-40 2 0.05 2 0.05 30 40 35
40-50 4 0.1 6 0.15 40 50 45
50-60 8 0.2 14 0.35 50 60 55
60-70 11 0.275 25 0.625 60 70 65
70-80 8 0.2 33 0.825 70 80 75
80-90 5 0.125 38 0.875 80 90 85
90-100 2 0.05 40 0.925 90 100 95
Total 40 3.8
C.
Classe
s
90-80-70-60-50-40-30-
0
0.00.0
0.07
0.
0.12
0.1
0.0.
0.22
Relative Frequency
Histogram0.
Relative
Frequecy

D.
40
30
20
10
0
E. Proportion of grade less than 60 = 35.00%
F. Proportion of grade more than 70= 37.50%
70-80 80-90
60-70
40-50
30-
Ogive
Cumulative
frequency

Question NO: 3
An increasing trend is evident in retail turnover per capita. This trend is observed from September 1987
until March 2019.
A continuously increasing Trend is observed from September 1987 till present for the final consumption
expenditure.
0.0
Sept-1987 Mar-1991 Sept-1994 Mar-1998 Sept-2001 Mar-2005 Sept-2008 Mar-2012
800.
1600.
2400.
3200.
Retail turnover per capita - Chain
Volume Measures ; Total
(State) ; Unit
$RETAIL TURNOVER

2400
1800
1200
600
B.
0 0 0 0 0
FINAL CONSUMPTION
EXPENDITURE: Chain
3200.2400.1600.0
Retail turnover per
800.0.
0
6000
1200
1800
2400
Scatter diagram between the final
consumption expenditure and the Retail
Final Consumption
expenditure

The above figure shows the scatter diagram between the final consumption expenditure and the
retail turnover per capita for the quarterly time series data for the period September 1983 to
March 2018. Here, retail turnover per capita is shown in X-axis whereas final consumption is
shown in Y-axis. Retail turnover per capita increases as the final consumption increases which
shows the direct relationship between these two. Final consumption expenditure is an
independent variable whereas the retail turnover per capita is a dependent variable. The
independent variable is the one the experimenter controls. The dependent variable is the variable
that changes in response to the independent variable. The two variables may be related by cause
and effect. If the independent variable changes, then the dependent variable is affected.
(Sources
 Carlson, Robert. A concrete introduction to real analysis. CRC Press, 2006. p.183.
 Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN
0-19-920613-9
 Everitt, B. S. (2002). The Cambridge Dictionary of Statistics (2nd ed.). Cambridge UP.
ISBN 0-521-81099-X.
Hence, in the given data as the independent variable changes, the dependent variable also
in response to it.
C. Summary table:
Retail turnover Consumption Expenditure
Mean 2205.8 146020
Median 2180.2 139137
Max 3014.6 233148
Min 1455.9 81889
Range 1558.7 151259
Standard deviation 543.1938837 46904.33095
Variance 295059.5953 2200016262
Coefficient of variation 24.63% 32.12%
Quartile 1 2180.525 103363.75
Quartile 2 42451.8 138567.5

Quartile 3 138852.25 192273.5
D. From the Excel formula CORREL =(CORREL(B4:B134,C4:C134)^2), coefficient of
correlation( r^2) = 0.975545 ( The above calculation is done in excel, if need reference can
provide the excel file too)
E. Simple linear equation
y = 85.287x - 42103
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.98769713
R Square 0.975545621
Adjusted R Square 0.975356052
Standard Error 7363.225229
Observations 131
ANOV
A
df SS MS F
5146.12886
Significanc
e F
Regression 1 2.79008E+11 2.79008E+11 4 7.9451E-106
Consumpption
expenditure
3200.2400.1600.0
Retail
turnover
800.0.
0
6000
0
12000
0
18000
0
24000
0
Simple Linear Regression
Model

Residual 129 6994004064 54217085.77
Total 130 2.86002E+11
Coeffici Standar P- Lower Upper Lower Upper
ents d Error t Stat value 95% 95% 95.0% 95.0%
-42102. 2700.16 -15.592 1.819E -47444. -36760. -47444.8 -36760.
Intercept 533 504 578 -31 876 191 76 19
RETAIL 85.2868 1.18888 71.7365 7.95E- 82.934 87.6390 82.93456 87.639
TURNOVE
R
091 963 239 106 562 564 188 056
e)
The regression equation for predicting consumption expenditure on the basis of retail turnover is given
by consumption expenditure = -42103 + 85.287*Retail turnover per capita
From the above regression equation, the value of stope is observed to be 85.29. The interpretation of
slope is with 1$ increase in Retail turnover per capita, there is 85.2 million $ increase in consumption
expenditure.
From the above regression equation, the value of intercept is observed to be -42102.5; the initial value of
consumption expenditure is -$42102.5 million when Retail turnover per capita is 0$. This value has no
practical significance as the consumption expenditure cannot be negative.
f)
The coefficient of determination (denoted by R square) is observed to have a value of 0.975545621.
The interpretation of the coefficient of determination is that is 97.5% variation in consumption
expenditure which is explain by retail turnover per capita. This percentage is is extremely high and
hence the fitted model is said to be a good fit for the data.
g)
The null hypothesis, Ho: final consumption expenditure has no effect on retail turnover per capita. Beta1

= 0.
An alternative hypothesis, H1: final consumption expenditure positively and significantly increases with
retail turnover per capita. Beta1 > 0.
With t=71.7, p<5%, the null hypothesis is rejected at 5% level of significance. There is sufficient
evidence to conclude that the final consumption expenditure positively and significantly increases with
retail turnover per capita.
h)
The Standard error of the estimate, (denoted by SE) is observed to have a value 7363.22. This value of
standard error is considered low. And hence the predictions based on the above linear regression model
are considered reliable.