STA510 Computer Application Project: GFCF and Australian GDP Analysis

This assignment analyzes the relationship between Private Gross Fixed Capital Formation (GFCF) and the Australian Gross Domestic Product (GDP) from 1986 to 2018. The project uses data from the Australian Bureau of Statistics, employing graphical descriptive techniques to visualize trends in GFCF and GDP over time, and examining their relationship through scatter plots. Numerical descriptions, including mean, standard error, and correlation coefficients, are provided to summarize the data. Simple linear regression is used to model the relationship, with the model equation and coefficient interpretations presented. The significance of the linear relationship is tested through hypothesis testing, and the fitness of the linear model is assessed. The analysis concludes that GFCF is a good predictor of Australian GDP, supported by a strong positive correlation and statistical significance. The project utilizes Excel for calculations and visualizations, offering insights into the economic relationship between GFCF and GDP.

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COMPUTER APPLICATIONS ASSIGNMENT
by Student’s Name
Code + Name of Course
Professor’s Name
University
City (State)
Date

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1. The table below is a screenshot of the first 10 rows of the sheet containing the data to be
analyzed for this assignment problem (Australian Bureau of Statistics, 2019).
2. Graphical descriptive techniques
a. Movements of the data series
Graphical display if the change in GFCF with change in time.
From the graph displayed above it can be concluded that the amount of GFCF has
been on an increasing trend from March 1986 to may 2008. From2008 to 2018 the
data do have a level trend with minimal increase and decrease in between.

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Graphical display of the change in GDP overtime
Looking at the graph if the GDP values from 1986 to 2017 shown above its evident
that the GDP of Australia have been on an increasing trend for the 85 years period.
From just below $ 100000 million in 1989 the GDP of the country surpassed $
500000 million as of November 2017.
b. The relationship between GFCF and GDP
To analyze the relationship between the variables GFCF and GDP, a scatter plot was
drawn as displayed in the figure below.
When the line of best fit was derived the value of R squared was obtained as
0.7643. This value indicates a strong positive relationship between GFCF and GDP. It

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can be explained as, around 76.43% of the changes in the values of the GDP are as a
result of the fluctuations of the GFCF values.
3. Numerical description
a. Numerical summary of GFCF and GDP data
GFCF ($ millions) Gross Domestic Product ($ millions)
Mean 13007.56061 Mean 231003.697
Standard Error 454.0848884 Standard Error 10941.0456
Median 12792.5 Median 194937.5
Mode #N/A Mode #N/A
Standard Deviation 5217.038176 Standard Deviation 125703.0437
Sample Variance 27217487.33 Sample Variance 15801255205
Kurtosis -1.290158186 Kurtosis -1.148915006
Skewness 0.03992977 Skewness 0.480689495
Range 18401 Range 437135
Minimum 4201 Minimum 62216
Maximum 22602 Maximum 499351
Sum 1716998 Sum 30492488
Count 132 Count 132
b. Strength and direction of relationship
The two data sets have strong positive relationship. This implies that changes in
the GCFC variable have a positive impact on the value of the GDP. The value of the
coefficient of determination is 0.8742 which is an evidence of the strong positive
association.
4. Simple linear regression
a. Linear regression model

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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.874226153
R Square 0.764271367
Adjusted R Square 0.76245807
Standard Error 61265.49324
Observations 132
ANOVA
df SS MS F Significance F
Regression 1 1.58201E+12 1.58201E+12 421.4815842 1.28322E-42
Residual 130 4.8795E+11 3753460662
Total 131 2.06996E+12
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -42990.54217 14371.91191 -2.991289012 0.003324408 -71423.65108 -14557.43326 -71423.65108 -14557.43326
GFCF ($ millions) 21.06422929 1.026021052 20.53001666 1.28322E-42 19.03436935 23.09408924 19.03436935 23.09408924
The table above gives the simple linear model that can be used to explain the
relationship between the GFCF and the GDP of Australia. The dependent variable is
the GDP while the independent variable is the GFCF. The GDP has been chosen to be
the independent variable as it values do depend on the performance of other aspects
of the economy. One of these aspects being the Private Gross Fixed Capital
Formation which has been selected as the independent variable.
b. Model estimation
From the excel output above the equation y=−42990+21.064 x can be used to
calculate the value of the GDP given any values of the GFCF.
c. The coefficient of the GFCF is 21.064. this can be interpreted as a change in the
GFCF value by one million will increase the GDP value by 21.064 million.
5. Statistical techniques
a. Testing for the significance of the simple linear relationship
This will be done through hypothesis testing which entails 6 major steps.
1st step; Specify the hypothesis
In this case the hypothesis to be tested will be
Ho :Coefficinet of x=0
Vs
H1 :Coefficient of x ≠0
2nd step is to determine the level of significance.

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The test will be carried out at 5% level of significance. This will mean the value of
α=0.05
3rd step; stating the decision rule.
This is a t test and the decision rule is to reject the null hypothesis if the observed
pvalue <0.05.
Step 4: calculate the test statistic
This has been calculated using excel as displayed in the regression model table above.
The coefficient’s p_ value is 1.2832∗10−42.
Step 5: decision making
Being that the value of the p_value is less than 0.05, we reject the null hypothesis and
conclude that, at 95% level of significance there is a significant linear relationship
between GFCF and the GDP data.
Step 6; Interpret the decision
From the question to test whether there is a significant linear relationship between the
GFCF and GDP data, we can use the hypothesis test to ascertain that the notion that
the growth of the GFCF contributes to the GDP growth of a nation is a fact as it is
supported statistically.
b. Fitness of the linear model
To assess the fitness of a linear model, the F statistics is used. From the output of the
linear regression in Q4 above the F statistic is 1.2832∗10−42 ,wwhich is lower than
0.05. At 95% level of significance, it can be concluded that the model is a significant
fit to illustrate the relationship between the two variables (Fay & Proschan, 2010).
6. Summary report
The aim of this study is to investigate if the Private Gross Fixed Capital
Formation is an appropriate predictor of the Australian GDP. To obtain this objective past
data from the Australian Bureau of Statistics was collected from the year 1986 to 2018
and several analyses conducted.
Graphical display of the data indicated that there has been a rising trend in the
values of the GFCF and GDP data in Australia over the years. When the association of
the two data sets was evaluated using a scatterplot, it was observed that the GFCF has a
strong positive correlation with the GDP values. This finding means that as the GFCF

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increases the GDP of Australia also goes up. Formulating a line of best fit gave the
equation y=−42990+21.064 x as the best predictor of the GDP using the GFCF data.
Overall, GFCF for the period since 1986 to 2018 have a mean of $ 13007 million with
standard deviation of $ 5217 million. On the other hand, the GDP of the nation have a
mean of $ 231003 million with a deviation of $ 125703 million.
Formulating a linear programming model gave the value of R squared as 0.7642,
this supports the initial finding of a strong positive correlation between GFCF and GDP
and farther illustrates that at least 76% of the changes in the GDP are explained by the
changed in the GFCF data. The hypothesis test result farther proves that the coefficient of
x in the equation y=−42990+21.064 x is not zero. This finding means that GFCF have
an impact on the GDP hence can be stated to be a good predictor of the Australian GDP.

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References
Australian Bureau of Statistics, 2019. Australian National Accounts: National Income,
Expenditure and Product, Dec 2018. [Online]
Available at: http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/5206.0Dec%202018?
OpenDocument
[Accessed 13 May 2019].
Fay, M. P. & Proschan, M. A., 2010. Wilcoxon–Mann–Whitney or t-test? On assumptions for
hypothesis tests and multiple interpretations of decision rules. Statistics Surveys, Volume 4, pp.
1-39.