Private Gross Fixed Capital Formation as a Predictor of Gross Domestic Product

The report aims to analyze whether Private Gross Fixed Capital Formation is a good predictor of Gross Domestic Product of the country. The report includes trend analysis, linear relationship between GFCF and GDP, hypothesis testing, and goodness of fit of the model.

Running head: STATISTICS
Statistics
Name of the Student
Name of the University
Course ID

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Table of Contents
Question 1........................................................................................................................................2
Question 2........................................................................................................................................2
Question a....................................................................................................................................2
Question b....................................................................................................................................4
Question 3........................................................................................................................................5
Question a....................................................................................................................................5
Question b....................................................................................................................................5
Question 4........................................................................................................................................6
Question a....................................................................................................................................6
Question b....................................................................................................................................7
Question c....................................................................................................................................7
Question 5........................................................................................................................................8
Question a....................................................................................................................................8
Question b..................................................................................................................................10
Question 6......................................................................................................................................10
Summary report.........................................................................................................................10
References......................................................................................................................................12

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Question 1
Screenshot of the data set
Question 2
Question a
Mar-1986
Oct-1987
May-1989
Dec-1990
Jul-1992
Feb-1994
Sep-1995
Apr-1997
Nov-1998
Jun-2000
Jan-2002
Aug-2003
Mar-2005
Oct-2006
May-2008
Dec-2009
Jul-2011
Feb-2013
Sep-2014
Apr-2016
Nov-2017
0
5000
10000
15000
20000
25000
Private Gross Fixed Capital Formation
(GFCF)
Quarter
GFCF(in $ million)
Figure 1: Movement of GFCF series

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The figure above summarizes movement of gross fixed capital formation series. The
series constitutes an overall upward rising trend. The GFCF series shows very much fluctuations
in the movement. This is because gross fixed capital formation especially spending on equipment
and machinery is the most volatile component of GDP. This is because investment decision is
long term process. Once demand shifts due to cyclical fluctuation investment varies as well. For
this this reason, the series shows much fluctuation.
Mar-1986
Oct-1987
May-1989
Dec-1990
Jul-1992
Feb-1994
Sep-1995
Apr-1997
Nov-1998
Jun-2000
Jan-2002
Aug-2003
Mar-2005
Oct-2006
May-2008
Dec-2009
Jul-2011
Feb-2013
Sep-2014
Apr-2016
Nov-2017
0
100000
200000
300000
400000
500000
600000
Gross Domestic Product (GDP)
Quarter
GDP (in $ million)
Figure 2: Movement of GDP series
Like gross fixed capital formation GDP also shown an overtime increasing trend. The
series is more or less stable unlike GFCF. This is because there are various other components in
GDP other than GFCF that make GDP relatively stable.

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Question b
0 5000 10000 15000 20000 25000
0
100000
200000
300000
400000
500000
600000
Scatter plot
GFCF
GDP
Figure 3: Relationship between GFCF and GDP
In order to analyze the relationship between GFCF and GDP, scatter plot has been
developed between the two variables1. The scatter plot shows a positive relationship between
GFCF and GDP. That means GDP increases with increase in GFCF.
1 Lewis-Beck Colin and Michael Lewis-Beck, Applied Regression: An Introduction Vol.22 (Sage Publication, 2015).

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Question 3
Question a
Table 1: Summary of GFCF and GDP
GFCF GDP
Mean 13007.56 Mean 231003.70
Standard Error 454.08 Standard Error 10941.05
Median 12792.50 Median 194937.50
Mode #N/A Mode #N/A
Standard
Deviation 5217.04
Standard
Deviation 125703.04
Sample Variance
27217487.3
3 Sample Variance
15801255204.6
1
Kurtosis -1.29 Kurtosis -1.15
Skewness 0.04 Skewness 0.48
Range 18401 Range 437135
Minimum 4201 Minimum 62216
Maximum 22602 Maximum 499351
Sum 1716998 Sum 30492488
Count 132 Count 132
Question b
Table 2: Correlation matrix
GFCF GDP
GFCF 1
GDP
0.87422
6 1
The coefficient of correlation shows strength and direction of the relationship. The
estimated correlation coefficient between GFCF and GDP is 0.87. The positive correlation

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coefficient suggests a positive relation between GDP and GFCF2. In other words, increase in
GFCF increase GDP as well. The obtained value of correlation coefficient is closer towards 1,
the line of perfect correlation. This therefore indicates a strong relationship between the two
variables.
Question 4
Question a
In order to explain the relationship between GFCF and GDP following has been
developed
GDP=β0+(β1 × GFCF)
‘ β0’ is the intercept terms of the regression and ‘ β1’ is the slope coefficient. In the above model,
GDP is taken as dependent variable and GFCF is taken as independent variable. Gross domestic
product (GDP) is a measure expressing monetary value of goods and services produced within a
nation. GDP is often expressed as a sum of expenditure on four different components –
consumption, investment, government expenditure and net export. Changes on any one
component leads to a change in GDP. Now spending on machinery and equipment is a part of
gross fixed capital formation which is include as investment in GDP computation3. Therefore,
changes in spending on machinery and equipment affects GDP through changing investment.
Following the macroeconomic theory in the above model GDP is considered as dependent
variable and GFCF is considered as independent variable.
2 Asis Kumar Chattopadhyay and Tanuka Chattopadhyay, Statistical Methods For Astronomical Data
Analysis (Springer New York, 2014).
3 Sebastian Dullien et al, Macroeconomics In Context (Routledge, 2015).

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Question b
Table 3: Regression result
Regression Statistics
Multiple R 0.87
R Square 0.76
Adjusted R Square 0.76
Standard Error
61265.4
9
Observations 132
ANOVA
df SS MS F Significance F
Regression 1 1.58E+12 1.58E+12 421.482 0.000
Residual 130 4.88E+11 3.75E+09
Total 131 2.07E+12
Coefficients
Standard
Error t Stat
P-
value Lower 95% Upper 95%
Intercept -42990.5422 14371.9119 -2.9913 0.0033 -71423.6511 -14557.4333
GFCF 21.0642 1.0260 20.5300 0.0000 19.0344 23.0941
Based on the regression result, the proposed model can be can be estimated as
GDP=−42990.5422+(21.0642×GFCF )
Question c
The estimated coefficient of the model is 21.0642. Positive estimated coefficient
indicates a positive relation between the model dependent and model independent variable. In the
context of proposed model, the positive estimated coefficient suggests a positive relation

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between GFCF and GDP4. More preciously, GDP increases with an associated increase in GFCF
and decreases with decrease in GFCF.
Question 5
Question a
Test for significance of linear relationship between GFCF and GDP.
Hypotheses
Null Hypothesis (H0): The coefficient of GFCF is not significantly different from zero.
β1=0
Alternative Hypothesis (H1): The coefficient of GFCF is significantly different from zero.
β1 ≠ 0
Level of significance
The test has been conducted based on 5% level of significance. The value of chosen level
of significance thus is 0.05.
Level of significance ( α ) =0.05
Test statistics
In order to conduct the proposed hypothesis test ‘t’ test is to be conducted. The estimate
for t statistics is given as follows
4 Samprit Chatterjee and Ali S Hadi, Regression Analysis By Example (John Wiley & Sons, 2015).

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T 0= ^β1− β1
SE ( β1)
This follows t distribution with (n – 2) degrees of freedom and α
2 level of significance.
Rejection region
The null hypothesis is rejected if computed T value fall outside the following region
−t α
2 ,n−2 <T0 <t α
2 ,n−2
−t α
2 ,n−2 and t α
2 ,n−2 are the critical t values for two sided hypothesis5. In other the null hypothesis
is rejected if
|T |>t α
2 ,n−2
Calculation
From the regression result the estimated value of the coefficient is 21.0642. The
associated standard error is 1.0260. Therefore, T value can be computed as
T 0=
^β1−β1
SE ( β1 ) 0.025 , 130
¿ 21.0642
1.0260
¿ 20.5300
Conclusion
5 Anthony R. Ives, "For Testing The Significance Of Regression Coefficients, Go Ahead And Log-Transform Count
Data" (2015) 6(7) Methods in Ecology and Evolution.

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The critical t value for 130 degrees of freedom 0.025 significance level is 1.9784. As the
computed T is greater than critical t, the null hypothesis that the coefficient is not significantly
different zero has been accepted. This in turn means that there exists a valid statistical relation
between GDP and GFCF.
Question b
Goodness of fit of a model depends on the explanatory power of the model. In other
words, more variation in the dependent variable is explained by the independent variable better
fit is the model. This can be understood from the value of R square or coefficient of
determination6. The R square value of the model is 0.76. This indicates that the independent
variable (GFCF) account 76 percent variation in the dependent variable (GDP). As GFCF
explains most of the variation in GDP, the model can be said as a good fit model.
Question 6
Summary report
The report aims to analyze whether Private Gross Fixed Capital Formation is a good
predictor of Gross Domestic Product of the country. Gross Domestic Product of a nation
measures sum of values of all produced goods and services in the country7. Total gross fixed
capital formation presents changes in physical stock of capital in a nation and included in GDP
as investment expenditure. This includes expenditure carried out by both public and private.
Now private fixed capital formation include investment made by private individual on machinery
and equipment. An increase in investment in machinery and equipment likely to increase
6 John Fox, Applied Regression Analysis And Generalized Linear Models (SAGE Publications, 2015).
7 Ben J Heijdra, Foundations Of Modern Macroeconomics (Oxford university press, 2017).

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productivity capacity of a nation which in turn influences gross domestic product in positive
way.8 Private gross fixed capital formation thus likely to an important predictor of gross
domestic product of a nation.
In order to test the claim data has been collected on private gross fixed capital formation
and gross domestic product of Australia for a sample period of 132 quarters (March 1986 to
December 2018). The trend analysis indicates that both the series gross fixed capital formation
and GDP increases overtime. The GFCF series however is more volatile than the composite GDP
series. This is because in GDP there are components other than GFCF that offset the volatility in
private capital formation resulting in stability in GDP series. The estimated linear relationship
between GFCF and GDP shows that GFCF is significantly influences GDP is a positive way.
The sample data therefore suggests that GFCF is statistically significant and good predictor of
GDP.
References
Chatterjee, Samprit and Ali S Hadi, Regression Analysis By Example (John Wiley & Sons, 2015)
8 Gregory N Mankiw, Brief Principles Of Macroeconomics (Cengage Learning, 2014).

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Chattopadhyay, Asis Kumar and Tanuka Chattopadhyay, Statistical Methods For Astronomical
Data Analysis (Springer New York, 2014)
Colin, Lewis-Beck and Michael Lewis-Beck, Applied Regression: An Introduction Vol.22 (Sage
Publication, 2015)
Dullien, Sebastian et al, Macroeconomics In Context (Routledge, 2015)
Fox, John, Applied Regression Analysis And Generalized Linear Models (SAGE Publications,
2015)
Heijdra, Ben J, Foundations Of Modern Macroeconomics (Oxford university press, 2017)
Ives, Anthony R., "For Testing The Significance Of Regression Coefficients, Go Ahead And
Log-Transform Count Data" (2015) 6(7) Methods in Ecology and Evolution
Mankiw, N Gregory, Brief Principles Of Macroeconomics (Cengage Learning, 2014)