Curtin University ECOM2000 Econometrics Project: Data Analysis Report

This econometrics project analyzes the Environmental Kuznets Curve (EKC) hypothesis, which examines the relationship between a country's national income and environmental degradation. The project uses data from 199 countries/areas and focuses on CO2 emissions per capita, GDP per capita, population density, and urban population percentage. The analysis includes descriptive statistics, confidence intervals, and a multiple regression model to assess the impact of independent variables on CO2 emissions. Key findings include the R-squared value of the regression model, the statistical significance of population density and urban population, and the correlation between GDP per capita and CO2 emissions. The project also calculates the level of per capita GDP where the marginal effect of per capita GDP on CO2 emissions changes its sign. The assignment concludes with a rejection of the null hypothesis for population density and urban population and a list of relevant bibliography.

ECONOMETRICS
Student name
Course title
Date

1
Question 1
0 20 40 60 80 100 120 140 160 180
0.000
10000.000
20000.000
30000.000
40000.000
50000.000
60000.000
70000.000
CO2 emissions per capita against per capita
GDP
CO2 emission per capita
GDP per capita
CO2 emissions per capita
Question 2
Sample statistics
Variable Mean Variance Standard
deviatio
n
Minimu
m
Maximu
m
Range
CO2 emission per
capita
4921.24
0
43322463.94
3
6581.98
0
20.755 59252.32
6
59231.57
1
GDP per capita 12.789 360.970 360.970 0.091 156.127 156.036
Population density 295.926 1904823.486 1380.15
3
0.100 17958.80
0
17958.70
0
Urban
population(percentage
)
56.806 558.316 23.629 9.400 100.000 90.600
Formulas used
Variable Mean Variance Standard deviation Minimum Maximum Range
CO2 emission per capita =AVERAGE(D3:D400) =VAR(D3:D400) =STDEV(D3:D400) =MIN(D3:D400) =MAX(D3:D400) =O5-N5
GDP per capita =AVERAGE(E3:E400) =VAR(E3:E400) =VAR(E3:E400) =MIN(E3:E400) =MAX(E3:E400) =O6-N6
Population density =AVERAGE(F3:F400) =VAR(F3:F400) =STDEV(F3:F400) =MIN(F3:F400) =MAX(F3:F400) =O7-N7
Urban population(percentage) =AVERAGE(G3:G400 =VAR(G3:G400) =STDEV(G3:G400) =MIN(G3:G400) =MAX(G3:G400) =O8-N8

2
)
Question 3
Confidence interval
Description Data
Significance
level 0.1
Standard
deviation 6581.980245
Sample size 398
Confidence
Interval 542.6780993
Excel Formulas
Description Data
Significance level 0.1
Standard deviation =STDEV(D3:D400)
Sample size =COUNT(D3:D400)
Confidence Interval
=CONFIDENCE.NORM(K17,K18,K19
)
The confidence interval provides an estimate of the mean by showing the range in which the true
mean lies.1 It is determined using the standard deviation for the whole population, the sample
size and a confidence significance level. With a significance level of 0.1, the confidence interval
is 542.68. Therefore, we are 90% confident that the population mean of CO2 emissions per
capita lies between 4378.560 kilograms per capita per year or 5463.92 kilograms per capita per
year.
1 Mishra, Srikanta, and Akhil Datta-Gupta. "Regression Modeling and Analysis." Applied
Statistical Modeling and Data Analytics, 2018, 69-96. DOI:10.1016/b978-0-12-803279-4.00004-
3.

3
Question 4
Regression Model Output
SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.675117803
R Square 0.455784048
Adjusted R Square 0.450244954
Standard Error 4880.24007
Observations 398
ANOVA
df SS MS F Significance F
Regression 4 7839038131 1959759533
82.2849506
1 1.08642E-50
Residual 393 9359980054
23816743.1
4
Total 397
1719901818
5
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept
-
921.2412718 685.3529655 -1.34418514
0.17966393
7 -2268.65796 426.1754162 -2268.65796 426.1754162
GDP per capita 332.2879436 33.59052205
9.89231257
2 9.45522E-21 266.2483519 398.3275352 266.2483519 398.3275352
GDP per capita
squared
-
2.160392352 0.333804316
-
6.47203241
3 2.88387E-10 -2.816657851 -1.504126853 -2.816657851 -1.504126853
Population
density
-
0.606258844 0.182238258 -3.32673749
0.00096144
9 -0.964542651 -0.247975037 -0.964542651 -0.247975037
Urban population 51.11413996 14.01702471
3.64657557
7
0.00030152
2 23.55640845 78.67187146 23.55640845 78.67187146
Regression equation is; Y = 332.29X1 – 2.16X2 – 0.606X3 + 51.114X4 – 921.24
Question 5

4
In multiple regression, the R-squared value measures the level of goodness-of-fit of the linear
regression model by indicating the variance between the dependent variable and the explanatory
variables.2 The R2 of the estimated multiple regression is 0.46. This implies that the independent
variables explain a variation of 46% in the CO2 emissions per capita. The goodness of fit of the
regression model is below average, therefore, there is a slightly low fit of the model to the
regression equation.3
Question 6
The regression coefficients provide a deeper insight into the level of significance contributed by
the independent variables to the regression model.4 Population density has a t statistic of -3.3267
with a p-value of 0.00096. Percent of the urban population has a t statistic of 3.6466 with a p-
value of 0.0003. Thus, the variables are statistically significant at a level of 0.1. This implies that
population density and percent of the urban population contribute significantly to CO2 emissions
per capita.5
Question 7
2 Mishra, Srikanta, and Akhil Datta-Gupta
3 Stigum, Bernt P. 2015. Econometrics in a Formal Science of Economics: Theory and the
Measurement of Economic Relations. MIT Press, 2015.
4 Bhatti, M. Ishaq, and Hatem Al-Shanfari. Econometric analysis of model selection and
model testing. Routledge, 2017.
5 Lee, Cheng-Few, and John C. Lee, eds. Handbook of financial econometrics and
statistics. Springer New York, 2015.

5
The null hypothesis for the test is that no non-zero correlation between population density and
CO2 emissions per capita. Conversely, the alternative hypothesis is that a non-zero correlation
between population density and CO2 emissions per capita. The test statistic of the regression
model is estimated by dividing a variable’s coefficient by the standard error.
From the multiple regression results;
Standard error = 0.182238258
Coefficient = -0.606258844
T stat for population density = coefficient
standard error
= -0.606258844
0.182238258
= -3.3267
Using the results of multiple regression, the p-value for population density is 0.00096. Since the
p-value is below the significance level of 0.1, rejection of the null hypothesis is approved.6 There
is enough evidence to show that there is a non-zero correlation between population density and
CO2 emissions per capita. The coefficient of population density is negative at a test size of 1%.
Question 8
Coefficient Interval
6 Hill, R. Carter, William E. Griffiths, and Guay C. Lim. Principles of econometrics. John
Wiley & Sons, 2018.

6
Description Data
Significance level 0.1
Standard deviation 14.01702471
Sample size 398
Confidence Interval 1.155690543
Excel Formulas
Description Data
Significance level 0.1
Standard deviation =M25
Sample size =COUNT(H3:H400)
Confidence Interval =CONFIDENCE.NORM(L32,L33,L34)
The confidence interval illustrates the range of the mean of a variable.7 The coefficient of the
percent of the urban population is 51.1%. The coefficient interval is estimated to be 1.1557.
Therefore, we are confident by 90% that the percent of urban population is either
51.1141+1.1557 or 51.1141 – 1.1557.
Question 9
7 Bhaumik, Sankar Kumar. "Principles of Econometrics: A Modern Approach Using
EViews." OUP Catalogue (2015).

7
0 20 40 60 80 100 120 140 160 180
-5000
0
5000
10000
15000
20000
Predicted CO2 Emission per Capita against GDP
per Capita
predicted CO2 emission per capita
Linear (predicted CO2 emission per capita)
GDP per capita
Predicted CO2 emissions per capita
As illustrated from the model, the relationship between CO2 emission per capita and GDP per
capita is linear and positive. Most of the data points on the predicted regression model are
clustered above the regression line and on the lower left of the graph. There are a few outliers
towards the right of the regression and the points are located in the horizontal direction. This
indicates that GDP per capita is highly influential on the CO2 emission per capita.

8
Question 10
The linear regression equation is Y = 332.29X1 – 2.16X2 – 0.606X3 + 51.114X4 – 921.24
Therefore, dy
dx =332.29-2.16-0.606+51.114-0
dy
dx = 380.638
Thus, the level of per capita GDP where the marginal effect of per capita GDP on CO2 emissions
changes its sign is at $380.638.
Question 11
Null hypothesis: the slope is equal to zero
Alternative hypothesis: the slope is not equal to zero
The p-values for both population density and share of the urban population are 0.000, which is
below the significance level of 0.05. Therefore, the null hypothesis is rejected. The slope
coefficients for both population density and share of the urban population are not equal to zero.

9
Bibliography
Stigum, Bernt P. 2015. Econometrics in a Formal Science of Economics: Theory and the
Measurement of Economic Relations. MIT Press, 2015.
Hill, R. Carter, William E. Griffiths, and Guay C. Lim. Principles of econometrics. John Wiley
& Sons, 2018.
Lee, Cheng-Few, and John C. Lee, eds. Handbook of financial econometrics and statistics.
Springer New York, 2015.
Bhaumik, Sankar Kumar. "Principles of Econometrics: A Modern Approach Using EViews."
OUP Catalogue (2015).
Bhatti, M. Ishaq, and Hatem Al-Shanfari. Econometric analysis of model selection and model
testing. Routledge, 2017.
Mishra, Srikanta, and Akhil Datta-Gupta. "Regression Modeling and Analysis." Applied
Statistical Modeling and Data Analytics, 2018, 69-96. DOI:10.1016/b978-0-12-803279-
4.00004-3.