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Masters of Science (MSc.) in
Global Financial Information Systems (GFIS)
Econometrics – Group Exercise
Group 6 – Question 1 – Parts F - J
Daire Naughton Garreth Conlon Robert Hoffman Denise Sheehy
Points
3 points
2 points
1 point
Y Variable Points
3 points
2 points
1 point
• The WEO database did not have information on Cuba
• Other sources - incomplete results
Cuba Omitted
Independent Variables
Compulsory Compulsory Intercept
Suppressed
Dummy Variable
X1:GDP based on PPP per
capita (UNITS)
X2:Population (Millions)
X3:Gross
national savings
X4:Annual
Temperature (AVG)
X5:Area (Sq. kms - 1,000s)
Histogram
Jarque-BeraResiduals
Mean -4.2E-15
Standard Error 5.670
Median -4.3483
Mode #N/AStandard Deviation 31.5699Sample Variance 996.6558
Kurtosis 0.8921
Skewness -0.2902
Range 150.4230
Minimum -80.6698
Maximum 69.7532
Sum -1.3E-13
Count 31 0.25 > 0.05 (Critical Value)
•R2 = 0.559 or 55.9%
•Adj R2 = 0.470 or 47%
Goodness of Fit
•R2 = 0.559 or 55.9%
•Adj R2 = 0.470 or 47%
Goodness of Fit
Not a particularly strong model
SSRm - SSRu/M F = (29899.67 - 19042.29)/3
SSRu/ (n - k - 1) u 19042.29/(22) = 4.181261
4.18 > 2.40
Ramsey Reset
SSRm - SSRu/M F = (29899.67 - 19042.29)/3
SSRu/ (n - k - 1) u 19042.29/(22) = 4.181261
4.18 > 2.40
Ramsey Reset
Null Hypothesis Rejected
• Internet Penetration as Proxy for Developed Nation
• Source: UN Statistical Pocketbook 2000-2012
Sixth Independent Variable
Compulsory Compulsory Intercept
Suppressed
Dummy Variable
X1:GDP based on PPP per
capita (UNITS)
X2:Population (Millions)
X3:Gross
national savings
X4:Annual
Temperature (AVG)
X5:Area (Sq. kms - 1,000s)
X6: Internet Users (% Penetration)
Internet Penetration - 2000
CountryInternet
Penetration Dummy Variable
CountryInternet
Penetration Dummy Variable
Ethiopia 0.00% 0 Spain 13.60% 1
Korea, Republic of 0.00% 0 France 14.30% 1
Kenya 0.30% 0 Italy 23.10% 1
Kazakhstan 0.70% 0 Norway 26.80% 1Ukraine 0.70% 0 United Kingdom 26.80% 1China 1.80% 0 Japan 30.00% 1
Belarus 1.90% 0 Germany 30.20% 1
Russian Fed. 2.00% 0 Denmark 39.20% 1
Brazil 2.90% 0 United States 43.10% 1
Jamaica 3.10% 0 Netherlands 44% 1
Romania 3.60% 0 Sweden 45.70% 1
Turkey 3.80% 0 Australia 46.80% 1
Bulgaria 5.40% 0 Switzerland 47.10% 1
Hungary 7.00% 0 Canada 51.30% 1
Poland 7.30% 0
Greece 9.10% 0
Czech Republic 9.80% 0
Regression Statistics 5 Variables
Including X6
Multiple R 0.747 0.748
R Square 0.559 0.559
Adjusted R Square 0.470 0.449
Standard Error 34.583 35.268
Observations 31 31
Interpret New Regression Coefficient
Note reduced Adj R2
CoefficientsStandard
Error t Stat P-valueLower 95%
Upper 95%
Intercept 3.403 22.556 0.151 0.881 -43.15149.95
7
X1: Population (Millions) 0.047 0.035 1.345 0.191 -0.025 0.118X2: GDP based on PPP per capita (UNITS) 0.001 0.001 0.580 0.567 -0.002 0.004
X3: Gross national savings 0.673 1.037 0.649 0.523 -1.468 2.813X4: Annual Temperature (AVG) - Intercept Supressed -0.349 1.021 -0.342 0.736 -2.455 1.758
X5: Area (Sq. kms - 1,000s) 0.006 0.002 3.562 0.002 0.003 0.010X6: Internet Users (>10% Penetration - Dummy Variable) 6.104 31.103 0.196 0.846 -58.090
70.297
Statistical Significance
CoefficientsStandard
Error t Stat P-valueLower 95%
Upper 95%
Intercept -43.15149.95
7
X1: Population (Millions) -0.025 0.118X2: GDP based on PPP per capita (UNITS) -0.002 0.004
X3: Gross national savings -1.468 2.813X4: Annual Temperature (AVG) - Intercept Supressed -2.455 1.758
X5: Area (Sq. kms - 1,000s) 0.003 0.010X6: Internet Users (>10% Penetration - Dummy Variable) -58.090
70.297
Confidence Intervals
CoefficientsStandard
Error t Stat P-valueLower 95%
Upper 95%
Intercept 0.881
X1: Population (Millions) 0.191X2: GDP based on PPP per capita (UNITS) 0.567
X3: Gross national savings 0.523X4: Annual Temperature (AVG) - Intercept Supressed 0.736
X5: Area (Sq. kms - 1,000s) 0.002X6: Internet Users (>10% Penetration - Dummy Variable) 0.846
P-Value
•Theory: Proxy for developed nation
•T-test: Variable’s estimate coefficient is not significant in the expected direction
•Adj R2: Reduced from 47% to 44.9%
•Bias: No significant changes to other variable
X6 - Relevance
•Theory: Proxy for developed nation
•T-test: Variable’s estimate coefficient is not significant in the expected direction
•Adj R2: Reduced from 47% to 44.9%
•Bias: No significant changes to other variables
•Conclusion: X6 is irrelevant
X6 - Relevance
Coefficients
Model
Unstandardized Coefficients
Standardized Coefficients
t Sig.B Std. Error Beta(Constant) 3.405 22.556 .151 .881X1_Population_Millions .047 .035 .222 1.345 .191
X2_GDP_Units .001 .001 .201 .580 .567
X3_Gross_National_Savings .673 1.037 .106 .648 .523
X4_Temp_Intcpt_Suppressed -.348 1.021 -.056 -.341 .736
X5_Area_sq_kms .006 .002 .569 3.562 .002X6_DV1_Internet_Penetration
6.105 31.103 .065 .196 .846
a. Dependent Variable: Y_National_Performance
Stepwise
Coefficients
Model
Unstandardized Coefficients
Standardized Coefficients
t Sig.B Std. Error Beta(Constant) 3.405X1_Population_Millions .047
X2_GDP_Units .001
X3_Gross_National_Savings .673
X4_Temp_Intcpt_Suppressed -.348
X5_Area_sq_kms .006X6_DV1_Internet_Penetration
6.105
a. Dependent Variable: Y_National_Performance
Positive Relationship
Coefficients
Model
Unstandardized Coefficients
Standardized Coefficients
t Sig.B Std. Error Beta(Constant) .881X1_Population_Millions .191
X2_GDP_Units .567
X3_Gross_National_Savings .523
X4_Temp_Intcpt_Suppressed .736
X5_Area_sq_kms .002X6_DV1_Internet_Penetration
.846
a. Dependent Variable: Y_National_Performance
Significance
Variables Entered
ModelVariables Entered
Variables
Removed Method
1 X5_Area_sq_kms
Stepwise (Criteria: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).
a. Dependent Variable: Y_National_Performance
Variables Entered
Variables RemovedVariables Removed
Model Beta In t Sig.Partial
Correlation
Collinearity Statistics
Tolerance VIFMinimum Tolerance
X1_Population_Millions .200 1.326 .196 .243 .793 1.260 .793
X2_GDP_Units .200 1.496 .146 .272 .998 1.002 .998
X3_Gross_National_Savings .144 .992 .330 .184 .882 1.134 .882
X4_Temp_Intcpt_Suppressed
.064 .443 .661 .083 .918 1.090 .918
X6_DV1_Internet_Penetration
.203b 1.517 .140 .276 .999 1.001 .999
•Not particularly good
•Too many unknown variables
Overall a Good Model?
End