REFINER'S FIRE: Testing our Co2 Model

By  Abimbola Shode

     Kingsley Onuoha

     Yetunde Esan

     Nneka Iyabode Eze

     Apresai Oghenemagan Kereokiye

REGRESSION RESULT AND INTERPRETATION

The result of the regression is shown in the table below;

Table 7: Regression result

F-statistics

The F value of the model is 29.2361. The critical value of F taken at a 5% level of significance, 7 numerator degrees of freedom and 81 denominator degrees of freedom is 2.13. The null and alternative hypotheses are as stated below;

Ho:  b₁ = b₂ = … = b_I = 0

Ha:  At least one of our parameters is non-zero.

Comparing the F value of 29.2361 to the critical value of 2.13, we see that F > Fcritical. As such, we reject the null hypothesis and conclude that our model and its parameters are statistically significant.

T –statistics

The regression result shows the t – stats for each of the parameters in the model. The test was performed at a 5% level of significance.

The null and alternate hypothesis is at stated below.

Ho :  b_I = 0

Ha :  b_I ¹ 0

The critical value (t_c) of 1.990 was obtained at a level of significance of 0.025 and 81 degrees of freedom. For all of the variables, the absolute value of their t statistics is greater than the critical value meaning that they are all statistically significant

Variable	|t|-value	Comparison	Result
Constant	5.8884	|t| >tc	Reject null hypothesis
REN	10.7753	|t| >tc	Reject null hypothesis
EI	3.8068	|t| >tc	Reject null hypothesis
EU	2.4256	|t| >tc	Reject null hypothesis
OM	2.6882	|t| >tc	Reject null hypothesis
EI,OM	1.9944	|t| >tc	Reject null hypothesis
EU,OM	1.4532	|t| >tc	Reject null hypothesis
REN,OM	3.4689	|t| >tc	Reject null hypothesis

Table 8: Summary of the t statistics

P – Value

The p value for the overall model is < 0.0001.

Since this is less than our 0.05 level of significance, we can say that our model is significant as a whole. The p value of the parameters is compared with the 0.05 level of significance as shown in the table below;

Variable	P value	Comparison	Result
Constant	< 0.0001	P < 0.05	Reject null hypothesis
REN	< 0.0001	P < 0.05	Reject null hypothesis
EI	0.0003	P < 0.05	Reject null hypothesis
EU	0.0179	P < 0.05	Reject null hypothesis
OM	0.0087	P < 0.05	Reject null hypothesis
EI,OM	0.0494	P < 0.05	Reject null hypothesis
EU,OM	0.1500	P > 0.05	Fail to reject null hypothesis
REN,OM	0.0008	P < 0.05	Reject null hypothesis

  Table 9: Summary of the P-statistics.

From the table we can see that the p stats for all variables (except EU,OM) is less than 0.05. This means that all the variables are statistically significant except the interaction between EU and OM. As such, EU,OM does not contribute to the model.

This may suggest that we may have mis-specified the model.

STANDARD ERROR AND CONFIDENCE INTERVAL

Table ten below gives a summary of the standard error and confidence interval for the variables.

Variable	Standard error	Confidence interval
Constant	0.186877884	0.7286,1.4721
REN	0.284569936	3.6324,2.5002
EI	0.608979965	1.1068,3.5297
EU	0.258869544	0.1103,1.1403
OM	0.413771453	0.2892,1.9354
EI,OM	1.612335059	6.4231,0.0082
EU,OM	0.370723181	1.2762,0.1987
REN,OM	0.862977462	1.2769,4.7103

Table 10:  Standard error and confidence interval.

The standard errors for most of the variables are below zero. The low value of standard errors have led to narrow confidence intervals for all variables except EI,OM suggesting that our estimates are reliable except EI,OM.

R – SQUARE

The R² is 71 percent. So this model can only explain 71 percent of the variations in our observations while the remaining 29% of the variations cannot be explained. This might suggest that our model may have been mis-specified.

As such, we shall check the model specification in the next section.

NUTSHELL:

This is the 3rd instalment in a 5-part series which seeks to employ a quantitative approach to investigating the impact of OECD and EU membership on Carbon (CO2) Emissions. In the second instalment, preliminary models were drawn up for us to be able to run a check on the existence- or otherwise- of causal relationships between Co2 and a number of variables. In this instalment, Oghenemagan has been able to conduct due diligence on these models by subjecting them to various tests.  His investigation reveals that though the model variables are overall statistically significant, there exist some mis-specifications in the model- which shall be re-examined going forward. To view Oghenemagan's professional profile and for more information on this article please click here.-->