Simple Regression, 'I' and 'A' in the IPAT model, Indian economy

This was a regression analysis of two variables of the IPAT model of effects of human activity on environment. It was submitted as a short empirical study, as apart of my assignment in an online course offered by The University of Edinburgh in critical reasoning[informal logic]. I'll put online all the regression output in Excel soon. This short analysis showed some interesting facts about the effects of Affluence factor on Environmental degradation. I had to use proxy variables as data availability was a critical issue here. Anyway, have a look. Let me know if more detailed study interests you on this topic.

Submitted material:

Hello. The homework section gives following instructions:

"For this week's homework, we would like you to do some research for yourselves and find one or more examples, in your own global context, where the environmental impact is being (or can be) mitigated through changes in A or T. Post a brief summary of what you have found, with references (e.g. links to websites), on the Homework/Population/Case Studies forum thread. Once you have done that, read and comment on the other submissions from fellow students, and upvote the examples that you think illustrate this principle best."

I’ve tried to do the following in context of Indian Economy[my nation of residency]. Hope I got it right. I understood it as giving one's own example. A simple empirical illustration too shall be admissible is what I've assumed here.

1.    Find a numerical value of the degree of relationship between the variables I[Environmental  degradation] and A[Affluence factor].

2.    Fit a regression line through the available data and predict the future behaviour of I with reference to a particular value of ‘A’.

3.    Also find out how much part of the variation in I is explained by A with the given data set. In short calculate the r-squared measure[coefficient of determination].

4.    All this using Microsoft Excel only. No use of advanced statistical packages has been done.

Proxy variables used:

1.    For ‘I’ [Environmental degradation], I used the Annual carbon dioxide emissions in tonnes per capita as a proxy variable.

2.    For ‘A’ [Affluence factor], I used GDP per capita in India at constant price [base year 2004-05]

3.    Isolated the data analysis to a statistical relation between ‘I’ and ‘A’ because the data was readily available.

Data used:

1.    For the variable ‘I’ {year 1990 to 2010}-http://en.wikipedia.org/wiki/List_of_countries_by_carbon_dioxide_emissions_per_capita

Please look at the row showing India’s data.

2.    For the variable ‘A’ {year 1990 to 2010}, in INR-

Handbook of Statistics on Indian Economy, 2012-2013, published by RBI. The section on ‘Macroeconomic aggregates at constant prices’ includes data on GDP per capital at constant price, base year being 2004-2005. Available here: http://rbidocs.rbi.org.in/rdocs/Publications/PDFs/002T_BST130913.pdf

3.    Data series used: Year 1990-91 to 2010-2011 for both I and A as explained above.

Results:

1. Correlation between 'I' and 'A' as per the data series is 0.978224 or 0.98[approx.]. This shows a strong degree of linear relation between both the variables in context of India.

2. Regression line produced: I = 0.612619153 + 1.98157E-05[A] 

3. r-squared comes out to be 0.9569 or 0.96[approx.]. Approximately 95% of the variation in I is explained by A.'I' being Environmental degradation measured by CO2 emissions, tonnes per capita in India between 1990-91 upto 2010-2011. And 'A' being GDP per capita at constant price, base year- 2004-05, from 1990-91 to 2010-2011.2.

4. Using the above Regression line, I found the following expected level of CO2 emissions[representing 'I'] for the year 2011-12 with GDP per capital being 55054.37 INR to be 1.70355 tonnes per capita per year

Data series:

The units have been stated above already.

Regression Output has been stated already above.

> Thus, it can be seen that in India, between 1990 to 2010, there has been a high correlation between I and A as stated here. The expected amount of environmental degradation[proxy- CO2 emissions in India] based on the data available for 2011 come out to be 1.70 tonnes per capita per year in India. More interpretations can be found out here.

Limitations of this analysis:

1. Proxy variables chosen might not be sufficient to explain all that needs to be explained. Also the isolated effect of one of the variable in the IPAT model, on 'I' has been explained. This was mainly due to data inavailability.

2. p-value, standard error, etc. has been ignored here. There's no autocorrelation[Error terms lacked linear correlation].

3. Data series might not be sufficient to explain the phenomenon satisfactorily.

4. High correlation does not imply causation. Hence this remains to be explained here.
5. Y variable has repetitive[same] values. Might be an issue.

Please let me know if this short analysis gave some insights to you. Your suggestions/criticisms/feedback are always welcomed.

- Thank you.

- Bhagirath Baria, Surat, Gujarat, India.