Application of regression analysis

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Application of regression analysis

• Economic structure and air pollution in a
  transition economy The case of the Czech republic

Gabriela Jandová Michaela Krcílková
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Structure of presentation

1. Definition of regression model
2. Compilation of regression model
3. Analysis of the results

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I. Regression model

• represents reality by using the system of
  equations.
• explains relationship between variables.
• enables quantification of these relationships.

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II. Compilation of regression model

• Conceptual model
• Hypotheses
• Equations
• Data collection
• Calculation
• Verification
• Errors of the model

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Compilation of regression model
Conceptual model

• is a graphical scheme.
• serves for specification of sought-after mutual
  relations.
• is a tool for defining of investigation matter.
• should clarify our minds and help during
  determination of researching methods.

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Our conceptual model
Political system
Economic system
Individual people
INPUTS production resources
OUTPUTS products, waste
Ecological system
Air
Soil
Water
Organisms
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Hypotheses
Compilation of regression model

• are formulated expectations and suppositions.
• Theirs confirmation or rejection is the goal of
  the regression analysis.

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Our hypotheses

• There is a relationship between economic
  structure and air pollution.
• Industry is the biggest polluter of air.
• There is a significant improvement of air quality
  during the 90th. Decrease of functioning of
  economy is not a cause of this fact.

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Equations
1.
Compilation of regression model

• should involve mainly essential relations between
  examined phenomenons, which have permanent
  character.
• consist from explained and explanatory variables.
  
• Partial correlation coefficients measure the
  effect of given explanatory variable on explained
  variable.

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Requests on the variables
2.
Compilation of regression model
Equations

• Measurability
• Accessibility
• Conclusiveness
• Testify ability
• Standardized methods of attaining

• Comparability
• Time series
• Inter-independence
• Uniqueness
• Convenience

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Our equations
Yn gn1X1 gn2X2 gn3X3 en

• WhereYn dependent variables (NO,CO, Dust)
• X1 Gross value added in agriculture
• X2 Gross value added in industry
• X3 Gross value added in services
• e Random error term
• g1g2g3 partial correlation
  coefficients

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Data collection
Compilation of regression model
Sources

• Statistical offices reports
• Library
• Internet
• Journal
• Interview

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Our data
1.

• Underlying data necessary for compilation of
  basic matrixes have been acquired from regional
  branches of Czech statistical office and from
  Czech Hydrometeorological office.

Form of indicators of one region.
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Our data
2.

• To acquire underlying data was necessary to
  contact all 14 regions.

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Our data
3.

• Underlying data were adjusted and used for
  compilation of basic mattrixes.

Example of basic mattrixes for NOx
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Calculation
Compilation of regression model

• Ordinary least square method (OLS)
• Two stage least square method
• Instrumental variables
• Maximum likelyhood method
• General least square
• Non-linear least square

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Our calculation

• Method of callculation OLS
• Results

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Verification
Compilation of regression model

• statistical verification
• R-squared
• R2 should be equal at least 0,66
• t-statistic
• Every attained t-value should be higher than
  critical t-values mentioned in statistical tables
  
• F-statistic
• Every attained F-value should be higher than
  critical F-values mentioned in statistical tables
  
• confidence interval
• Estimated intervals have not include zero.
• logical verification

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Verification of our model
1.
Statistical verification
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Verification of our model
2.
Statistical verification

• Confidence interval

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Verification of our model
Logical verification

• Coefficients of industry have a positive slope.
• Coefficients for services and agriculture have
  negative slope.

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Errors of the model
Compilation of regression model

• Indicators of the errors
• Low value of R-squared
• Coefficients are not significant
• Zero lies in the confidence intervals
• Reasons of the errors
• Bad choice of variables
• Omission of important factors
• Equations are not identificated
• Errors in data collection
• Low number of executed observation

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Experiments with our model

• Calculation with additive constant

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III. Analysis of the results

• is an important step for correct interpretation
  of the model.
• is crowned and concluded by confirmation or
  rejection of hypothesis.

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Analysis of results
1.
First hypothesis
There is a relationship between economic
structure and air pollution.

• The significance of coefficients comfirms our
  first hypothesis.

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Analysis of results
2.
Second hypothesis
Industry is the biggest polluter of air.

• The coefficients for industry have the biggest
  value and positive slope. This fact confirms our
  second hypothesis.

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Analysis of results
3.
Third hypothesis
There is a significant improvement of air quality
during the 90th. Decrease of functioning of
economy is not a cause of this fact.

• All coefficients decrease during the time, that
  confirms our third hypothesis.

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Conclusion

• All hypotheses are confirmed.
• Our recommendation is
• to use the model in the conditions of
  non-transition economy.
• to use the model in a country with higher number
  of regions.

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END