application of regression analysis

Application of regression analysis

Economic structure and air pollution in a transition economy: The

case of the Czech republic

Gabriela Jandová

Michaela Krčílková

Structure of presentation

I. Definition of regression model

II. Compilation of regression model

III. Analysis of the results

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

I. Regression model

II. Compilation of regression model

Conceptual modelHypothesesEquations Data collectionCalculation VerificationErrors of the 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.

Compilation of regression model

Conceptual model

Our conceptual model

Agriculture

Industry Services

Individual people

Economic system

Air

Soil Water

Organisms

Ecological system

Political system

INPUTS: production resources

OUTPUTS: products, waste

Hypotheses

are formulated expectations and suppositions.

Theirs confirmation or rejection is the goal of the regression analysis.


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.

Equations

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.


1.

Requests on the variables:Measurability

Accessibility

Conclusiveness

Testify ability

Standardized methods of attaining

Compilation of regression model Equations

2.

Comparability

Time series

Inter-independence

Uniqueness

Convenience

Our equations

Where:Yn = dependent variables (NO,CO, Dust) X1 = Gross value added in agriculture

X2 = Gross value added in industry

X3= Gross value added in services

= Random error term 123 = partial correlation coefficients

Yn = n1X1 + n2X2 + n3X3 + n

Data collection

Statistical office´s reportsLibraryInternetJournalInterview


Sources:

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

Tab. č. P.1. Regionální makroekonomické ukazatele Jihočeský kraj1993 1994 1995 1996 1997 1998 1999

Hrubá přidaná hodnotav základních cenách (mil. Kč) 54426 62649 71 278 80985 87061 94350 95532Hrubý domácí produktv tržních cenách (mil. Kč) 57613 66261 76274 87533 93491 100985 103321Podíl kraje na HDP České republikyv % (ČR = 100) 5,6 5,6 5,5 5,6 5,6 5,5 5,5Hrubý domácí produkt

v mil ECU 1 686 1 940 2198 2540 2602 2780 2801v mil. PPS 5677 5907 6252 6898 7029 6918 7 171

Hrubý domácí produktna 1 obyvatelev Kč 92061 105733 121 614 139692 149 207 161 165 164986v ECU 2694 3096 3505 4054 4153 4437 4473v PPS 1) 9072 9425 9968 11 008 11 217 11 040 11 451

Hrubý domácí produktna 1 obyvatele

průměr ČR= 100 93,2 92,4 91,0 92,0 91,5 90,7 89,9v PPS(EUR15=100) 2) 56,8 56,4 56,5 59,6 57,8 54,5 53,9vPPS(EUR25 = 100) 3) . . 65,6 68,9 66,7 62,9 62,2vPPS(CECC10=100) 4) . . 150,8 154,0 148,3 141,0 140,0

1) PPS - jednotka pro měření kupní síly 2)EUR15 - průměr zemí Evropské unie 3)EUR25 = EUR15 + CECC104)CECC10 - průměr zemí: Bulharsko, Česká republika, Estonsko, Litva, Lotyšsko, Maďarsko, Polsko, Rumunsko,

1.

Form of indicators of one region.

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

Tab. č. P.2. Struktura hrubé přidané hodnoty podle odvětví OKEČ

v % Jihočeský krajOdvětví 1993 1994 1995 1996 1997 1998 1999

Hrubá přidaná hodnota celkem 100,0 100,0 100,0 100,0 100,0 100,0 100,0

v tom:

A Zemědělství, myslivost, lesnictví 9,6 9,1 9,1 9,7 8,4 8,1 7,8

B Rybolov 0,4 0,4 0,5 0,4 0,3 0,3 0,3

C Dobývání nerostných surovin 0,4 0,3 0,4 0,4 0,3 0,4 0,3

D Zpracovatelský průmysl 22,9 24,7 26,3 29,3 31,1 30,4 30,3

E Výroba a rozvod elektřiny, plynu, vody 7,6 8,3 7,5 8,9 6,1 6,3 6,4

F Stavebnictví 10,5 9,7 11,8 10,0 10,0 8,8 9,1

G Obchod, opravy motorových vozidel

a spotřebního zboží 12,9 10,7 9,9 8,2 9,8 10,8 10,7

H Pohostinství a ubytování 1,6 2,1 1,9 1,5 1,6 1,3 1,2

l Doprava, skladování,

pošty a telekomunikace 8,7 8,2 7,9 7,3 7,7 8,2 7,9

J Peněžnictví a pojišťovnictví 5,7 4,7 3,8 2,9 2,8 3,9 3,6

K Činnosti v oblasti nemovitostí,

pronajímání nemovitostí, služby

pro podniky, výzkum a vývoj 7,3 8,5 7,3 7,2 7,3 7,2 7,0

L Veřejná správa, obrana, povinné sociální

zabezpečení 4,4 4,1 4,3 4,6 5,5 5,4 5,6

M Školství 3,3 3,6 3,6 3,8 3,6 3,2 3,9

N Zdravotnictví, veterinární

a sociální činnosti 3,0 3,4 3,6 3,4 3,5 3,5 3,6

O Ostatní veřejné sociální

a osobní služby 1,8 2,0 2,3 2,3 2,0 2,1 2,3

P Soukromé domácnosti s personálem 0,0 0,0 0,0 0,0 0,0 0,0 0,0

Q Exteritoriální organizace a spolky 0,0 0,0 0,0 0,0 0,0 0,0 0,0

Our data 2.

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

Our data 3.

Y1 X1 X2 X3

1995 NOx

GVA in agriculture

GVA in industry

GVA in SERVICES

[t/year] [t/year] [t/year] [t/year]STR 29165,60 7344,72 51209,02 43558,27PLZ 7811,00 5661,14 29755,50 33621,60KVA 8622,00 1330,23 15577,70 18098,10LIB 4464,50 1256,89 21627,16 20413,61HKR 7577,20 4288,26 27058,33 28991,07PAR 12782,30 4107,95 24967,80 24220,90VYS 3356,90 5977,97 25117,50 19139,54JIHM 9699,50 6523,43 50180,26 68746,96OLO 6718,60 5250,74 29444,00 31770,27ZLI 4723,60 3296,60 35827,20 23076,20MSL 38261,00 4053,76 80640,79 60372,01BUD 7593,30 6842,69 32787,88 31789,99PHA 7536,20 263,62 54305,93 208787,83

Y1 X1 X2 X3

1998 NOx

GVA in agriculture

GVA in industry

GVA in SERVICES

[t/year] [t/year] [t/year] [t/year]STR 17412,10 8680,00 67163,24 66309,47PLZ 6236,10 6420,74 38260,60 43274,10KVA 9373,30 1374,52 18910,00 21409,10LIB 2553,00 1698,94 28663,82 27520,32HKR 4063,00 5110,49 37051,00 37689,80PAR 9298,60 5010,54 32744,90 32815,50VYS 2648,30 7759,32 32459,80 24506,50JIHM 5721,70 8214,84 61024,60 98410,50OLO 4510,70 6013,80 36500,40 41010,80ZLI 4016,80 3762,37 41984,70 39761,40MSL 23062,60 4554,83 94740,40 82715,60BUD 7593,00 7925,40 43306,65 43023,60PHA 7536,20 389,85 67833,73 322015,27

Example of basic mattrixes for NOx

Calculation

Ordinary least square method (OLS)Two stage least square methodInstrumental variablesMaximum likelyhood methodGeneral least squareNon-linear least square


Our calculation

Method of callculation: OLSResults:

NO 1995 1998 DUST 1995 1998 CO 1995 1998 11- AGRICULTURE -0,97 -0,62 11- AGRICULTURE -0,39 -0,04 11- AGRICULTURE -15,65 -10,68

12 - INDUSTRY 0,59 0,30 12 - INDUSTRY 0,50 0,15 12 - INDUSTRY 4,44 2,61 13 - SERVICES -0,12 -0,04 13 - SERVICES -0,10 -0,03 13 - SERVICES -1,03 -0,47

Verification

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


Verification of our modelStatistical verification

1995 R2t-test -

agriculturet-test -

industryt-test -

servicesNO 0,735 -1,411 5,031 -2,654CO 0,835 -4,241 7,123 -4,339

DUST 0,723 -0,630 4,821 -2,490

1998 R2t-test -

agriculturet-test -

industryt-test -

servicesNO 0,691 -1,598 4,928 -2,245CO 0,811 -4,304 6,621 -4,033

DUST 0,629 -0,177 3,875 -2,428

tc 0,1 1,383

tc 0,05 1,833

tc 0,01 2,821

critical value of t-test

1.

Verification of our model

Statistical verification

2.

1995 CO0,1 -20,753 -10,546 3,579 5,303 -1,354 -0,699

0,05 -22,413 -8,886 3,298 5,584 -1,460 -0,5930,01 -26,059 -5,240 2,682 6,200 -1,694 -0,359

NO0,1 -1,928 -0,019 0,425 0,748 -0,179 -0,056

0,05 -2,238 0,292 0,373 0,800 -0,199 -0,0360,01 -2,920 0,973 0,258 0,916 -0,242 0,007

DUST0,1 -1,240 0,464 0,358 0,646 -0,153 -0,044

0,05 -1,517 0,741 0,311 0,693 -0,171 -0,0260,01 -2,126 1,350 0,208 0,795 -0,210 0,013

11-AGRICULTURE 12 - INDUSTRY 13 - SERVICES



1998 CO0,1 -14,115 -7,249 2,066 3,158 -0,636 -0,311

0,05 -15,232 -6,132 1,889 3,335 -0,689 -0,2580,01 -17,684 -3,680 1,499 3,725 -0,805 -0,142

NO0,1 -1,155 -0,083 0,218 0,389 -0,067 -0,016

0,05 -1,329 0,091 0,191 0,416 -0,075 -0,0080,01 -1,712 0,474 0,130 0,477 -0,093 0,011

DUST0,1 -0,387 0,299 0,098 0,207 -0,045 -0,012

0,05 -0,499 0,411 0,081 0,225 -0,050 -0,0070,01 -0,744 0,656 0,042 0,264 -0,062 0,005

13 - SERVICES


11-AGRICULTURE

12 - INDUSTRY 13 - SERVICES

12 - INDUSTRY

11-AGRICULTURE

Confidence interval:

Verification of our model

Logical verification

Coefficients of industry have a positive slope.

Coefficients for services and agriculture have negative slope.

Errors of the 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


Experiments with our model

Calculation with additive constant1995 NO CO DUST

10- ADDITIVE -4170,18 -35130,38 -2152,0111- AGRICULTURE -0,50 -11,70 -0,15

12 - INDUSTRY 0,62 4,71 0,5213 - SERVICES -0,11 -0,93 -0,09

1998 NO CO DUST10- ADDITIVE -426,67 -28732,85 -370,57

11- AGRICULTURE -0,58 -8,30 -0,0112 - INDUSTRY 0,31 2,85 0,1613 - SERVICES -0,04 -0,44 -0,03

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.

Analysis of results

The significance of coefficients comfirms our first hypothesis.

First hypothesis

CO 11-AGRICULTURE 12 - INDUSTRY

13 - SERVICES1995 -4,241 7,123 -4,3391998 -4,304 6,621 -4,033

NOx11-AGRICULTURE

12 - INDUSTRY 13 - SERVICES

1995 -1,411 5,031 -2,6541998 -1,598 4,928 -2,245

DUST 11-AGRICULTURE 12 - INDUSTRY

13 - SERVICES1995 -0,630 4,821 -2,490

1998 -0,177 3,875 -2,428

Critical values for t-testtc 0,1 1,383tc 0,05 1,833tc 0,01 2,821

1.

There is a relationship between economic structure and air pollution.

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

Analysis of resultsSecond hypothesis

2.



Industry is the biggest polluter of

air.

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

Analysis of resultsThird hypothesis

3.



There is a significant improvement of air quality during the 90th. Decrease of functioning of

economy is not a cause of this fact.

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.

application of regression analysis

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