MODELE LINIARE SI NELINIARE

GERMANIA

1. STATISTIC DESCRIPTIV

PIB 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Trim.1 515,500.0 591,220.8 584,319.1 582,126.0 591,478.8 587,157.2 612,441.7 638,887.4 652,239.2 609,474.7 625,342.0 662,946.4 672,944.2 661,656.4 679,007.3

Trim.2 523,900.0 596,703.4 597,606.4 589,737.2 599,218.9 606,765.6 621,278.5 642,434.9 662,236.9 610,248.7 639,016.4 662,752.9 664,752.5 669,461.1 676,040.2

Trim.3 536,120.0 606,701.1 613,215.8 608,055.6 611,603.2 619,472.4 641,273.9 662,494.9 669,719.1 632,050.2 661,075.9 682,167.9 682,941.9 689,650.0 697,906.2

Trim.4 540,960.0 604,185.6 603,605.0 601,670.0 607,217.1 613,151.3 641,209.4 654,496.7 642,370.4 627,083.6 654,690.2 666,494.0 664,817.0 672,621.6 683,393.4

0

100000

200000

300000

400000

500000

600000

700000

800000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

PIB

TRIM 1

TRIM 2

TRIM 3

TRIM 4

1.1. INDICATORI STATISTIC DESCRIPTIV

2000

2001

2002

2003

2004

2005

2006

2007

Mean 529120 Mean 599702.725 Mean 599686.58 Mean 595397.2 Mean 602379.5 Mean 606636.625 Mean 629050.9 Mean

Standard Error 5787.474982 Standard

Error 3535.68031

Standard Error

6047.5918 Standard

Error 5829.118428

Standard Error

4446.849712 Standard

Error 6992.035607

Standard Error

7265.825 Standard

Error

Median 530010 Median 600444.5 Median 600605.7 Median 595703.6 Median 603218 Median 609958.45 Median 631244 Median

Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode

Standard Deviation

11574.94996 Standard Deviation







Sample Variance

133979466.7 Sample

Variance 50004141

Sample Variance

146293466 Sample

Variance 135914486.6

Sample Variance

79097889.43 Sample

Variance 195554247.7

Sample Variance

2.11E+08 Sample

Variance

Kurtosis -2.87682921 Kurtosis -2.7559703 Kurtosis 0.4442144 Kurtosis -2.805009556 Kurtosis -1.7761818 Kurtosis 1.57324884 Kurtosis -4.23641 Kurtosis

Skewness -0.28630671 Skewness -0.3852736 Skewness -0.415053 Skewness -0.102477149 Skewness -0.40647695 Skewness -1.21896455 Skewness -0.31021 Skewness

Range 25460 Range 15480.3 Range 28896.7 Range 25929.6 Range 20124.4 Range 32315.2 Range 28832.2 Range

Minimum 515500 Minimum 591220.8 Minimum 584319.1 Minimum 582126 Minimum 591478.8 Minimum 587157.2 Minimum 612441.7 Minimum

Maximum 540960 Maximum 606701.1 Maximum 613215.8 Maximum 608055.6 Maximum 611603.2 Maximum 619472.4 Maximum 641273.9 Maximum

Sum 2116480 Sum 2398810.9 Sum 2398746.3 Sum 2381588.8 Sum 2409518 Sum 2426546.5 Sum 2516204 Sum

Count 4 Count 4 Count 4 Count 4 Count 4 Count 4 Count 4 Count

Eroare SP 1.09379252

0.58957216

1.0084588

0.979030205

0.738213985

1.152590417

1.155046

2008 2009 2010 2011 2012 2013 2014

Mean 656641.4 Mean 619714.3 Mean 645031.1 Mean 668590.3 Mean 671363.9 Mean 673347.3 Mean 684086.8

Standard Error 5953.827 Standard Error 5780.196

Standard Error 8034.152





Median 657238.1 Median 618666.2 Median 646853.3 Median 664720.2 Median 668880.6 Median 671041.4 Median 681200.4

Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode #N/A

Standard Deviation 11907.65







Sample Variance 1.42E+08



Sample Variance 84891514




Kurtosis -1.5488 Kurtosis -5.07774 Kurtosis -2.17088 Kurtosis 3.234944 Kurtosis -0.409 Kurtosis 1.868999 Kurtosis 2.090954

Skewness -0.22899 Skewness 0.153488 Skewness -0.45294 Skewness 1.802821 Skewness 1.025242 Skewness 1.08437 Skewness 1.45331

Range 27348.7 Range 22575.5 Range 35733.9 Range 19415 Range 18189.4 Range 27993.6 Range 21866

Minimum 642370.4 Minimum 609474.7 Minimum 625342 Minimum 662752.9 Minimum 664752.5 Minimum 661656.4 Minimum 676040.2

Maximum 669719.1 Maximum 632050.2 Maximum 661075.9 Maximum 682167.9 Maximum 682941.9 Maximum 689650 Maximum 697906.2

Sum 2626566 Sum 2478857 Sum 2580125 Sum 2674361 Sum 2685456 Sum 2693389 Sum 2736347

Count 4 Count 4 Count 4 Count 4 Count 4 Count 4 Count 4

Eroare SP 0.906709

0.932719

1.245545

0.689036

0.642274

0.876602

0.708642

2. Model Regresie Liniar Simpl

YEAR GDP General Government expenditure

2000 2,116,480.0 947,098.0

2001 2,179,850.0 1,022,525.0

2002 2,209,290.0 1,044,200.0

2003 2,220,080.0 1,061,545.0

2004 2,270,620.0 1,051,570.0

2005 2,300,860.0 1,062,999.0

2006 2,393,250.0 1,069,695.0

2007 2,513,230.0 1,076,099.0

2008 2,561,740.0 1,116,223.0

2009 2,460,280.0 1,170,508.0

2010 2,580,060.0 1,219,219.0

2011 2,703,120.0 1,208,565.0

2012 2,754,860.0 1,224,500.0

2013 2,820,820.0 1,255,570.0

2014 2,915,650.0 1,290,699.0

Regression Statistics

Multiple R 0.943560064

R Square 0.890305594

Adjusted R Square 0.881867563


Observations 15

ANOVA

df SS MS

F

Significance F

Regression 1 7.95E+11 7.95346E+11

105.5110574 1.31689E-

07

Residual 13 9.8E+10 7538035000

FINV

2.483

Total 14 8.93E+11

Coefficients Standard

Error t Stat T INV P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept -

209899.5086 261536.5

-0.802562988

2.144786681 0.436654386 -

774914.7476 355115.7 -774915 355115.7

Government revenue, expenditure and main aggregates

2.386816885 0.232365 10.27185755

1.31689E-07 1.884823516 2.88881 1.884824 2.88881

0.0

500,000.0

1,000,000.0

1,500,000.0

2,000,000.0

2,500,000.0

3,000,000.0

3,500,000.0

0.0 400,000.0 800,000.0 1,200,000.0

GD

P


Government revenue, expenditure and main aggregates Line Fit Plot

GDP

Predicted GDP

3. Model Regresie Liniar Multipl

YEAR GDP(mil euro) (Y) EXPORTS of good and services Imports of goods and services DOMESTIC DEMAND Final consumption

expenditure of households, services

Government expenditure

2000 2,116,480.0 683,550.0 677,250.0 2,041,200.0 554,420.0 923,360.0

2001 2,179,850.0 731,230.0 689,550.0 2,060,220.0 575,080.0 1,000,780.0

2002 2,209,290.0 760,570.0 664,670.0 2,036,300.0 584,650.0 1,022,330.0

2003 2,220,080.0 767,080.0 682,930.0 2,063,350.0 603,750.0 1,040,720.0

2004 2,270,620.0 846,440.0 735,670.0 2,084,930.0 618,400.0 1,033,600.0

2005 2,300,860.0 919,070.0 803,080.0 2,108,410.0 634,440.0 1,043,450.0

2006 2,393,250.0 1,053,140.0 923,090.0 2,183,850.0 648,950.0 1,049,290.0

2007 2,513,230.0 1,145,410.0 975,430.0 2,258,520.0 666,310.0 1,056,760.0

2008 2,561,740.0 1,191,190.0 1,035,360.0 2,317,970.0 673,930.0 1,090,460.0

2009 2,460,280.0 1,008,090.0 891,370.0 2,257,480.0 683,210.0 1,146,270.0

2010 2,580,060.0 1,188,590.0 1,048,390.0 2,354,800.0 712,180.0 1,194,130.0

2011 2,703,120.0 1,321,430.0 1,185,780.0 2,474,250.0 733,840.0 1,178,650.0

2012 2,754,860.0 1,381,030.0 1,223,120.0 2,508,490.0 749,410.0 1,191,490.0

2013 2,820,820.0 1,387,190.0 1,219,360.0 2,569,770.0 770,400.0 1,223,130.0

3.1. Analiz 1 Model Regresie liniar multipl



R Square 0.999841608



Observations 14

ANOVA

df SS MS F

Significance F

FINV T INV

Regression 5 6.7726E+11 1.35452E+11 10099.90465 5.67839E-15 2.576927085 2,160

Residual 8 107289782.7 13411222.84

Total 13 6.77368E+11

Coefficients

Standard Error

t Stat P-value Lower 95% Upper 95% Lower 95.0%

Upper 95.0%

INTERCEPT 93875.55859 51057.23983 1.838633638 0.103261504 -

23862.64748 211613.7647

-23862.64748

211613.7647

EXPORTS of good and services 1.046888567 0.052350652 19.99762247 4.07773E-08 0.926167748 1.167609386 0.926167748 1.167609386

Imports of goods and services -0.974111032 0.075318222 -

12.93327168 1.20915E-06

-1.147795164

-0.8004269 -

1.147795164 -0.8004269

DOMESTIC DEMAND 0.980728738 0.048510821 20.2167006 3.74304E-08 0.868862585 1.092594891 0.868862585 1.092594891

Final consumption expenditure of households, services

-0.257072656 0.153245601 -

1.677520631 0.13196175

-0.610457645

0.096312332 -

0.610457645 0.096312332


0.11767892 0.058396442 2.01517277 0.078645037 -

0.016983517 0.252341357

-0.016983517

0.252341357

3.2. Analiz 2 Model Regresie liniar multipl



R Square 0.999997741



Observations 14

ANOVA

df SS MS F Significance F

Regression 3 8.36597E+13 2.79E+13 1623101.152 9.88904E-29

Residual 11 188991537.5 17181049

Total 14 8.36599E+13

Coefficients Standard Error

t Stat P-value Lower 95% Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A

EXPORTS of good and services 1.040244248 0.040223322 25.86172 3.34075E-11 0.951713314 1.128775 0.951713 1.128775

Imports of goods and services -1.053262486 0.049576492 -21.2452 2.79306E-10 -1.162379609

-0.94415 -1.16238 -0.94415

DOMESTIC DEMAND 1.03946821 0.003819985 272.1132 2.0724E-22 1.031060479 1.047876 1.03106 1.047876

T inv = 2,160

4. MODELE NELINIARE

YEAR GDP(mil. euro)(Y) Final consumption expenditure (% of GDP) (X) 1/x lnX lnY X^2 X^3

2000 2,116,480.0 54.1 0.018484288 3.990834 14.56526489 2,926.81 158,340.421

2001 2,179,850.0 54.3 0.018416206 3.994524 14.59476663 2,948.49 160,103.007

2002 2,209,290.0 53.8 0.018587361 3.985273 14.60818175 2,894.44 155,720.872

2003 2,220,080.0 54.4 0.018382353 3.996364 14.61305379 2,959.36 160,989.184

2004 2,270,620.0 54.3 0.018416206 3.994524 14.63556348 2,948.49 160,103.007

2005 2,300,860.0 54.7 0.018281536 4.001864 14.64879352 2,992.09 163,667.323

2006 2,393,250.0 54.1 0.018484288 3.990834 14.68816283 2,926.81 158,340.421

2007 2,513,230.0 52.3 0.019120459 3.956996 14.73707934 2,735.29 143,055.667

2008 2,561,740.0 52.4 0.019083969 3.958907 14.75619727 2,745.76 143,877.824

2009 2,460,280.0 54.5 0.018348624 3.998201 14.71578572 2,970.25 161,878.625

2010 2,580,060.0 53.2 0.018796992 3.974058 14.76332321 2,830.24 150,568.768

2011 2,703,120.0 52.5 0.019047619 3.960813 14.80991722 2,756.25 144,703.125

2012 2,754,860.0 52.7 0.018975332 3.964615 14.82887718 2,777.29 146,363.183

2013 2,820,820.0 52.3 0.019120459 3.956996 14.85253818 2,735.29 143,055.667

2014 2,915,650.0 51.5 0.019417476 3.941582 14.88560334 2,652.25 136,590.875

4.1. Modelul Hiperbolic



R Square 0.732084827



Observations 15

ANOVA

df SS MS F `Significance F

Regression 1 6.54001E+11 6.54001E+11 35.52282103

4.75E-05

Residual 13 2.39339E+11 18410728806

Total 14 8.9334E+11

Coefficients Standard Error t Stat P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept -8599095.615 1856972.248 -4.630707662 0.0004707 -1.3E+07 -

4587351 -1.3E+07 -4587351

1/x 590777164.5 99121981.71 5.960102435 4.74504E-05 3.77E+08 8.05E+08 3.77E+08 8.05E+08

0.0

500,000.0

1,000,000.0

1,500,000.0

2,000,000.0

2,500,000.0

3,000,000.0

3,500,000.0

0.018 0.0185 0.019 0.0195

GD

P(m

il. e

uro

)(Y

)

1/x

1/x Line Fit Plot

GDP(mil. euro)(Y)

Predicted GDP(mil. euro)(Y)

4.2. Model logaritmic



R Square 0.730776651



Observations 15

ANOVA df SS MS F Significance

F

Regression 1 6.53E+11 6.53E+11 35.28705 4.9E-05

Residual 13 2.41E+11 1.85E+10

Total 14 8.93E+11

Coefficients

Standard Error


Lower 95.0%

Upper 95.0%

Intercept 46590518.15 7427976 6.272303 2.87E-05 30543351 62637685 30543351 62637685

LN X Cht consum final -11092637.17 1867356 -5.94029 4.9E-05 -1.5E+07 -7058459 -1.5E+07 -7058459

0.0

500,000.0

1,000,000.0

1,500,000.0

2,000,000.0

2,500,000.0

3,000,000.0

3,500,000.0

3.92 3.94 3.96 3.98 4 4.02

GD

P(m

il. e

uro

)(Y

)

lnx

lnx Line Fit Plot

GDP(mil. euro)(Y)


4.3. Model exponenial



R Square 0.717640317



Observations 15

ANOVA


Regression 1 0.103758 0.103758 33.04057 6.73E-05

Residual 13 0.040824 0.00314

Total 14 0.144582

Coefficients Standard Error


Lower 95.0%

Upper 95.0%

Intercept 19.15101141 0.772126 24.80297 2.48E-12 17.48294 20.81909 17.48294 20.81909

Final consumption expenditure (% of GDP) (X) -0.083088332 0.014455 -5.74809 6.73E-05 -0.11432 -0.05186 -0.11432 -0.05186

14.5

14.55

14.6

14.65

14.7

14.75

14.8

14.85

14.9

14.95

51.0 52.0 53.0 54.0 55.0

lny

Final consumption expenditure (% of GDP) (X)

Final consumption expenditure (% of GDP) (X) Line Fit Plot

lny

Predicted lny

4.4. Model Parabolic (polinomial de ordin 2)



R Square 0.744043497



Observations 15

ANOVA


Regression 2 6.64684E+11 3.32E+11 17.44148 0.000281188

Residual 12 2.28656E+11 1.91E+10

Total 14 8.9334E+11

Coefficients

Standard Error


Lower 95.0%

Upper 95.0%

Intercept 126148457.5 135782949.2 0.929045 0.371177 -169697174 4.22E+08 -1.7E+08 4.22E+08


-4438628.314

5102764.644 -0.86985 0.401448 -15556597.37 6679341 -1.6E+07 6679341

x^2 39733.50075 47925.78205 0.829063 0.423254 -64687.80793 144154.8 -64687.8 144154.8

0.0

500,000.0

1,000,000.0

1,500,000.0

2,000,000.0

2,500,000.0

3,000,000.0

3,500,000.0

51.0 52.0 53.0 54.0 55.0

GD

P(m

il. e

uro

)(Y

)



GDP(mil. euro)(Y)


0.0

500,000.0

1,000,000.0

1,500,000.0

2,000,000.0

2,500,000.0

3,000,000.0

3,500,000.0

2,600.002,700.002,800.002,900.003,000.003,100.00

GD

P(m

il. e

uro

)(Y

)

x^2

x^2 Line Fit Plot

GDP(mil. euro)(Y)


4.5. Model polinomial de ordin 3



R Square 0.769730583



Observations 15

ANOVA

df SS MS F

Significance F

Regression 3 6.87632E+11 2.29E+11 12.25671 0.000787 Residual 11 2.05709E+11 1.87E+10

Total 14 8.9334E+11

Coefficients Standard Error t Stat P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept -

7554866883 6935291381 -1.08934 0.299295 -2.3E+10 7.71E+09 -2.3E+10 7.71E+09


430111140 392319551.8 1.096329 0.296356 -4.3E+08 1.29E+09 -4.3E+08 1.29E+09

x^2 -

8153452.086 7396497.477 -1.10234 0.293848 -2.4E+07 8126129 -2.4E+07 8126129

x^3 51482.30557 46475.31709 1.107734 0.291611 -50809.2 153773.8 -50809.2 153773.8

0.0500,000.0

1,000,000.01,500,000.02,000,000.02,500,000.03,000,000.03,500,000.0

51.0 52.0 53.0 54.0 55.0

GD

P(m

il. e

uro

)(Y

)



GDP(mil. euro)(Y)


0.0

500,000.0

1,000,000.0

1,500,000.0

2,000,000.0

2,500,000.0

3,000,000.0

3,500,000.0

2,600.002,700.002,800.002,900.003,000.003,100.00

GD

P(m

il. e

uro

)(Y

)

x^2

x^2 Line Fit Plot

GDP(mil. euro)(Y)


0.0

1,000,000.0

2,000,000.0

3,000,000.0

4,000,000.0

130000 140000 150000 160000 170000

GD

P(m

il. e

uro

)(Y

)

x^3

x^3 Line Fit Plot

GDP(mil. euro)(Y)


5. REZULTATE MODELE NELINIARE

Column1 Model

Hiperbolic Model

Logaritmic Model

exponential Model polinomial de

ord 2 Model polinomial de

ord 3

Multiple R

0.855619557 0.854854755 0.84713654 0.86257956 0.87734291

R Square 0.732084827 0.730776651 0.717640317 0.744043497 0.769730583

F 35.52282103 35.28704517 33.0405673 17.44148295 12.25670999

T stat (a) -4.630707662 6.272303196 24.80296967 0.929044908 -1.089336622

T stat (b) 5.960102435 -5.94028999 -5.748092492 -0.869847744 1.096328587

T stat (b2)

0.829063169 -1.102339602

T stat (b3)

1.107734359

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MODELE LINIARE SI NELINIARE