8 8.1 8.2 8.3 8.4

8.1 y=0+1ex + 8.1 , x=exyxy=0+1x+

8.1 y=0+1x+2x2++pxp + 8.2x1=x,x2=x2,xp=xpyx1,x2,xpy=0+1x1+2x2++pxp+ (8.2)xpp

8.1 y=aeb xe 8.3, lny=lna+bx+y=lny, 0=lna,1=b,yxy=0+1x+

8.1 , y= aeb x +8.4 b (8.3) (8.4)

8.1 8.3y=aeb xe y=aeb x

8.1 SPSS10

Linear

y=b0+b1t

Logarithm

y=b0+b1lnt

Inverse

y=b0+b1/t

Quadratic

y=b0+b1t+b2t2

Cubic

y=b0+b1t+b2t2+b3t3

Power

y=b0

Compound

y=b0

S

S

y=exp(b0+b1/t)

Logistic

u

Growth

y=exp(b0+b1t)

Exponent

y=b0exp(b1t)

_1030013797.unknown

_1030013951.unknown

_1030013744.unknown

8.1 SPSS,1.

8.1 (a>0, b>0)

8.1 2. S Sa>0b>0x x+y1/a ; x-y0 y=0y=1/a S S

8.1

8.1 SPSSSy=exp(b0+b1/t): b10ttS SPSS0

8.1 8.1GDP()GDPGDPt1981t=11998 t=18198119988.1

8.1

tyeiy=lny198114862.44296.35566.058.489198225294.75123.04171.668.574198335934.56108.80-174.308.689198447171.07284.24-113.248.878198558964.48685.86278.549.1011986610202.210357.16-154.969.2301987711962.512350.06-387.569.3901988814928.314726.42201.889.6111989916909.217560.04-650.849.73619901018547.920938.89-2390.999.82819911121617.824967.89-3350.099.98119921226638.129772.14-3134.0410.19019931334634.435500.81-866.4110.45319941446759.442331.774427.6310.75319951558478.150477.138000.9710.97619961667884.660189.807694.8011.12619971774462.671771.352691.2511.21819981879395.785581.38-6185.6811.282

8.1 1. SPSSCurve EstimationGDP8.2

8.1

8.1

8.2

y=b0+b1t

Multiple R .92528

R Square .85615

Adjusted R Square .84716

Standard Error 9964.23063

Analysis of Variance:

DF Sum of Squares Mean Square F Signif F

Regression 1 9454779005.1 9454779005.1 95.22782 .0000

Residuals 16 1588574273.6 99285892.1

Variable B SE B Beta T Sig T

Time 4417.522807 452.685809 .925284 9.758 .0000

(Constant) -13374.922222 4900.032018 -2.730 .0148

8.1

8.3

y=b0

Multiple R .99593

R Square .99188

Adjusted R Square .99138

Standard Error .08760

Analysis of Variance:

DF Sum of Squares Mean Square F Signif F

Regression 1 15.004878 15.004878 1955.31315 .0000

Residuals 16 .122782 .007674

Variable B SE B Beta T Sig T

Time 1.192417 .004746 2.707250 251.269 .0000

(Constant) 3603.061130 155.215413 23.213 .0000

_1031938334.unknown

8.1 SSE =262467769=2.625108 R2=1-262467769/11043353279=0.97623

8.1 b0=3603.06,b1=1.192417 b1=1.192417=119.2417%GDP19.2417% GDPGDP

8.1 2. y=b0lny=lnb0+ln(b1) ty=lny, 0=lnb0,1=ln(b1),yty=0+1ty=lny8.4yt

8.1

8.1

=8.190

=0.176

EMBED Equation.3

SPSSCurve Estimation

_1031303507.unknown

_1031303538.unknown

_1031303610.unknown

_1031303491.unknown

8.2 yi=0+1xi+11+iyi=0+1xi+11111 yi=0+1xi+11+111+i

8.2

yi=0+1xi1+2xi2+11

+22

+12xi1xi2+i

12

112212

x1x2

_1031036694.unknown

_1031036715.unknown

8.2 8.2 8.5183544: x1 x2 y

8.2

yi=0+1xi1+2xi2+11

+22

+12xi1xi2+i

_1031036694.unknown

_1031036715.unknown

8.2

xi1xi2yi12345678910111213141516171866.29040.96472.99645.01057.20426.85238.12235.84075.79637.40854.37646.18646.13030.36639.06079.38052.76655.916751064546952743518619663252841261449492664910598771456245133133

8.2

x1x2

x1x2

yx1Block 1 of Next,

x1x2

Block 2 of Next,

x1x2

_1031039584.unknown

_1031041474.unknown

8.2

8.2

8.2 8.6

F

x1

x2|x1

|x1,x2

| x1,x2,

x1x2|x1,x2,

,

104474

2284

1238

3

6

3567

1283

45

42

36

1

2

11

22

12

-

-

1238/45/14=385

3/42/13=0.93

6/36/12=2.00

108005

5

_1031039610.unknown

_1031041474.unknown

_1031041519.unknown

_1031039584.unknown

8.2

=-62.349+0.840x1+5.685x2+0.0371

(0.164)(0.164) (0.785)

_1031045671.unknown

_1031045822.unknown

8.2 8.3 C3EDTAX1X2X3 7U7741236.9

8.2 6.9

EDTA

X1g

X2g

X3g

y

1/y

1

0.00

30

0.6

1.160

0.862

2

0.02

38

1.2

0.312

3.205

3

0.04

46

0.4

0.306

3.263

4

0.06

26

1.0

1.318

0.759

5

0.08

34

0.2

0.877

1.140

6

0.10

42

0.8

0.147

6.803

7

0.12

50

1.4

0.204

4.902

8.2 6.1y = 2.63 + 0.77 X1 - 0.0524 X2 - 0.087 X3P=0.1040R-square= 83.9% AdjR-sq= 67.8%

8.2 9

8.2 6.10

X1

X2

X3

X11

X22

X33

X12

X13

X23

y

0.00

0.02

0.04

0.06

0.08

0.10

0.12

30

38

46

26

34

42

50

0.6

1.2

0.4

1.0

0.2

0.8

1.4

0.0000

0.0004

0.0016

0.0036

0.0064

0.0100

0.0144

900

1444

2116

676

1156

1764

2500

0.360

1.440

0.160

1.000

0.040

0.640

1.960

0.00

0.76

1.84

1.56

2.72

4.20

6.00

0.000

0.024

0.016

0.060

0.016

0.080

0.168

18.0

45.6

18.4

26.0

6.8

33.6

70.0

1.160

0.312

0.306

1.318

0.877

0.147

0.204

8.2 710 SPSSP=0.05P=0.10x2 OptionP0.30P0.50

8.2 6.12 2

Step

1

2

3

4

5

Constant

2.579

5.957

7.311

7.873

9.165

X2

Prob>F

-0.0516

0.004

-0.2376

0.053

-0.3034

0.021

-0.3126

0.030

-0.378

0.016

X22

Prob>F

0.00245

0.100

0.00336

0.033

0.00323

0.048

0.0046

0.019

X3

Prob>F

-0.292

0.107

-1.115

0.168

-1.430

0.033

X23

Prob>F

0.0206

0.251

0.0317

0.039

X13

Prob>F

-2.33

0.058

R-square

83.14

92.12

97.11

98.73

99.99

8.2 5X2 X22= X3X23=X2 X3X13= X1 X355: X2 X22= yX2 X2=48.548y=0.1976y=0.147

8.2 yX3X3=1.4X2X3X2=45.145X3=1.4y=0.0746y=0.147

8.2 X31.115 X3+0.0206 X2X3X254X3X24845X254yX3X3yX3=1.4 X3=1.4X2X2=43.944X2=44X3=1.4y=0.080

8.2 X1X3EDTAX1X3yX1=0.12X3=1.4X2=41.241y= 0.128

8.2 3 97.1198.7399.99% 6y7 0.0806y=0.1476.13

8.2 6.13

X1g

X2g

X3g

0.00

0.00

0.00

0.12

48

45

44

41

0.0

1.4

1.4

1.4

0.197

0.074

0.080

0.000

8.2 [17]yX1=0.12X2=38X3=1.4

8.3 yi = f (xi,)+i , i=1,2,,n 8.9yi xi=(xi1,xi2,xik) =(0,1,p ) i

8.3

,

_1030953497.unknown

8.3

f

Q()

fj0p+1

_1030953513.unknown

Q()

_1030953513.unknown

8.3 SST=SSR+SSE

8.3 8.4 x y 3c0c1c2c0100% 3c0=100c1=5c2=4.89

8.3 8.3

x 1 2 3 4 5 6 7 8 9y(%)0.5 2.3 3.4 24.0 54.7 82.1 94.8 96.2 96.4

8.3 SPSSRegressionNonlinearymodel Expressionc0-c0/(1+(x/c2)**c1),Parameters

8.3

Iteration Residual SS C0 C1 C2 1 172.7877170 100.000000 5.00000000 4.80000000 1.1 32.60704344 97.7943996 6.57938197 4.74460195 2 32.60704344 97.7943996 6.57938197 4.74460195 2.1 20.20240372 99.5785656 6.73691756 4.80074972 3 20.20240372 99.5785656 6.73691756 4.80074972 3.1 20.18814307 99.5334852 6.76307026 4.79941696 4 20.18814307 99.5334852 6.76307026 4.79941696 4.1 20.18803580 99.5411768 6.76104089 4.79966204 5 20.18803580 99.5411768 6.76104089 4.79966204 5.1 20.18803473 99.5404448 6.76127044 4.79964160 6 20.18803473 99.5404448 6.76127044 4.79964160 6.1 20.18803472 99.5405197 6.76124802 4.79964382

8.3

Nonlinear Regression Summary Statistics

Source DF Sum of Squares Mean Square

Regression 3 37839.85197 12613.28399

Residual 6 20.18803 3.36467

Uncorrected Total 9 37860.04000

(Corrected Total) 8 14917.88889

R squared = 1 - Residual SS / Corrected SS = .99865

8.3

Asymptotic 95 %

Asymptotic Confidence Interval

Parameter Estimate Std. Error Lower Upper

C0 99.540519687 1.567325937 95.705411276 103.37562810

C1 6.761248019 .421980049 5.728700036 7.793796003

C2 4.799643816 .050165521 4.676893208 4.922394423

8.3

xye110.500.5-50.48889222.30.272.03-50.21889333.43.98-0.58-46.50889442422.481.52-28.008895554.756.61-1.916.121116682.181.520.5831.031117794.892.342.4641.851118896.296.49-0.2946.001119996.498.14-1.7447.65111550.4888950.203330.285556-0.285566014917.8915156.5519.4316215156.5528537860.0437839.8520.1880315157.28

8.3 SSR=15156.55SST=14917.89

8.3 yx

8.3 8.4 Gompertz k k8.12

8.3 8.8

tyty1980111.4119931468.211981213.5519941569.371982313.2819951678.081983412.9219961778.021984515.2819971892.061985617.12199819100.141986721.6719992099.891987824.0220002199.451988924.55200122103.6719891030.55200223106.3219901134.04200324103.4219911238.17200425115.5219921353.36

8.3 SPSS AnalyzeRegressionNonlinear k*a**(b**t),k115.52k120ab010.531

8.3

8.3

Dependent variable: y

a R squared = 1 - (Residual Sum of Squares) / (Corrected Sum of Squares) = .976.

8.3 k=150.0a=0.012 43b=0.892 7k=150.0 8.4Excel8.4

Chart3

11.412.99

13.554.55

13.286.62

12.929.25

15.2812.47

17.1216.29

21.6720.67

24.0225.57

24.5530.92

30.5536.63

34.0442.62

38.1748.78

53.3655.03

68.2161.28

69.3767.46

78.0873.5

78.0279.35

92.0684.96

100.1490.3

99.8995.35

99.448100.1

103.6737104.54

106.32108.67

103.42112.49

115.52116.02

2005119.26

2006122.23

2007124.94

2008127.41

2009129.66

2010131.7

2.1

yx

26.23.4

17.81.8

31.34.6

23.12.3

27.53.1

365.5

14.10.7

22.33

19.62.6

31.34.3

242.1

17.31.1

43.26.1

36.44.8

26.13.8

2.2

xy

1980460234.75

1981489259.26

1982525280.58

1983580305.97

1984692347.15

1985853433.53

1986956481.36

19871104545.4

19881355687.51

19891512756.27

19901634797.08

19911879890.66

199222871063.39

199329391323.22

199439231736.32

199548542224.59

199655762627.06

199760532819.36

199863922958.18

3.1

x1x2x3x4x5x6x7x8x9x10x11x12y

1.944.5154.45207.33246.87277.64135.7930.58110.6780.8351.8314.092384

0.336.49133.16127.29120.17114.8881.2114.0535.71627.12.93202

6.1617.18313.4386.96202.98204.2279.4332.4279.3814.54128.1342.15100

5.359.3123.8122.94101.5996.8434.6713.9937.285.9363.913.1238

3.784.26106.0595.4927.5822.7534.2414.0628.24.6935.729.51126

11.178.17271.96533.15164.4123.78187.758.6390.5231.7184.0511.61262

2.843.61109.37130.852.4962.2638.1521.8244.5325.7848.4914.2238

8.6411.41160.06246.57109.18115.3268.7134.5558.0813.5272.0521.17121

3.646.67244.42412.04459.63512.21160.4543.5189.9348.5548.637.051218

30.8919.08435.77724.85376.04381.81210.3971.82150.6423.74188.2819.65529

6.266.3321.75665.8157.94172.19147.1652.4478.1610.993.059.45361

4.138.87152.29258.683.4285.175.7426.7563.475.8947.022.6651

5.855.61347.25332.59157.32172.48115.1633.877.278.6979.018.24651

6.76.8145.4143.5497.4100.543.2817.7151.035.4162.0318.2543

10.811.73442.2665.33411.89429.88115.0787.45145.2521.39187.77110.2220

4.1622.51299.63316.81132.57139.7684.7953.9384.2312.36116.8910.38101

4.647.65195.56373.04161.84180.14101.585880.5321.61100.695.1688

7.0810.99216.49291.73119.22125.6247.0548.1997.9712.07139.3916.67156

16.324.1688.83827.16271.07268.2331.5571.44146.1523.38145.7716.522942

4.014125.04243.552.0631.2247.2525.5955.274.4960.1313.64156

0.82.0735.0360.929.230.1420.224.2212.191.39.290.2796

4.422.1178.93138.4368.3173.8479.9818.4243.320.0148.480.7288

11.189.42196.27328.46204.49144.45101.2143.0174.2215.8590.611.0584

2.012.0325.0469.9740.8636.4527.0213.826.832.8625.636.7648

6.436.0888.9170.1588.8689.8433.6629.251.258.640.474.81261

1.910.985.0811.130.671.691.942.955.020.897.590.1733

5.499.9115.4294.6376.5753.1447.8822.0856.9714.0248.6438.17247

3.977.839.3299.2341.6450.5511.418.8115.986.3316.467.0230

1.313.0813.6718.7918.3718.573.153.148.661.2614.31.23

1.12.116.1119.6417.8516.524.163.036.761.067.523.181

4.5810.3592.03103.3449.1950.228.1411.8237.954.5239.493.5382

3.2

x1x2y

253547.79553.96

20896.34208.55

6750.323.1

10012087.052815.4

5251639.311052.12

8253357.73427

120808.47442.82

28520.2770.12

7671.13122.24

5322863.321400

751160464

40862.757.5

187672.99224.18

122901.76538.94

743546.182442.79

2949158.153600

195015.51965.6511

195125.635.7025

195235.74825.7704

195345.87965.8517

195456.02665.9443

195566.14656.0466

195676.28286.1577

195786.46536.2764

195896.59946.4020

1959106.72076.5337

1960116.62076.6709

1961126.58596.8129

1962136.72956.9592

1963146.91727.1093

1964157.04997.2628

1965167.25387.4191

1966177.45427.5778

1967187.63687.7386

1968197.85347.9012

1969208.06718.0650

1970218.29928.2299

1971228.52298.3955

1972238.71778.5615

1973248.92118.7277

1974259.08598.8937

1975269.2429.0594

1976279.37179.2246

1977289.49749.3889

1978299.62599.5523

1979309.75429.7144

1980319.87059.8753

19813210.007210.0346

19823310.154110.1923

19833410.249510.3481

19843510.347510.5021

19853610.453210.6540

19863710.572110.8038

19873810.72410.9513

19883910.897811.0965

19894011.270411.2392

19904111.433311.3795

19914211.582311.5173

19924311.717111.6524

19934411.851711.7849

19944511.98511.9148

19954612.112112.0419

19964712.238912.1662

19974812.362612.2878

19984912.476112.4066

19995012.578612.5227

20005112.674312.6359

20015212.762712.7463

20025312.845312.8540

20035412.922712.9588

20045512.998813.0609

20055613.075613.1603

20065713.2569

20075813.3508

20085913.4421

20096013.5306

20106113.6166

20116213.7000

20126313.7809

20136413.8592

20146513.9351

20156614.0086

20166714.0796

20176814.1484

20186914.2148

20197014.2791

20207114.3411

20217214.4010

20227314.4588

20237414.5145

20247514.5682

20257614.6200

20267714.6699

20277814.7180

20287914.7642

20298014.8087

20308114.8515

20318214.8926

20328314.9321

20338414.9701

20348515.0066

20358615.0416

20368715.0752

20378815.1074

20388915.1383

20399015.1679

20409115.1962

20419215.2234

20429315.2494

20439415.2743

20449515.2981

20459615.3209

20469715.3426

20479815.3634

20489915.3833

204910015.4023

205010115.4204

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0

0

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0

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0

0

0

0

0

0

0

0

0

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0

0

0

0

0

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0

0

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0

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0

0

0

0

0

0

0

0

0

0

li8.

ty

1980111.412.99

1981213.554.55

1982313.286.62

1983412.929.25

1984515.2812.47

1985617.1216.29

1986721.6720.67

1987824.0225.57

1988924.5530.92

19891030.5536.63

19901134.0442.62

19911238.1748.78

19921353.3655.03

19931468.2161.28

19941569.3767.46

19951678.0873.5

19961778.0279.35

19971892.0684.96

199819100.1490.3

19992099.8995.35

20002199.448100.1

200122103.6737104.54

200223106.32108.67

200324103.42112.49

200425115.52116.02

200526119.26

200627122.23

200728124.94

200829127.41

200930129.66

201031131.7

li8.

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

Sheet1

199319.546.633.919.947.432.7-0.4-0.81.2100.019.546.633.9

199419.746.533.820.347.831.9-0.6-1.31.9100.019.746.533.8

199519.747.233.120.548.830.7-0.8-1.62.4100.019.747.233.1

199619.547.533.020.449.530.1-0.9-2.02.9100.019.547.533.0

199718.147.534.419.150.030.9-1.0-2.53.5100.018.147.534.4

199817.346.236.518.649.332.1-1.3-3.14.4100.017.346.236.5

199916.245.838.017.649.432.9-1.4-3.75.199.916.245.838.0

200014.845.939.316.450.233.4-1.5-4.35.8100.014.845.939.3

200114.145.240.715.850.134.1-1.7-4.96.6100.014.145.240.7

200213.544.841.715.350.434.3-1.8-5.67.4100.013.544.841.7

200312.546.041.514.452.233.4-1.9-6.28.1100.012.546.041.5

200413.146.240.715.252.931.9-2.1-6.78.8100.013.146.240.7

GDP

199018547.95017.07717.45813.5

199121617.85288.69102.27227.0

199226638.15800.011699.59138.6

199334634.46882.116428.511323.8

199446759.49457.222372.214930.0

199558478.111993.028537.917947.2

199667884.613844.233612.920427.5

199774462.614211.237222.723028.7

199878345.214552.438619.325173.5

199982067.514472.040557.827037.7

200089468.114628.244935.329904.6

200197314.815411.848750.033153.0

2002104790.616117.353540.735132.6

SUMMARY OUTPUT

Multiple R0.9998190104

R Square0.9996380536

Adjusted R Square0.9996051494

586.4816333583

13

dfSSMSFSignificance F

110449609223.34810449609223.34830380.24121059550

113783567.76893328343960.706266662

1210453392791.1169

Coefficientst StatP-valueLower 95%Upper 95% 95.0% 95.0%

Intercept4134.2489719396367.720989829611.24289634340.00000022663324.90053077424943.5974131053324.90053077424943.597413105

X Variable 11.90096847330.0109063469174.299286316901.87696376571.92497318091.87696376571.9249731809

199018547.950177717.45813.518547.9

199121617.85288.69102.2722721617.8

199226638.1580011699.59138.626638.1

199334634.46882.116428.511323.834634.4

199446759.49457.222372.21493046759.4

199558478.11199328537.917947.258478.1

199667884.613844.233612.920427.567884.6

199774462.614211.237222.723028.774462.6

199878345.214552.438619.325173.578345.2

199982067.51447240557.827037.782067.5

200089468.114628.244935.329904.689468.1

200197314.815411.8487503315397314.8

2002104790.616117.353540.735132.6104790.6

SUMMARY OUTPUTSUMMARY OUTPUT

Multiple R1Multiple R0.9986922681

R Square1R Square0.9973862464

Adjusted R Square1Adjusted R Square0.9968634956

0730.238812478

77

dfSSMSFSignificance FdfSSMSFSignificance F

31020082220.85429340027406.95142938496757177629394000000000000000011017415977.238041017415977.238041907.95764317750.0000001187

30052666243.61624623533248.723249246

61020082220.8542961020082220.85429

Coefficientst StatP-valueLower 95%Upper 95% 95.0% 95.0%Coefficientst StatP-valueLower 95%Upper 95% 95.0% 95.0%

Intercept0.00000000010.00000000010.88933388360.4393368096-0.00000000020.0000000003-0.00000000020.0000000003Intercept5716.32804942921833.8045625953.11719589210.02633557071002.383352437210430.27274642121002.383352437210430.2727464212

X Variable 11015104323513538401111X Variable 11.8648954650.042694322743.68017448660.00000011871.75514621461.97464471541.75514621461.9746447154

X Variable 21055881074840137701111

X Variable 31054596202838836201111

4.3

yx

12648777

21059210

3909954

413110508

512210979

610711912

740612747

850313499

943114269

1058815522

1189816730

1295017663

1377918575

1481919635

15122221163

16170222880

17157824127

18165425604

19140026500

20182927670

21220028300

22201727430

23210529560

24160028150

25225032100

26242032500

27257035250

28172033500

29190036000

30210036200

31230038200

3.3

yx1x2x3x4x5

1978231301018888149114.89180.92

1979298335021958638916.00420.39

1980343368825319220419.53570.25

1981401394127999530021.82776.71

1982445425830549992223.27792.43

19833914736335810604422.91947.70

19845545652390511035326.021285.22

19857447020487911211027.721783.30

19869977859555210857932.432281.95

198713109313638611242938.912690.23

1988144211738803812264537.383169.48

1989128313176900511380747.192450.14

199016601438496639571250.682746.20

1991217816557109699508155.913335.65

1992288620223129859969383.663311.50

19933383248821594910545896.084152.70

8.3 Constraints k130k>116

8.3 [15]13

8.3 8.6 8.919502005Weibullka >0, 0< b 0

8.3 8.9

tyty195015.51961978299.6259195125.631979309.7542195235.74821980319.8705195345.879619813210.0072

1975269.24220035412.92271976279.371720045512.99881977289.497420055613.0756

8.3 16k=16b=0.5c=1 t=11950=5.5196

8.7k=15.76168.5Excel

8.3

8.7Parameter Estimates

Parameter

Estimate

Std. Error

95% Confidence Interval

Lower Bound

Upper Bound

k

15.760

.650

14.455

17.064

a

10.135

.693

8.746

11.525

b

.997

.000

.996

.998

c

1.551

.071

1.408

1.694

8.3

ANOVA(a)

Source

Sum of Squares

df

Mean Squares

Regression

5266.738

4

1316.685

Residual

.884

52

.017

Uncorrected Total

5267.622

56

Corrected Total

319.677

55

Dependent variable: y

a R squared = 1 - (Residual Sum of Squares) / (Corrected Sum of Squares) = .997.

8.3 8.5

Chart2

5.51965.6511

5.635.7025

5.74825.7704

5.87965.8517

6.02665.9443

6.14656.0466

6.28286.1577

6.46536.2764

6.59946.402

6.72076.5337

6.62076.6709

6.58596.8129

6.72956.9592

6.91727.1093

7.04997.2628

7.25387.4191

7.45427.5778

7.63687.7386

7.85347.9012

8.06718.065

8.29928.2299

8.52298.3955

8.71778.5615

8.92118.7277

9.08598.8937

9.2429.0594

9.37179.2246

9.49749.3889

9.62599.5523

9.75429.7144

9.87059.8753

10.007210.0346

10.154110.1923

10.249510.3481

10.347510.5021

10.453210.654

10.572110.8038

10.72410.9513

10.897811.0965

11.270411.2392

11.433311.3795

11.582311.5173

11.717111.6524

11.851711.7849

11.98511.9148

12.112112.0419

12.238912.1662

12.362612.2878

12.476112.4066

12.578612.5227

12.674312.6359

12.762712.7463

12.845312.854

12.922712.9588

12.998813.0609

13.075613.1603

200613.2569

200713.3508

200813.4421

200913.5306

201013.6166

201113.7

201213.7809

201313.8592

201413.9351

201514.0086

201614.0796

201714.1484

201814.2148

201914.2791

202014.3411

202114.401

202214.4588

202314.5145

202414.5682

202514.62

202614.6699

202714.718

202814.7642

202914.8087

203014.8515

14.8926

14.9321

14.9701

15.0066

15.0416

15.0752

15.1074

15.1383

15.1679

15.1962

15.2234

15.2494

15.2743

15.2981

15.3209

15.3426

15.3634

15.3833

15.4023

15.4204

2.1

yx

26.23.4

17.81.8

31.34.6

23.12.3

27.53.1

365.5

14.10.7

22.33

19.62.6

31.34.3

242.1

17.31.1

43.26.1

36.44.8

26.13.8

2.2

xy

1980460234.75

1981489259.26

1982525280.58

1983580305.97

1984692347.15

1985853433.53

1986956481.36

19871104545.4

19881355687.51

19891512756.27

19901634797.08

19911879890.66

199222871063.39

199329391323.22

199439231736.32

199548542224.59

199655762627.06

199760532819.36

199863922958.18

3.1

x1x2x3x4x5x6x7x8x9x10x11x12y

1.944.5154.45207.33246.87277.64135.7930.58110.6780.8351.8314.092384

0.336.49133.16127.29120.17114.8881.2114.0535.71627.12.93202

6.1617.18313.4386.96202.98204.2279.4332.4279.3814.54128.1342.15100

5.359.3123.8122.94101.5996.8434.6713.9937.285.9363.913.1238

3.784.26106.0595.4927.5822.7534.2414.0628.24.6935.729.51126

11.178.17271.96533.15164.4123.78187.758.6390.5231.7184.0511.61262

2.843.61109.37130.852.4962.2638.1521.8244.5325.7848.4914.2238

8.6411.41160.06246.57109.18115.3268.7134.5558.0813.5272.0521.17121

3.646.67244.42412.04459.63512.21160.4543.5189.9348.5548.637.051218

30.8919.08435.77724.85376.04381.81210.3971.82150.6423.74188.2819.65529

6.266.3321.75665.8157.94172.19147.1652.4478.1610.993.059.45361

4.138.87152.29258.683.4285.175.7426.7563.475.8947.022.6651

5.855.61347.25332.59157.32172.48115.1633.877.278.6979.018.24651

6.76.8145.4143.5497.4100.543.2817.7151.035.4162.0318.2543

10.811.73442.2665.33411.89429.88115.0787.45145.2521.39187.77110.2220

4.1622.51299.63316.81132.57139.7684.7953.9384.2312.36116.8910.38101

4.647.65195.56373.04161.84180.14101.585880.5321.61100.695.1688

7.0810.99216.49291.73119.22125.6247.0548.1997.9712.07139.3916.67156

16.324.1688.83827.16271.07268.2331.5571.44146.1523.38145.7716.522942

4.014125.04243.552.0631.2247.2525.5955.274.4960.1313.64156

0.82.0735.0360.929.230.1420.224.2212.191.39.290.2796

4.422.1178.93138.4368.3173.8479.9818.4243.320.0148.480.7288

11.189.42196.27328.46204.49144.45101.2143.0174.2215.8590.611.0584

2.012.0325.0469.9740.8636.4527.0213.826.832.8625.636.7648

6.436.0888.9170.1588.8689.8433.6629.251.258.640.474.81261

1.910.985.0811.130.671.691.942.955.020.897.590.1733

5.499.9115.4294.6376.5753.1447.8822.0856.9714.0248.6438.17247

3.977.839.3299.2341.6450.5511.418.8115.986.3316.467.0230

1.313.0813.6718.7918.3718.573.153.148.661.2614.31.23

1.12.116.1119.6417.8516.524.163.036.761.067.523.181

4.5810.3592.03103.3449.1950.228.1411.8237.954.5239.493.5382

3.2

x1x2y

253547.79553.96

20896.34208.55

6750.323.1

10012087.052815.4

5251639.311052.12

8253357.73427

120808.47442.82

28520.2770.12

7671.13122.24

5322863.321400

751160464

40862.757.5

187672.99224.18

122901.76538.94

743546.182442.79

2949158.153600

195015.51965.6511

195125.635.7025

195235.74825.7704

195345.87965.8517

195456.02665.9443

195566.14656.0466

195676.28286.1577

195786.46536.2764

195896.59946.4020

1959106.72076.5337

1960116.62076.6709

1961126.58596.8129

1962136.72956.9592

1963146.91727.1093

1964157.04997.2628

1965167.25387.4191

1966177.45427.5778

1967187.63687.7386

1968197.85347.9012

1969208.06718.0650

1970218.29928.2299

1971228.52298.3955

1972238.71778.5615

1973248.92118.7277

1974259.08598.8937

1975269.2429.0594

1976279.37179.2246

1977289.49749.3889

1978299.62599.5523

1979309.75429.7144

1980319.87059.8753

19813210.007210.0346

19823310.154110.1923

19833410.249510.3481

19843510.347510.5021

19853610.453210.6540

19863710.572110.8038

19873810.72410.9513

19883910.897811.0965

19894011.270411.2392

19904111.433311.3795

19914211.582311.5173

19924311.717111.6524

19934411.851711.7849

19944511.98511.9148

19954612.112112.0419

19964712.238912.1662

19974812.362612.2878

19984912.476112.4066

19995012.578612.5227

20005112.674312.6359

20015212.762712.7463

20025312.845312.8540

20035412.922712.9588

20045512.998813.0609

20055613.075613.1603

20065713.2569

20075813.3508

20085913.4421

20096013.5306

20106113.6166

20116213.7000

20126313.7809

20136413.8592

20146513.9351

20156614.0086

20166714.0796

20176814.1484

20186914.2148

20197014.2791

20207114.3411

20217214.4010

20227314.4588

20237414.5145

20247514.5682

20257614.6200

20267714.6699

20277814.7180

20287914.7642

20298014.8087

20308114.8515

20318214.8926

20328314.9321

20338414.9701

20348515.0066

20358615.0416

20368715.0752

20378815.1074

20388915.1383

20399015.1679

20409115.1962

20419215.2234

20429315.2494

20439415.2743

20449515.2981

20459615.3209

20469715.3426

20479815.3634

20489915.3833

204910015.4023

205010115.4204

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

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00

00

00

00

00

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00

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00

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00

00

00

00

00

00

00

00

00

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00

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00

00

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00

00

00

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00

00

00

00

00

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00

00

00

00

00

00

00

00

00

00

00

00

00

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

0

0

0

0

0

li8.

ty

1980111.41

1981213.55

1982313.28

1983412.92

1984515.28

1985617.12

1986721.67

1987824.02

1988924.55

19891030.55

19901134.04

19911238.17

19921353.36

19931468.21

19941569.37

19951678.08

19961778.02

19971892.06

199819100.14

19992099.89

20002199.448

200122103.6737

200223106.32

200324103.42

200425115.52

Sheet1

199319.546.633.919.947.432.7-0.4-0.81.2100.019.546.633.9

199419.746.533.820.347.831.9-0.6-1.31.9100.019.746.533.8

199519.747.233.120.548.830.7-0.8-1.62.4100.019.747.233.1

199619.547.533.020.449.530.1-0.9-2.02.9100.019.547.533.0

199718.147.534.419.150.030.9-1.0-2.53.5100.018.147.534.4

199817.346.236.518.649.332.1-1.3-3.14.4100.017.346.236.5

199916.245.838.017.649.432.9-1.4-3.75.199.916.245.838.0

200014.845.939.316.450.233.4-1.5-4.35.8100.014.845.939.3

200114.145.240.715.850.134.1-1.7-4.96.6100.014.145.240.7

200213.544.841.715.350.434.3-1.8-5.67.4100.013.544.841.7

200312.546.041.514.452.233.4-1.9-6.28.1100.012.546.041.5

200413.146.240.715.252.931.9-2.1-6.78.8100.013.146.240.7

GDP

199018547.95017.07717.45813.5

199121617.85288.69102.27227.0

199226638.15800.011699.59138.6

199334634.46882.116428.511323.8

199446759.49457.222372.214930.0

199558478.111993.028537.917947.2

199667884.613844.233612.920427.5

199774462.614211.237222.723028.7

199878345.214552.438619.325173.5

199982067.514472.040557.827037.7

200089468.114628.244935.329904.6

200197314.815411.848750.033153.0

2002104790.616117.353540.735132.6

SUMMARY OUTPUT

Multiple R0.9998190104

R Square0.9996380536

Adjusted R Square0.9996051494

586.4816333583

13

dfSSMSFSignificance F

110449609223.34810449609223.34830380.24121059550

113783567.76893328343960.706266662

1210453392791.1169

Coefficientst StatP-valueLower 95%Upper 95% 95.0% 95.0%

Intercept4134.2489719396367.720989829611.24289634340.00000022663324.90053077424943.5974131053324.90053077424943.597413105

X Variable 11.90096847330.0109063469174.299286316901.87696376571.92497318091.87696376571.9249731809

199018547.950177717.45813.518547.9

199121617.85288.69102.2722721617.8

199226638.1580011699.59138.626638.1

199334634.46882.116428.511323.834634.4

199446759.49457.222372.21493046759.4

199558478.11199328537.917947.258478.1

199667884.613844.233612.920427.567884.6

199774462.614211.237222.723028.774462.6

199878345.214552.438619.325173.578345.2

199982067.51447240557.827037.782067.5

200089468.114628.244935.329904.689468.1

200197314.815411.8487503315397314.8

2002104790.616117.353540.735132.6104790.6

SUMMARY OUTPUTSUMMARY OUTPUT

Multiple R1Multiple R0.9986922681

R Square1R Square0.9973862464

Adjusted R Square1Adjusted R Square0.9968634956

0730.238812478

77

dfSSMSFSignificance FdfSSMSFSignificance F

31020082220.85429340027406.95142938496757177629394000000000000000011017415977.238041017415977.238041907.95764317750.0000001187

30052666243.61624623533248.723249246

61020082220.8542961020082220.85429

Coefficientst StatP-valueLower 95%Upper 95% 95.0% 95.0%Coefficientst StatP-valueLower 95%Upper 95% 95.0% 95.0%

Intercept0.00000000010.00000000010.88933388360.4393368096-0.00000000020.0000000003-0.00000000020.0000000003Intercept5716.32804942921833.8045625953.11719589210.02633557071002.383352437210430.27274642121002.383352437210430.2727464212

X Variable 11015104323513538401111X Variable 11.8648954650.042694322743.68017448660.00000011871.75514621461.97464471541.75514621461.9746447154

X Variable 21055881074840137701111

X Variable 31054596202838836201111

4.3

yx

12648777

21059210

3909954

413110508

512210979

610711912

740612747

850313499

943114269

1058815522

1189816730

1295017663

1377918575

1481919635

15122221163

16170222880

17157824127

18165425604

19140026500

20182927670

21220028300

22201727430

23210529560

24160028150

25225032100

26242032500

27257035250

28172033500

29190036000

30210036200

31230038200

3.3

yx1x2x3x4x5

1978231301018888149114.89180.92

1979298335021958638916.00420.39

1980343368825319220419.53570.25

1981401394127999530021.82776.71

1982445425830549992223.27792.43

19833914736335810604422.91947.70

19845545652390511035326.021285.22

19857447020487911211027.721783.30

19869977859555210857932.432281.95

198713109313638611242938.912690.23

1988144211738803812264537.383169.48

1989128313176900511380747.192450.14

199016601438496639571250.682746.20

1991217816557109699508155.913335.65

1992288620223129859969383.663311.50

19933383248821594910545896.084152.70

8.3 8.6 C-DCobbDouglas y,K()L()A>0abKLAab

8.3 a1% b1% a+b returns to scalea+b =111a+b 111a+b 111

8.3

(1)

(2)

lny=lnA+ lnK+lnL

y=lny,0=lnA,x1=lnK,x2=lnL,y=0+ x1+x2+

_1239827757.unknown

_1239827781.unknown

8.3

tGDPKL lnGDPlnKlnL197813624.1 1377.9 401528.1953617.22831610.60043197924038.2 1474.2 410248.3035547.29587110.62191198034517.8 1590.0 423618.4157807.37148910.65398198144862.4 1581.0 437258.4892877.36581310.68568198255294.7 1760.2 452958.5744627.47318310.72095198365934.5 2005.0 464368.6885387.60339910.74583198477171.0 2468.6 481978.8778007.81140610.78305198588964.4 3386.0 498739.1010168.12740510.817241986910202.2 3846.0 512829.2303598.25478910.8451019871011962.5 4322.0 527839.3895328.37147410.8739419881114928.3 5495.0 543349.6110148.61159410.9029119891216909.2 6095.0 553299.7356138.71522410.9210519901318547.9 6444.0 647499.8281128.77090511.0782719911421617.8 7517.0 654919.9812728.92492211.0896719921526638.1 9636.0 6615210.190109.17326111.0997119931634634.4 14998.0 6680810.452609.61567211.1095819941746759.4 19260.6 6745510.752779.86581711.1192219951858478.1 23877.0 6806510.9764110.0806711.1282219961967884.6 26867.2 6895011.1255610.1986611.1411419972074462.6 28457.6 6982011.2180510.2561711.1536819982178345.2 29545.9 7063711.2688810.293711.1653119992282067.5 30701.6 7139411.3153010.3320711.1759720002389468.1 32611.4 7208511.4016410.3924211.1856020012497314.8 37460.8 7302511.4857110.5310511.19856200225105172.3 42355.4 7374011.5633610.6538511.20830

8.3 yGDP () K () L() (1)8.158.14SPSS

8.3

ANOVA

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

32.236

2

16.118

5917.774

.000

Residual

.060

22

.003

Total

32.296

24

Coefficients(a)

Unstandardized Coefficients

Standardized Coefficients

t

Sig

B

Std. Error

Beta

(Constant)

-2.086

1.903

-1.096

.285

lnK

.902

.035

.936

25.863

.000

lnL

.361

.201

.065

1.794

.087

a Dependent Variable: lnGDP

8.3 a=0.902b =0.361a+b =0.902+0.361=1.2631A==0.1242b P=0.087C-D

8.3 ,818.95%-0.555 1.56500C-D

8.3

Parameter Estimates

Parameter

Estimate

Std. Error

95% Confidence Interval

Lower Bound

Upper Bound

A

.020

.104

-.196

.236

alpha

.922

.064

.789

1.056

beta

.505

.511

-.555

1.565

8.3

yt l nyt

yt

ytyt

8.3 VIF=15.5k=0.20R20.998 140.980 58****** Ridge Regression with k = 0.20 ****** B SE(B) Beta B/SE(B)lnK .49700385 .02048319 .51558506 24.26398868lnL 2.18274631 .11798929 .39309616 18.49952910Constant -18.43784255 1.27336521 .00000000 -14.47961853

8.3 a=0.4970b =2.183A= b =2.183

8.3 ,

8.3 SPSS3.2SPSS

8.3 1yModel Expressionsb0+b1*x1+b2*x2 2.b0=-213.7,b1=2.185,b2=0.368Continue; 3.Options,OptionsLevenberg-Marquardt,Sequential quadratic programContinue 4LossLoss FunctionSum of squared residuals,User-defiend loss functionABS(y-b0-b1*x1-b2*x2)Continue 5Save

8.3

Iteration Loss funct B0 B1 B2 0.1 4511.684440 -213.70000 2.18500000 .368000000 1.1 4393.393596 -213.69997 2.19431077 .403145685 2.1 4362.671030 -213.69984 2.13568898 .431261430 3.1 4354.739136 -213.78915 2.12883998 .429074345 4.1 4352.083704 -213.78515 2.13523424 .427309206

=-213.79+2.1352x1+0.4273x2

_1031994335.unknown

8.3

x1

x2

yi

eia

ei

1

25

3547.79

553.96

1355.6

-801.64

1385.63

-831.67

2

20

896.34

208.55

211.93

-3.38

133.52

75.03

3

6

750.32

3.10

119.64

-116.54

36.62

-33.52

4

1001

2087.05

2815.40

2815.4

0

2688.57

126.83

5

525

1639.31

1052.12

1607.71

-555.59

1509.71

-457.59

6

825

3357.70

3427.00

2982.56

444.44

2925.4

501.6

7

120

808.47

442.82

387.91

54.91

295.96

146.86

8

28

520.27

70.12

68.32

1.8

-26.34

96.46

9

7

671.13

122.24

87.94

34.3

1.57

120.67

10

532

2863.32

1400.00

2145.68

-745.68

2097.28

-697.28

11

75

1160.00

464.00

442.04

21.96

369

95

12

40

862.75

7.50

240.29

-232.79

158.51

-151.01

13

187

672.99

224.18

473.08

-248.9

368.92

-144.74

14

122

901.76

538.94

432.04

106.9

343.73

195.21

15

74

3546.18

2442.79

1459.54

983.25

1484.64

958.15

_1031995501.unknown

_1257582779.unknown