Bang tra kinh tế lượng

Bộ mơn Tốn – Thống kê

Bài giảng Kinh tế lượng

PHỤ LỤC: CÁC BẢNG THỐNG KÊ
Bảng phụ lục I: Bảng giá trị tới hạn của phân phối t (student):
𝑃(𝑡 > 𝑡𝛼 (𝑘)) = 𝛼 ℎ𝑎𝑦: 𝑃(|𝑡| > 𝑡𝛼 (𝑘)) = 2𝛼
𝛼

0.001

0.002

0.005

0.01

0.02

0.025

0.05

0.1

0.2

318.309
22.327
10.215
7.173

5.893
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.787
3.733
3.686
3.646
3.610
3.579
3.552
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
3.375
3.365
3.356
3.348

3.340
3.333
3.326
3.319
3.313
3.307
3.301
3.296
3.291
3.286
3.281
3.277
3.273
3.269
3.265

159.153
15.764
8.053
5.951
5.030
4.524
4.207
3.991
3.835
3.716
3.624
3.550
3.489
3.438

3.395
3.358
3.326
3.298
3.273
3.251
3.231
3.214
3.198
3.183
3.170
3.158
3.147
3.136
3.127
3.118
3.109
3.102
3.094
3.088
3.081
3.075
3.070
3.064
3.059
3.055
3.050
3.046
3.042
3.038

3.034
3.030
3.027
3.024
3.021

63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797

2.787
2.779
2.771
2.763
2.756
2.750
2.744
2.738
2.733
2.728
2.724
2.719
2.715
2.712
2.708
2.704
2.701
2.698
2.695
2.692
2.690
2.687
2.685
2.682
2.680

31.821
6.965
4.541
3.474

3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.453
2.449
2.445
2.441

2.438
2.434
2.431
2.429
2.426
2.423
2.421
2.418
2.416
2.414
2.412
2.410
2.408
2.407
2.405

15.895
4.849
3.482
2.999
2.757
2.612
2.517
2.449
2.398
2.359
2.328
2.303
2.282
2.264

2.249
2.235
2.224
2.214
2.205
2.197
2.189
2.183
2.177
2.172
2.167
2.162
2.158
2.154
2.150
2.147
2.144
2.141
2.138
2.136
2.133
2.131
2.129
2.127
2.125
2.123
2.121
2.120
2.118
2.116

2.115
2.114
2.112
2.211
2.110

12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064

2.060
2.056
2.052
2.048
2.045
2.042
2.040
2.037
2.035
2.032
2.030
2.028
2.026
2.024
2.023
2.021
2.020
2.018
2.017
2.015
2.014
2.013
2.012
2.011
2.010

6.314
2.920
2.353
2.132

2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.696
1.694
1.692
1.691

1.690
1.688
1.687
1.686
1.685
1.684
1.683
1.682
1.681
1.680
1.679
1.679
1.678
1.677
1.677

3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345

1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.309
1.309
1.308
1.307
1.306
1.306
1.305
1.304
1.304
1.303
1.303
1.302
1.302
1.301

1.301
1.300
1.300
1.299
1.299

1.376
1.061
0.978
0.941
0.920
0.906
0.896
0.889
0.883
0.879
0.876
0.873
0.870
0.868
0.866
0.865
0.863
0.862
0.861
0.860
0.859
0.858
0.858
0.857

0.856
0.856
0.855
0.855
0.854
0.854
0.853
0.853
0.853
0.852
0.852
0.852
0.851
0.851
0.851
0.851
0.850
0.850
0.850
0.850
0.850
0.850
0.849
0.849
0.849

k
1
2
3

4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33

34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49

< 145 >


Bộ mơn Tốn – Thống kê

Bài giảng Kinh tế lượng

Bảng giá trị tới hạn 𝒕𝜶 (𝒌) của phân phối Student (tiếp theo)
𝛼

0.001

0.002

0.005

0.01

0.02

0.025

0.05

0.1

0.2

50
51
52
53
54
55
56
57
58
59
60
61

3.261
3.258

3.255
3.251
3.248
3.245
3.242
3.239
3.237
3.234
3.232
3.229

3.018
3.015
3.012
3.009
3.007
3.005
3.002
3.000
2.998
2.996
2.994
2.992

2.678
2.676
2.674
2.672
2.670
2.668

2.667
2.665
2.663
2.662
2.660
2.659

2.403
2.402
2.400
2.399
2.397
2.396
2.395
2.394
2.392
2.391
2.390
2.389

2.109
2.108
2.107
2.106
2.105
2.104
2.103
2.102
2.101
2.100

2.099
2.099

2.009
2.008
2.007
2.006
2.005
2.004
2.003
2.002
2.002
2.001
2.000
2.000

1.676
1.675
1.675
1.674
1.674
1.673
1.673
1.672
1.672
1.671
1.671
1.670

1.299

1.298
1.298
1.298
1.297
1.297
1.297
1.297
1.296
1.296
1.296
1.296

0.849
0.849
0.849
0.848
0.848
0.848
0.848
0.848
0.848
0.848
0.848
0.848

k

Bảng phụ lục II: Bảng giá trị tới hạn 𝑭𝜶 (𝒌, 𝒎) của phân phối F
𝑃(𝐹(𝑘, 𝑚) > 𝐹𝛼 (𝑘, 𝑚)) = 𝛼, với 𝛼 = 0.01
k

m

1

2

3

4

5

6

7

8

2
3
4
5
6

98,503
34,116
21,198
16,258
13,745

99,000
30,817
18,000
13,274
10,925

99,166
29,457
16,694
12,060
9,780

99,249
28,710
15,977
11,392
9,148

99,299
28,237
15,522
10,967
8,746

99,333
27,911
15,207
10,672
8466

99,356
27,672
14,976
10,456
8,260

99,374
27,489
14,799
10,289
8,102

7
8
9
10
11

12,246
11,259
10,561
10,044
9,646

9,547
8,649
8,022
7,559
7,206

8,451
7,591
6,992
6,552
6,217

7,847
7,006
6,422
5,994
5,668

7,460
6,632
6,057
5,636
5,316

7,191
6,371
5,802
5,386
5,069

6,993
6,178
5,613
5,200
4,886

6,840
6,029
5,467
5,057
4,744

12
13
14
15
16

9,330
9,074
8,862
8,683
8,531

6,927
6,701
6,515
6,359
6,226

5,953
5,739
5,564
5,417
5,292

5,412
5,205
5,035
4,893
4,773

5,064
4,862
4,695
4,556
4,437

4,821
4,620
4,456
4,318
4,202

4,640
4,441
4,278
4,142
4,026

4,499
4,302
4,140
4,004
3,890

17
18
19
20
21

8,400
8,285
8,185
8,096
8,017

6,112
6,013
5,926
5,849
5,780

5,185
5,092
5,010
4,938
4,874

4,669
4,579
4,500
4,431
4,369

4,336
4,248
4,171
4,103
4,042

4,102
4,015
3,939
3,871
3,812

3,927
3,841
3,765
3,699
3,640

3,791
3,705
3,631
3,564
3,506

22
23
24
25
26

7,945
7,881
7,823
7,770
7,721

5,719
5,664
5,614
5,568
5,526

4,817
4,765
4,718
4,675
4,637

4,313
4,264
4,218
4,177
4,140

3,988
3,939
3,895
3,855
3,818

3,758
3,710
3,667
3,627
3,591

3,587
3,539
3,496
3,457
3,421

3,453
3,406
3,363
3,324
3,288

27
28
29
30

7,677
7,636
7,598
7,562

5,488
5,453

5,420
5,390

4,601
4,568
4,538
4,510

4,106
4,074
4,045
4,018

3,785
3,754
3,725
3,699

3,558
3,528
3,499
3,473

3,388
3,358
3,330
3,304

3,256
3,226

3,198
3,173

< 146 >


Bộ mơn Tốn – Thống kê

Bài giảng Kinh tế lượng

Bảng giá trị tới hạn 𝐅𝛂 (𝐤, 𝐦) của phân phối F, với 𝛂 = 𝟎. 𝟎𝟏 (tiếp theo)
k
m

9

10

11

12

13

14

15

16

2
3

99,388
27,345

99,399
27,229

99,408
27,133

99,416
27,052

99,422
26,983

99,428
26,924

99,433
26,872

99,437
26,827

4
5
6

14,659
10,158
7,976

14,546
10,051
7,874

14,452
9,963
7,790

14,374
9,888
7,718

14,307
9,825
7,657

14,249
9,770
7,605

14,198
9,722
7,559

14,154

9,680
7,519

7
8

6,719
5,911

6,620
5,814

6,538
5,734

6,469
5,667

6,410
5,609

6,359
5,559

6,314
5,515

6,275
5,477

9
10
11

5,351
4,942
4,632

5,257
4,849
4,539

5,178
4,772
4,462

5,111
4,706
4,397

5,055
4,650
4,342

5,005
4,601
4,293

4,962
4,558

4,251

4,924
4,520
4,213

12
13

4,388
4,191

4,296
4,100

4,220
4,025

4,155
3,960

4,100
3,905

4,052
3,857

4,010
3,815

3,972
3,778

14
15
16

4,030
3,895
3,780

3,939
3,805
3,691

3,864
3,730
3,616

3,800
3,666
3,553

3,745
3,612
3,498

3,698
3,564
3,451

3,656
3,522
3,409

3,619
3,485
3,372

17
18

3,682
3,597

3,593
3,508

3,519
3,434

3,455
3,371

3,401
3,316

3,353
3,269

3,312
3,227

3,275
3,190

19
20
21

3,523
3,457
3,398

3,434
3,368
3,310

3,360
3,294
3,236

3,297
3,231
3,173

3,242
3,177
3,119

3,195
3,130
3,072

3,153
3,088
3,030

3,116
3,051
2,993

22
23

3,346
3,299

3,258
3,211

3,184
3,137

3,121
3,074

3,067
3,020

3,019
2,973

2,978
2,931

2,941
2,894

24
25
26

3,256
3,217
3,182

3,168
3,129
3,094

3,094
3,056
3,021

3,032
2,993
2,958

2,977

2,939
2,904

2,930
2,892
2,857

2,889
2,850
2,815

2,852
2,813
2,778

27
28

3,149
3,120

3,062
3,032

2,988
2,959

2,926
2,896

2,871
2,842

2,824
2,795

2,783
2,753

2,746
2,716

29
30
31

3,092
3,067
3,043

3,005
2,979
2,955

2,931
2,906
2,882

2,868
2,843

2,820

2,814
2,789
2,765

2,767
2,742
2,718

2,726
2,700
2,677

2,689
2,663
2,640

32
33

3,021
3,000

2,934
2,913

2,860
2,840

2,798
2,777

2,744
2,723

2,696
2,676

2,655
2,634

2,618
2,597

< 147 >


Bộ mơn Tốn – Thống kê

Bài giảng Kinh tế lượng

Bảng giá trị tới hạn 𝑭𝜶 (𝒌, 𝒎) của phân phối F, với 𝜶 = 𝟎. 𝟎𝟓
k
m

1

2

3

4

5

6

7

8

2

18,513

19,000

19,164

19,247

19,296

19,330

19,353

19,371

3

10,128

9,552

9,277

9,117

9,013

8,941

8,887

8,845

4

7,709

6,944

6,591

6,388

6,256

6,163

6,094

6,041

5

6,608

5,786

5,409

5,192

5,050

4,950

4,876

4,818

6

5,987

5,143

4,757

4,534

4,387

4,284

4,207

4,147

7

5,591

4,737

4,347

4,120

3,972

3,866

3,787

3,726

8

5,318

4,459

4,066

3,838

3,687

3,581

3,500

3,438

9

5,117

4,256

3,863

3,633

3,482

3,374

3,293

3,230

10

4,965

4,103

3,708

3,478

3,326

3,217

3,135

3,072

11

4,844

3,982

3,587

3,357

3,204

3,095

3,012

2,948

12

4,747

3,885

3,490

3,259

3,106

2,996

2,913

2,849

13

4,667

3,806

3,411

3,179

3,025

2,915

2,832

2,767

14

4,600

3,739

3,344

3,112

2,958

2,848

2,764

2,699

15

4,543

3,682

3,287

3,056

2,901

2,790

2,707

2,641

16

4,494

3,634

3,239

3,007

2,852

2,741

2,657

2,591

17

4,451

3,592

3,197

2,965

2,810

2,699

2,614

2,548

18

4,414

3,555

3,160

2,928

2,773

2,661

2,577

2,510

19

4,381

3,522

3,127

2,895

2,740

2,628

2,544

2,477

20

4,351

3,493

3,098

2,866

2,711

2,599

2,514

2,447

21

4,325

3,467

3,072

2,840

2,685

2,573

2,488

2,420

22

4,301

3,443

3,049

2,817

2,661

2,549

2,464

2,397

23

4,279

3,422

3,028

2,796

2,640

2,528

2,442

2,375

24

4,260

3,403

3,009

2,776

2,621

2,508

2,423

2,355

25

4,242

3,385

2,991

2,759

2,603

2,490

2,405

2,337

26

4,225

3,369

2,975

2,743

2,587

2,474

2,388

2,321

27

4,210

3,354

2,960

2,728

2,572

2,459

2,373

2,305

28

4,196

3,340

2,947

2,714

2,558

2,445

2,359

2,291

29

4,183

3,328

2,934

2,701

2,545

2,432

2,346

2,278

30

4,171

3,316

2,922

2,690

2,534

2,421

2,334

2,266

< 148 >


Bộ mơn Tốn – Thống kê

Bài giảng Kinh tế lượng

Bảng giá trị tới hạn 𝑭𝜶 (𝒌, 𝒎) của phân phối F, với 𝜶 = 𝟎. 𝟎𝟓 (tiếp theo)
k
m

9

10

11

12

13

14

15

16

2

19,385

19,396

19,405

19,413

19,419

19,424

19,429

19,433

3

8,812

8,786

8,763

8,745

8,729

8,715

8,703

8,692

4

5,999

5,964

5,936

5,912

5,891

5,873

5,858

5,844

5

4,772

4,735

4,704

4,678

4,655

4,636

4,619

4,604

6

4,099

4,060

4,027

4,000

3,976

3,956

3,938

3,922

7

3,677

3,637

3,603

3,575

3,550

3,529

3,511

3,494

8

3,388

3,347

3,313

3,284

3,259

3,237

3,218

3,202

9

3,179

3,137

3,102

3,073

3,048

3,025

3,006

2,989

10

3,020

2,978

2,943

2,913

2,887

2,865

2,845

2,828

11

2,896

2,854

2,818

2,788

2,761

2,739

2,719

2,701

12

2,796

2,753

2,717

2,687

2,660

2,637

2,617

2,599

13

2,714

2,671

2,635

2,604

2,577

2,554

2,533

2,515

14

2,646

2,602

2,565

2,534

2,507

2,484

2,463

2,445

15

2,588

2,544

2,507

2,475

2,448

2,424

2,403

2,385

16

2,538

2,494

2,456

2,425

2,397

2,373

2,352

2,333

17

2,494

2,450

2,413

2,381

2,353

2,329

2,308

2,289

18

2,456

2,412

2,374

2,342

2,314

2,290

2,269

2,250

19

2,423

2,378

2,340

2,308

2,280

2,256

2,234

2,215

20

2,393

2,348

2,310

2,278

2,250

2,225

2,203

2,184

21

2,366

2,321

2,283

2,250

2,222

2,197

2,176

2,156

22

2,342

2,297

2,259

2,226

2,198

2,173

2,151

2,131

23

2,320

2,275

2,236

2,204

2,175

2,150

2,128

2,109

24

2,300

2,255

2,216

2,183

2,155

2,130

2,108

2,088

25

2,282

2,236

2,198

2,165

2,136

2,111

2,089

2,069

26

2,265

2,220

2,181

2,148

2,119

2,094

2,072

2,052

27

2,250

2,204

2,166

2,132

2,103

2,078

2,056

2,036

28

2,236

2,190

2,151

2,118

2,089

2,064

2,041

2,021

29

2,223

2,177

2,138

2,104

2,075

2,050

2,027

2,007

30

2,211

2,165

2,126

2,092

2,063

2,037

2,015

1,995

31

2,199

2,153

2,114

2,080

2,051

2,026

2,003

1,983

32

2,189

2,142

2,103

2,070

2,040

2,015

1,992

1,972

33

2,179

2,133

2,093

2,060

2,030

2,004

1,982

1,961

< 149 >

Bộ mơn Tốn – Thống kê

Bài giảng Kinh tế lượng

Bảng phụ lục III: Giá trị tới hạn 𝝌𝟐𝜶 (𝒌) của phân phối Chi – square:
𝑃(𝜒 2 (𝑘) > 𝜒𝛼2 (𝑘)) = 𝛼
𝛼
k

0,01

0,99

0,025

0,975

0,05

0,95

1

6.6349

0.0002

5.0239

0.0010

3.8415

0.0039

2

9.2103

0.0201

7.3778

0.0506

5.9915

0.1026

3

11.3449

0.1148

9.3484

0.2158

7.8147

0.3518

4

13.2767

0.2971

11.1433

0.4844

9.4877

0.7107

5

15.0863

0.5543

12.8325

0.8312

11.0705

1.1455

6

16.8119

0.8721

14.4494

1.2373

12.5916

1.6354

7

18.4753

1.2390

16.0128

1.6899

14.0671

2.1673

8

20.0902

1.6465

17.5345

2.1797

15.5073

2.7326

9

21.6660

2.0879

19.0228

2.7004

16.9190

3.3251

10

23.2093

2.5582

20.4832

3.2470

18.3070

3.9403

11

24.7250

3.0535

21.9200

3.8157

19.6751

4.5748

12

26.2170

3.5706

23.3367

4.4038

21.0261

5.2260

13

27.6882

4.1069

24.7356

5.0088

22.3620

5.8919

14

29.1412

4.6604

26.1189

5.6287

23.6848

6.5706

15

30.5779

5.2293

27.4884

6.2621

24.9958

7.2609

16

31.9999

5.8122

28.8454

6.9077

26.2962

7.9616

17

33.4087

6.4078

30.1910

7.5642

27.5871

8.6718

18

34.8053

7.0149

31.5264

8.2307

28.8693

9.3905

19

36.1909

7.6327

32.8523

8.9065

30.1435

10.1170

20

37.5662

8.2604

34.1696

9.5908

31.4104

10.8508

21

38.9322

8.8972

35.4789

10.2829

32.6706

11.5913

22

40.2894

9.5425

36.7807

10.9823

33.9244

12.3380

23

41.6384

10.1957

38.0756

11.6886

35.1725

13.0905

24

42.9798

10.8564

39.3641

12.4012

36.4150

13.8484

25

44.3141

11.5240

40.6465

13.1197

37.6525

14.6114

26

45.6417

12.1981

41.9232

13.8439

38.8851

15.3792

27

46.9629

12.8785

43.1945

14.5734

40.1133

16.1514

28

48.2782

13.5647

44.4608

15.3079

41.3371

16.9279

< 150 >


Bộ mơn Tốn – Thống kê

Bài giảng Kinh tế lượng

Giá trị tới hạn 𝝌𝟐𝜶 (𝒌) của phân phối Chi – square (tiếp theo)
𝛼
k

0.01

0.99

0.025

0.975

0.05

0.95

29

49.5879

14.2565

45.7223

16.0471

42.5570

17.7084

30

50.8922

14.9535

46.9792

16.7908

43.7730

18.4927

31

52.1914

15.6555

48.2319

17.5387

44.9853

19.2806

32

53.4858

16.3622

49.4804

18.2908

46.1943

20.0719

33

54.7755

17.0735

50.7251

19.0467

47.3999

20.8665

34

56.0609

17.7891

51.9660

19.8063

48.6024

21.6643

35

57.3421

18.5089

53.2033

20.5694

49.8018

22.4650

36

58.6192

19.2327

54.4373

21.3359

50.9985

23.2686

37

59.8925

19.9602

55.6680

22.1056

52.1923

24.0749

38

61.1621

20.6914

56.8955

22.8785

53.3835

24.8839

39

62.4281

21.4262

58.1201

23.6543

54.5722

25.6954

40

63.6907

22.1643

59.3417

24.4330

55.7585

26.5093

41

64.9501

22.9056

60.5606

25.2145

56.9424

27.3256

42

66.2062

23.6501

61.7768

25.9987

58.1240

28.1440

43

67.4593

24.3976

62.9904

26.7854

59.3035

28.9647

44

68.7095

25.1480

64.2015

27.5746

60.4809

29.7875

45

69.9568

25.9013

65.4102

28.3662

61.6562

30.6123

46

71.2014

26.6572

66.6165

29.1601

62.8296

31.4390

47

72.4433

27.4158

67.8206

29.9562

64.0011

32.2676

48

73.6826

28.1770

69.0226

30.7545

65.1708

33.0981

49

74.9195

28.9406

70.2224

31.5549

66.3386

33.9303

50

76.1539

29.7067

71.4202

32.3574

67.5048

34.7643

51

77.3860

30.4750

72.6160

33.1618

68.6693

35.5999

52

78.6158

31.2457

73.8099

33.9681

69.8322

36.4371

53

79.8433

32.0185

75.0019

34.7763

70.9935

37.2759

54

81.0688

32.7934

76.1920

35.5863

72.1532

38.1162

55

82.2921

33.5705

77.3805

36.3981

73.3115

38.9580

56

83.5134

34.3495

78.5672

37.2116

74.4683

39.0813

57

84.7328

35.1305

79.7522

38.0267

75.6237

40.6459

58

85.9502

35.9135

80.9356

38.8435

76.7778

41.4920

59

87.1657

36.6982

82.1174

39.6619

77.9305

42.3393

60

88.3794

37.4849

83.2977

40.4817

79.0819

43.1880

< 151 >