Capítulo 4 As distribuições de probabilidade mais importantes em controle estatístico de qualidade (CEQ): atributos12.2 Fórmulas e gráficos do coeficiente de correlação
12.3 Exemplo: a correlação entre tempo de secagem e a dureza de Brinell
12.4 Intervalo de Confiança
12.5 Teste de hipótese
12.6 As suposições que garantem a representatividade do coeficiente de correlação estimado
12.6.1 Linearidade
12.6.2 Estacionaridade
12.6.3 Normalidade
12.7 Autocorrelação
12.10 Conclusões do capítulo
12.1 Introdução
É muito comum em pesquisas baseadas em variáveis quantitativas e mensuráveis tentar medir o grau de relacionamento entre elas. No caso da relação ser linear, isto pode ser feito através do coeficiente de correlação linear. É o caso, por exemplo, quando se propõe uma teoria ou hipótese que interliga dois fenômenos, e então comprova estatisticamente a existência da relação, utilizando-se amostras das variáveis.
Isso não significa necessariamente que as duas variáveis possuem uma relação de causa e efeito. O relacionamento é necessário para comprovar causa e efeito, mas não é suficiente para ser prova definitiva.
*
12.2 Fórmulas e gráficos do coeficiente de correlação
A covariância e variância são matematicamente conceitos muito próximos. A diferença é que a covariância mede a relação entre duas variáveis distintas enquanto a variância depende de uma única variável. veja capítulo 2. Por definição, a covariância populacional é dada pela seguinte expressão:
A variância populacional é uma expressão similar, mas com apenas uma única variável,
A covariância amostral (n é o tamanho da amostra):
Os valores do coeficiente de correlação estão sempre contidos no intervalo [-1; +1], ou seja, -1 ≤ r ≤ 1. Este é um resultado muito importante, por que pelo fato de ser padronizado, o coeficiente de correlação não depende da unidade de medida.
r =
*
Figura 12.1 – Nuvens de dados com relação fraca e mal definida.
Nuvem de dados,
*
Figura 12.2 – Nuvens de dados com relação perfeita entre variáveis, r igual a 1,0 ou -1,0
A inclinação da reta não afeta o valor numérico de r reforçando a idéia de que o r não é uma medida de inclinação, mas sim uma medida de adesão e representação de correlação sobre os pares de dados da amostra, e por inferência da população.
Y
X
*
12.3 Exemplo: a correlação entre tempo de secagem e a dureza de Brinell
*
Tabela 12.1 – O cálculo do coeficiente de correlação entre dureza e minutos de secagem.
COEFICIENTE DE CORRELAÇÃO = 0,986
12.4 Intervalo de Confiança
Uma vez definido o nível de confiança desejado (1 – α), os elementos do cálculo do intervalo são o coeficiente estimado r, o desvio padrão sr e o valor da distribuição normal padronizada (Z) que corresponde ao nível de confiança exigido pelo pesquisador.
*
Continuação: 12.4 Intervalo de Confiança
O coeficiente de correlação não segue a distribuição normal, pois é assimétrica. No entanto, foi desenvolvida uma expressão pelo famoso Estatístico R. A. Fisher que transforma o coeficiente r em variável que segue a normalidade, z de Fisher
A estatística z de Fisher é distribuída normalmente e tem desvio padrão igual a
σz de Fisher = 1/√n-3
*
Continuação (ainda): 12.4 Intervalo de Confiança
O valor z de Fisher = 3,02 significa que r = 0,995. Este resultado vem diretamente da equação 0,5*ln[(1+r)/(1-r)] = 3,02. O limite inferior do intervalo de confiança para r é do valor z = 1,934 transformado para r = 0,959 da expressão 0,5*ln[(1+r)/(1-r)] = 1,934.
IC(ρ; 0,95) = (0,995; 0,959)
a hipótese nula (H0) é ρ = 0.
A hipótese alternativa (H1) é ρ não = 0.
É possível mostrar que a seguinte expressão:
com n - 2 graus de liberdade
*
Continuação: 12.5 Teste de hipótese
Para calcular o valor de t de Gosset utilizamos os números, n = 16, r = 0,986, o que produziu um valor t = 22,125 e valor-p é praticamente zero.
*
*
12.6 As suposições que garantem a representatividade do coeficiente de correlação estimado
Se os dados não são bem comportados, então há grande possibilidade de que os resultados não são confiáveis, as estimativas não representam fielmente a relação. Relações fracas podem aparecer enganosamente fortes e vice-versa.
Dados mal-comportados têm que ser tratados com vários tipos de transformações antes de entrar nas fórmulas.
Os dados devem seguir fielmente pelo menos três características:
linearidade, normalidade, e estacionaridade.
12.6.1 Linearidade
O coeficiente de correlação é uma medida de relacionamento, sempre supondo que a relação entre elas é linear. No gráfico de dispersão de XY, a relação linear é representada por uma linha reta.
Uma relação forte e bem definida, mas em forma não-linear, por exemplo, quadrática, vai produzir um r com valor artificialmente baixo, e levará o pesquisador a não enxergar relações existentes e às decisões erradas.
*
Tabela 12.3 – Dados de volume e pressão do experimento de Boyle
Plan1
VOLUME
PRESSÃO
48
29.125
46
30.5625
44
31.9375
42
33.5
40
35.3125
38
36.78947
36
39.3125
34
41.11765
32
44.1875
30
46.6
28
50.3125
26
54.3125
24
58.25
23
61.3125
22
63.54545
21
66.57143
20
70
19
74.25
18
77.666
17
82.75
16
87.875
15
93.0625
14
100.4375
13
107.8125
12
117.5625
Plan2
Plan3
*
Figura 12.3 – A relação não-linear entre volume (V) e pressão (P)
Gráf1
29.125
30.5625
31.9375
33.5
35.3125
36.78947
39.3125
41.11765
44.1875
46.6
50.3125
54.3125
58.25
61.3125
63.54545
66.57143
70
74.25
77.666
82.75
87.875
93.0625
100.4375
107.8125
117.5625
PRESSÃO
VOLUME
48
46
44
42
40
38
36
34
32
30
28
26
24
23
22
21
20
19
18
17
16
15
14
13
12
Utilize a Opção "Regressão" na Barra de Menu.
Dica inicial:
Tabela 1.1 Neter et al., 1996 p. 21
DATA
weight
intervalo
dmes
t
t2
dano
dout
dnov
ddez
djan
dfev
dmar
dabril
dmaio
djun
t4/100000
t3/10000
dsam
t3
t4
c+
c-
x
VOLUME
PRESSÃO
1
958.541076315
26.4614437683
1834.2011041241
260
572
157
1
23
Produto
Custo
N_trim
Trimestre
PIB
Tam_Lote
Horas_T
10/28/02
91.7
0
28
1
1
300
1
0
0
0
0
0
0
0
0
0.00001
0.0001
2
1
1
0
-0.0207758074
73.9742241926
48
29.125
2
1101.3762926807
49.9453245639
1455.0252027802
280
570
161
2
59
1
193
1
1970-1
2872.8
Mes
balanço
letrasAAA
letras3-4
80
399
10/29/02
92.4
0
29
2
4
301
1
0
0
0
0
0
0
0
0
0.00016
0.0008
3
8
16
0.0094767
-0.0012991074
74.0144767
46
30.5625
3
1319.8233151427
32.7441649561
1500.3843751983
240
645
168
3
36
2
226
2
1970-2
2860.3
1
360.071
5.94
5.31
30
121
10/31/02
91.4
1
31
3
9
303
1
0
0
0
0
0
0
0
0
0.00081
0.0027
5
27
81
0
-0.0090967438
73.9872023636
44
31.9375
4
1707.6484008242
35.3986616674
1431.1808096536
260
645
186
4
99
3
240
3
1970-3
2896.6
2
361.217
6.00
5.60
50
221
11/1/02
91.9
0
1
4
16
304
0
1
0
0
0
0
0
0
0
0.00256
0.0064
6
64
256
0
-0.0106325433
73.9934642005
42
33.5
5
826.9155100463
44.9997879614
1517.4638330463
240
645
183
5
36
4
244
4
1970-4
2873.7
3
358.774
6.08
5.49
90
376
11/4/02
91.2
2
4
5
25
307
0
1
0
0
0
0
0
0
0
0.00625
0.0125
2
125
625
0.0025771368
0
74.0075771368
40
35.3125
6
919.2243052018
47.0577016231
1549.5936092193
260
671
184
6
74
5
257
5
1971-1
2942.9
4
360.271
6.17
5.80
70
361
11/5/02
91.1
0
5
6
36
308
0
1
0
0
0
0
0
0
0
0.01296
0.0216
3
216
1296
0.0022442543
0
74.0046671175
38
36.78947
7
1283.7731843454
49.3861217465
1348.7908214884
260
675
180
7
30
6
260
6
1971-2
2947.4
5
360.139
6.14
5.61
60
224
11/7/02
91
1
7
7
49
310
0
1
0
0
0
0
0
0
0
0.02401
0.0343
5
343
2401
0.0059903419
0
74.0087460876
36
39.3125
8
802.103872715
51.8782736536
1554.1375584362
260
670
175
8
54
7
274
7
1971-3
2966
6
362.164
6.09
5.28
120
546
11/8/02
91.4
0
8
8
64
311
0
1
0
0
0
0
0
0
0
0.04096
0.0512
6
512
4096
0.0069477596
0
74.0059574177
34
41.11765
9
1280.0995124188
44.7843400353
1422.7047737804
260
710
193
9
17
8
297
8
1971-4
2980.8
7
362.901
5.87
5.19
80
352
11/11/02
91.9
2
11
9
81
314
0
1
0
0
0
0
0
0
0
0.06561
0.0729
2
729
6561
0
-0.0087184998
73.9862815002
32
44.1875
10
935.3835631457
45.8151272242
1513.4722313305
260
656
184
10
36
9
350
9
1972-1
3037.3
8
361.878
5.84
5.18
100
353
11/12/02
92.7
0
12
10
100
315
0
1
0
0
0
0
0
0
0
0.1
0.1
3
1000
10000
0
-0.0148758852
73.9888426146
30
46.6
11
982.0033259159
42.7760393095
1838.8940967852
280
640
179
11
89
10
420
10
1972-2
3089.7
9
360.922
5.99
5.30
50
157
11/14/02
92
1
14
11
121
317
0
1
0
0
0
0
0
0
0
0.14641
0.1331
5
1331
14641
0.0019399448
-0.0029359404
74.0069399448
28
50.3125
12
748.7274743737
43.8944108383
1401.9062215666
260
599
164
12
77
11
1972-3
3125.8
10
361.307
6.12
5.23
40
160
11/16/02
91.8
1
16
12
144
319
0
1
0
0
0
0
0
0
0
0.20736
0.1728
7
1728
20736
0.000166309
0
74.0032263642
26
54.3125
13
793.6162754588
45.9063495428
1654.0785206089
280
569
154
13
86
12
1972-4
3175.5
11
362.290
6.42
5.64
70
252
11/18/02
92.7
1
18
13
169
321
0
1
0
0
0
0
0
0
0
0.28561
0.2197
2
2197
28561
0
-0.0043983772
73.9906016228
24
58.25
14
1193.514914675
32.5756355879
1524.4284592554
280
564
157
14
33
13
1973-1
3253.3
12
367.382
6.48
5.62
90
389
11/19/02
93
0
19
14
196
322
0
1
0
0
0
0
0
0
0
0.38416
0.2744
3
2744
38416
0
-0.001807856
73.9975905212
23
61.3125
15
765.6070291466
36.9988778048
1461.573564633
280
573
164
15
90
14
1973-2
3267.6
13
371.031
6.52
5.67
20
113
11/21/02
91.7
1
21
15
225
324
0
1
0
0
0
0
0
0
0
0.50625
0.3375
5
3375
50625
0
0
74.0013153567
22
63.54545
16
1084.3290968835
35.4480927045
1281.1673893011
280
667
188
16
74
15
1973-3
3264.3
14
373.734
6.64
5.83
110
435
11/22/02
91.6
0
22
16
256
325
0
1
0
0
0
0
0
0
0
0.65536
0.4096
6
4096
65536
0.0005779765
0
74.0055779765
21
66.57143
17
996.4888018692
46.6192569648
1550.843596
260
700
191
17
7
16
1973-4
3289.1
15
373.463
6.75
5.53
100
420
11/25/02
92.2
2
25
17
289
328
0
1
0
0
0
0
0
0
0
0.83521
0.4913
2
4913
83521
0
0
74.00138715
20
70
18
883.5227813313
44.9017444326
1455.4452188022
240
637
180
18
54
17
1974-1
3259.4
16
375.518
6.73
5.76
30
212
11/26/02
92
0
26
18
324
329
0
1
0
0
0
0
0
0
0
1.04976
0.5832
3
5832
104976
0
-0.0041096126
73.9908903874
19
74.25
19
590.6135705606
45.9109652284
1635.3805600957
260
650
172
19
98
18
1974-2
3267.6
17
374.804
6.89
6.09
50
268
11/28/02
91.4
1
28
19
361
331
0
1
0
0
0
0
0
0
0
1.30321
0.6859
5
6859
130321
0.0138484591
0
74.0188484591
18
77.666
20
1300.4111789121
37.1841589286
1196.4888850925
260
655
184
20
50
19
1974-3
3239.1
18
375.457
6.98
6.52
90
377
11/29/02
92
0
29
20
400
332
0
1
0
0
0
0
0
0
0
1.6
0.8
6
8000
160000
0.0137204404
0
74.0048719812
17
82.75
21
1050.8333790397
44.8825995691
1583.6159301798
240
665
179
21
86
20
1974-4
3226.4
19
375.423
6.98
6.68
110
421
11/30/02
91.7
0
30
21
441
333
0
1
0
0
0
0
0
0
0
1.94481
0.9261
7
9261
194481
0.0094428293
0
74.0007223889
16
87.875
22
1338.3788471991
36.4997982715
1610.0356712413
260
599
169
22
90
21
1975-1
3154
20
374.365
7.10
7.07
30
273
12/2/02
91.7
1
2
22
484
335
0
0
1
0
0
0
0
0
0
2.34256
1.0648
2
10648
234256
0.0127412408
0
74.0082984116
15
93.0625
23
453.5677172583
37.6864614837
1536.5323558071
240
605
160
23
65
22
1975-2
3190.4
21
372.314
7.19
7.12
90
468
12/3/02
91.7
0
3
23
529
336
0
0
1
0
0
0
0
0
0
2.79841
1.2167
3
12167
279841
0.0163613179
0
74.0086200771
14
100.4375
24
1021.2268418711
37.5212801928
1492.7739509076
280
24
20
23
1975-3
3249.9
22
373.765
7.29
7.25
40
244
12/4/02
91.5
0
4
24
576
337
0
0
1
0
0
0
0
0
0
3.31776
1.3824
4
13824
331776
0.0049960033
-0.0013653147
73.9936346853
13
107.8125
25
1036.7439516493
44.0067789087
1330.1136656664
240
25
17
24
1975-4
3292.5
23
372.776
7.65
7.85
80
342
12/9/02
93.9
4
9
25
625
342
0
0
1
0
0
0
0
0
0
3.90625
1.5625
2
15625
390625
0
-0.0055972316
73.9907680831
12
117.5625
26
1144.3424788097
34.6844127408
1523.7193944486
240
26
45
25
1976-1
3356.7
24
374.134
7.75
8.02
70
323
12/10/02
94
0
10
26
676
343
0
0
1
0
0
0
0
0
0
4.56976
1.7576
3
17576
456976
0.0061118879
0
74.0111118879
27
894.6862213769
45.0473090596
1615.1768174168
240
27
9
26
1976-2
3369.2
25
374.880
7.72
7.87
12/11/02
93.2
0
11
27
729
344
0
0
1
0
0
0
0
0
0
5.31441
1.9683
4
19683
531441
0
-0.0070117875
73.9879882125
28
883.4715807586
40.4072262527
1324.3446270863
280
28
72
27
1976-3
3381
26
376.735
7.67
7.14
12/12/02
93
0
12
28
784
345
0
0
1
0
0
0
0
0
0
6.14656
2.1952
5
21952
614656
0
-0.0176007086
73.9844110789
29
1130.5503527318
38.0125096499
1861.5732566686
260
29
33
28
1976-4
3416.3
27
374.841
7.66
7.20
12/14/02
92.6
1
14
29
841
347
0
0
1
0
0
0
0
0
0
7.07281
2.4389
7
24389
707281
0.002113249
-0.0054874596
74.007113249
30
1255.7770399916
31.0472979536
1532.4437223753
240
30
17
29
1977-1
3466.4
28
375.622
7.89
7.59
12/16/02
92.7
1
16
30
900
349
0
0
1
0
0
0
0
0
0
8.1
2.7
2
27000
810000
0.0034973106
0
74.0063840616
31
697.4665949336
43.6120184177
1819.4400051143
280
31
3
30
1977-2
3525
29
375.461
8.14
7.74
12/17/02
93
0
17
31
961
350
0
0
1
0
0
0
0
0
0
9.23521
2.9791
3
29791
923521
0.0205541943
0
74.0220568836
32
1648.2895565366
33.4715219752
1443.627472021
280
32
29
31
1977-3
3574.4
30
377.694
8.21
7.51
12/19/02
92.1
1
19
32
1024
352
0
0
1
0
0
0
0
0
0
10.48576
3.2768
5
32768
1048576
0.0299917405
0
74.0144375463
33
949.6742135155
37.2631485434
1603.7927290781
260
33
30
32
1977-4
3567.2
31
380.119
8.05
7.46
12/21/02
91.9
1
21
33
1089
354
0
0
1
0
0
0
0
0
0
11.85921
3.5937
7
35937
1185921
0.0380307795
0
74.013039039
34
1448.3374751442
39.1108211361
1696.0968347703
280
34
68
33
1978-1
3591.8
32
382.288
7.94
7.09
12/23/02
91.8
1
23
34
1156
356
0
0
1
0
0
0
0
0
0
13.36336
3.9304
2
39304
1336336
0.0341603833
0
74.0011296038
35
1002.40288098
39.5186556134
1382.5448983553
240
35
87
34
1978-2
3707
33
383.270
7.88
6.82
12/26/02
92.4
2
26
35
1225
359
0
0
1
0
0
0
0
0
0
15.00625
4.2875
5
42875
1500625
0.029179892
0
74.0000195087
36
1394.703421264
42.1223399926
1219.7423908801
260
36
44
35
1978-3
3735.6
34
387.978
7.79
6.22
12/27/02
92.3
0
27
36
1296
360
0
0
1
0
0
0
0
0
0
16.79616
4.6656
6
46656
1679616
0.0287169063
0
74.0045370143
37
1204.6822022142
43.5497350837
1600.5224703476
260
36
1978-4
3784.3
35
394.041
7.41
5.61
1/9/03
95
12
9
37
1369
8
0
0
0
1
0
0
0
0
0
18.74161
5.0653
5
50653
1874161
0.0234617589
0
73.9997448526
38
1030.9137481761
31.6281467449
1452.2447069467
260
37
1979-1
3807.5
36
403.423
7.18
5.48
1/15/03
92.9
5
15
38
1444
14
0
0
0
1
0
0
0
0
0
20.85136
5.4872
4
54872
2085136
0.0079150083
-0.0055467507
73.9894532493
39
729.720165841
46.0853381001
1675.3139713401
260
38
1979-2
3814.6
37
412.727
7.15
4.78
1/27/03
92.4
11
27
39
1521
26
0
0
0
1
0
0
0
0
0
23.13441
5.9319
2
59319
2313441
0
-0.0182948122
73.9822519385
40
1188.4925701081
39.8272699031
1519.5451548279
240
39
1979-3
3830.8
38
423.417
7.27
4.14
1/30/03
92.4
2
30
40
1600
29
0
0
0
1
0
0
0
0
0
25.6
6.4
5
64000
2560000
0.0032833139
-0.0050114982
74.0082833139
41
975.2114161613
35.2853158902
1492.4407347862
240
40
1979-4
3732.6
39
429.948
7.37
4.64
2/1/03
92.2
1
1
41
1681
31
0
0
0
0
1
0
0
0
0
28.25761
6.8921
7
68921
2825761
0.0027255589
0
74.004442245
42
1202.0228715385
41.7280456177
1658.8632585481
260
41
1980-1
3733.5
40
437.821
7.54
5.52
2/3/03
92.5
1
3
42
1764
33
0
0
0
0
1
0
0
0
0
31.11696
7.4088
2
74088
3111696
0.0039046204
0
74.0061790615
43
969.4408746412
37.2119098857
1599.5478899313
260
42
1980-2
3808.5
41
441.703
7.58
5.95
2/4/03
92.4
0
4
43
1849
34
0
0
0
0
1
0
0
0
0
34.18801
7.9507
3
79507
3418801
0.0010393523
0
74.0021347319
44
1229.4222482204
46.0446268435
1226.2443685031
280
43
1980-3
3860.5
42
446.663
7.62
6.20
2/6/03
92.1
1
6
44
1936
36
0
0
0
0
1
0
0
0
0
37.48096
8.5184
5
85184
3748096
0
-0.0052693093
73.9897306907
45
1088.5151458432
45.8757223087
1600.0204292723
260
44
1980-4
3844.4
43
447.964
7.58
6.03
2/8/03
91.8
1
8
45
2025
38
0
0
0
0
1
0
0
0
0
41.00625
9.1125
7
91125
4100625
0.0073819518
0
74.0123819518
46
1167.2849891368
41.9239053017
1923.4170773998
240
45
1981-1
3864.5
44
449.118
7.48
5.60
2/10/03
91.4
1
10
46
2116
40
0
0
0
0
1
0
0
0
0
44.77456
9.7336
2
97336
4477456
0
0
73.9968878683
47
780.2982887454
36.6640757521
1383.8965211689
260
46
1981-2
3803.1
45
449.234
7.35
5.26
2/12/03
90.8
1
12
47
2209
42
0
0
0
0
1
0
0
0
0
48.79681
10.3823
4
103823
4879681
0
-0.0033992177
73.9916007823
48
1121.1978900098
42.9782540878
1581.1475047158
240
47
1981-3
3756.1
46
454.162
7.19
4.96
2/13/03
91.8
0
13
48
2304
43
0
0
0
0
1
0
0
0
0
53.08416
11.0592
5
110592
5308416
0
-0.0066104996
73.991788718
49
1676.2068677138
47.1735257734
1296.7224771855
260
48
1981-4
3771.1
47
456.692
7.19
5.28
2/15/03
91.4
1
15
49
2401
45
0
0
0
0
1
0
0
0
0
57.64801
11.7649
7
117649
5764801
0
-0.005900427
73.9957100727
50
712.358224623
41.4332727005
1218.6837390473
260
49
1982-1
3754.4
48
465.117
7.11
5.37
2/17/03
92.8
1
17
50
2500
47
0
0
0
0
1
0
0
0
0
62.5
12.5
2
125000
6250000
0
-0.0054340421
73.9954663849
51
992.7421527748
43.7438667277
1539.5896222471
260
50
1982-2
3759.6
49
470.408
7.16
5.53
2/19/03
91.8
1
19
51
2601
49
0
0
0
0
1
0
0
0
0
67.65201
13.2651
4
132651
6765201
0.0015623453
0
74.0065623453
52
708.081773714
45.0035737331
1359.9851096515
260
51
1982-3
3783.5
50
475.600
7.22
5.72
2/21/03
92.8
1
21
52
2704
51
0
0
0
0
1
0
0
0
0
73.11616
14.0608
6
140608
7311616
0
0
73.9966444307
53
731.1548839509
44.397770681
1534.8678099726
240
52
1982-4
3886.5
51
475.857
7.36
6.04
2/24/03
91.8
2
24
53
2809
54
0
0
0
0
1
0
0
0
0
78.90481
14.8877
2
148877
7890481
0
0
73.9985494924
54
1011.0472252193
38.9240222931
1473.2779087935
240
53
1983-1
3944.4
52
480.259
7.34
5.66
2/26/03
91.4
1
26
54
2916
56
0
0
0
0
1
0
0
0
0
85.03056
15.7464
4
157464
8503056
0
-0.0010086563
73.9939913437
55
653.0243164064
39.5520738594
1588.1447022039
260
54
1983-2
4012.1
53
483.432
7.30
5.75
2/28/03
92.4
1
28
55
3025
58
0
0
0
0
1
0
0
0
0
91.50625
16.6375
6
166375
9150625
0
0
73.9984543365
56
1044.8657562704
31.2489101916
1593.4649051487
260
55
1983-3
1089.5
54
488.536
7.30
5.82
3/3/03
92
2
3
56
3136
61
0
0
0
0
0
1
0
0
0
98.34496
17.5616
2
175616
9834496
0
-0.0173353709
73.9776646291
57
903.653142236
42.6801558306
1547.8275978821
260
56
1983-4
4144
55
493.182
7.27
5.90
3/6/03
90.4
2
6
57
3249
64
0
0
0
0
0
1
0
0
0
105.56001
18.5193
5
185193
10556001
0
-0.013670782
73.9986645889
58
1026.0000179777
38.0265727118
1683.2842144722
240
57
1984-1
4166.4
56
494.242
7.30
6.11
3/8/03
91.3
1
8
58
3364
66
0
0
0
0
0
1
0
0
0
113.16496
19.5112
7
195112
11316496
0
-0.0219627742
73.9867080078
59
1042.6331315187
41.1540123523
1545.4790551885
240
58
1984-2
4194.2
57
493.484
7.31
6.05
3/10/03
91.4
1
10
59
3481
68
0
0
0
0
0
1
0
0
0
121.17361
20.5379
2
205379
12117361
0
-0.0153969767
74.0015657974
60
1124.7005651142
41.4400484361
1440.0647539005
260
59
1984-3
4221.8
58
498.186
7.26
5.98
3/12/03
91.7
1
12
60
3600
70
0
0
0
0
0
1
0
0
0
129.6
21.6
4
216000
12960000
0.0000302333
-0.0053667434
74.0050302333
61
1295.0732847087
48.7281932792
1490.6247580839
280
60
1984-4
4254.8
59
500.064
7.24
6.00
3/14/03
91.4
1
14
61
3721
72
0
0
0
0
0
1
0
0
0
138.45841
22.6981
6
226981
13845841
0.0082010808
0
74.0131708475
62
1319.4058895941
34.5988292893
1499.9942019713
260
61
1985-1
4309
60
506.684
7.25
6.24
3/15/03
91.4
0
15
62
3844
73
0
0
0
0
0
1
0
0
0
147.76336
23.8328
7
238328
14776336
0
-0.0011929541
73.9938070459
63
886.8782832586
32.6788632365
1564.0596908852
240
62
1985-2
4333.5
3/17/03
91.4
1
17
63
3969
75
0
0
0
0
0
1
0
0
0
157.52961
25.0047
2
250047
15752961
0
-0.003672593
73.992520361
64
1072.0146687929
49.1823949333
1494.6458615341
240
63
1985-3
4390.5
3/19/03
91
1
19
64
4096
77
0
0
0
0
0
1
0
0
0
167.77216
26.2144
4
262144
16777216
0
0
74.0014636498
65
1003.6565182452
38.5332124197
1486.8272198
240
64
1985-4
4387.7
3/21/03
91.7
1
21
65
4225
79
0
0
0
0
0
1
0
0
0
178.50625
27.4625
6
274625
17850625
0
0
73.9976856998
66
1079.1995899665
44.2208739615
1513.2418449539
260
65
1986-1
4412.6
3/24/03
91.6
2
24
66
4356
82
0
0
0
0
0
1
0
0
0
189.74736
28.7496
2
287496
18974736
0
0
73.9979168933
67
800.6747877879
33.7149027573
1633.0176928605
240
66
1986-2
4427.1
3/26/03
91.5
1
26
67
4489
84
0
0
0
0
0
1
0
0
0
201.51121
30.0763
4
300763
20151121
0.0107720024
0
74.0157720024
68
1142.1874761389
38.1725352427
1494.014387994
280
67
1986-3
4460
3/28/03
91.1
1
28
68
4624
86
0
0
0
0
0
1
0
0
0
213.81376
31.4432
6
314432
21381376
0.0061488515
0
74.0003768491
69
1240.9905245839
34.7485889606
1522.6160636885
240
68
1986-4
4515.3
3/31/03
93.3
2
31
69
4761
89
0
0
0
0
0
1
0
0
0
226.67121
32.8509
2
328509
22667121
0
0
73.9985402155
70
973.2945821809
40.1478554168
1604.1868245011
280
69
1987-1
4559.3
4/2/03
91.1
1
2
70
4900
91
0
0
0
0
0
0
1
0
0
240.1
34.3
4
343000
24010000
0.0133032171
0
74.0183032171
71
1062.2727130474
41.0317819488
1423.4898950817
280
70
1987-2
4625.5
4/4/03
91.3
1
4
71
5041
93
0
0
0
0
0
0
1
0
0
254.11681
35.7911
6
357911
25411681
0.0019958713
-0.0013073458
73.9936926542
72
951.2265747651
37.1275087773
1506.0430807025
240
71
1987-3
4655.3
4/7/03
91.8
2
7
72
5184
96
0
0
0
0
0
0
1
0
0
268.73856
37.3248
2
373248
26873856
0.0097072421
0
74.0127113708
73
1343.1415674084
43.0548790164
1950.2435331233
280
72
1987-4
4704.8
4/8/03
91.8
0
8
73
5329
97
0
0
0
0
0
0
1
0
0
283.98241
38.9017
3
389017
28398241
0.0045538558
0
73.9998466137
74
966.4401132829
38.6335524227
1554.8730554328
240
73
1988-1
4734.5
4/10/03
90.8
1
10
74
5476
99
0
0
0
0
0
0
1
0
0
299.86576
40.5224
5
405224
29986576
0
0
73.9993558276
75
1163.8294235843
47.7790218711
1545.1188952866
240
74
1988-2
4779.7
4/29/03
92
18
29
75
5625
118
0
0
0
0
0
0
1
0
0
316.40625
42.1875
3
421875
31640625
0.0111015578
0
74.0161015578
76
1647.3119556984
40.6746518011
1709.8825007124
260
75
1988-3
4809.8
4/30/03
90.9
0
30
76
5776
119
0
0
0
0
0
0
1
0
0
333.62176
43.8976
4
438976
33362176
0.0097278723
0
74.0036263145
77
1074.4715884618
45.0155676945
1816.193109029
280
76
1988-4
4832.4
5/2/03
91.8
1
2
77
5929
121
0
0
0
0
0
0
0
1
0
351.53041
45.6533
6
456533
35153041
0.0090984605
0
74.0043705882
78
1169.5604983878
38.6005718711
1481.276289418
260
77
1989-1
4845.6
5/5/03
90.5
2
5
78
6084
124
0
0
0
0
0
0
0
1
0
370.15056
47.4552
2
474552
37015056
0.001747212
0
73.9976487516
79
1231.3310081616
41.3569206203
1696.1507223314
260
78
1989-2
4859.7
5/13/03
91
7
13
79
6241
132
0
0
0
0
0
0
0
1
0
389.50081
49.3039
3
493039
38950081
0.0035804845
0
74.0068332724
80
1488.785751789
40.9740233509
1792.3038664448
260
79
1989-3
4880.8
5/15/03
90.4
1
15
80
6400
134
0
0
0
0
0
0
0
1
0
409.6
51.2
5
512000
40960000
0
0
73.9993136498
81
798.8942095187
42.5242343327
1749.2183739378
260
80
1989-4
4900.3
5/26/03
89.9
10
26
81
6561
145
0
0
0
0
0
0
0
1
0
430.46721
53.1441
2
531441
43046721
0
-0.002360768
73.992639232
82
1277.5237420185
33.260314568
1502.7482656151
260
81
1990-1
4903.3
5/27/03
89.6
0
27
82
6724
146
0
0
0
0
0
0
0
1
0
452.12176
55.1368
3
551368
45212176
0
-0.0083360953
73.9890246727
83
1297.5423399978
42.6207317205
1593.0054966375
260
82
1990-2
4855.1
5/30/03
90.4
2
30
83
6889
149
0
0
0
0
0
0
0
1
0
474.58321
57.1787
6
571787
47458321
0
-0.0012990887
74.0020370067
84
1399.7547560932
46.0295633375
1635.2942717858
240
83
1990-3
4824
5/31/03
89.5
0
31
84
7056
150
0
0
0
0
0
0
0
1
0
497.87136
59.2704
7
592704
49787136
0
-0.0061124683
73.9901866204
85
1002.1591734669
40.3654122338
1492.8656961856
240
84
1990-4
4840.7
6/4/03
91.1
3
4
85
7225
154
0
0
0
0
0
0
0
0
1
522.00625
61.4125
4
614125
52200625
0.0143957931
0
74.0193957931
86
1128.9840361854
42.8756517167
1558.7316435485
260
85
1991-1
4862.7
6/6/03
90.1
1
6
86
7396
156
0
0
0
0
0
0
0
0
1
547.00816
63.6056
6
636056
54700816
0.0081236373
0
73.9987278443
87
1154.4585234872
34.4504452287
1460.8616008118
240
86
1991-2
4868
0
-0.0108763214
73.9841236786
88
1197.7001121202
39.2689481587
1548.5284772367
280
87
1991-3
0
-0.0092294692
73.9966468522
89
1050.8102501397
45.1430902204
1432.3134716178
280
88
1991-4
0.004572318
0
74.009572318
90
822.4557339957
34.3891225485
1384.792487137
240
0
0
73.9961702997
91
1088.037814602
44.0507018184
1532.0562776324
260
0
-0.0015386416
73.9934613584
92
862.8632186662
43.3096853258
1608.7781811293
280
0
-0.0102024808
73.9863361609
93
1017.5953715168
35.6788656164
1557.7666128265
260
0
-0.0020413273
74.0031611535
94
1087.3247593871
32.0873506198
1496.023575477
280
0
0
73.9983629095
95
1047.7991785222
46.9085899668
1566.3424088998
240
0.0007125362
0
74.0057125362
96
1255.8141818124
37.1975967128
1029.5002008788
260
0
-0.0013737389
73.9936262611
97
919.4175735131
47.5559228208
1772.7310857153
240
0
0
73.9965382244
98
1035.4532295002
38.4683995535
1793.4621079476
280
0
0
74.0028593831
99
500.9588197616
38.5204340192
1475.9668298793
240
0
0
73.9966897121
100
1599.022174659
38.2268150234
1495.0362052914
240
0
0
74.0021222149
101
1257.7390542582
47.6544438343
1636.4184072372
260
102
1060.8373153025
43.3565015656
1503.3451215131
260
103
835.7055763689
55.3529981617
1492.0040067991
240
104
1260.0053388404
43.9553128772
1559.4260427533
260
105
1066.5222490473
40.4594426173
1600.3788838716
280
106
1054.9257226415
37.2311002239
1493.1069964987
280
107
922.7245037572
39.9080046109
1310.5841996221
260
108
1077.2643432658
40.6395453056
1562.3417690804
280
109
634.1266637071
42.8248109629
1520.6682670978
280
110
669.9503554534
42.6102043194
1354.6270489896
240
111
1099.7576683706
38.1659925652
1790.7868292823
260
112
1126.2576170827
47.520179679
1525.9761918642
260
113
841.144052041
45.9503918237
1463.0065303791
240
114
1411.3902465077
40.0900797659
1511.3075202535
260
115
1007.9536062761
35.5148382469
1422.7439957394
260
116
916.4248482278
33.6528865874
1683.6481260398
260
117
1093.4793407294
35.7203897338
1623.6039111063
240
118
730.2055783923
43.9762653614
1476.8150473756
260
119
1127.2292514234
42.1798257421
1668.1974026724
240
120
1194.7613026989
43.3445303416
1566.8744633003
260
121
1118.9910979873
43.7428549149
1744.1611286486
260
122
1423.1468677365
33.3252183837
1561.0929760114
240
123
1229.5581199076
46.7349446908
1549.1817786496
240
124
1265.9847485422
43.7992776925
1612.7873474616
260
125
1063.1293909994
43.5354787542
1536.7687107428
280
126
1012.2299095109
46.4223058871
1523.7773747358
280
127
1084.6532062395
35.9498268254
1385.5922740404
240
128
1244.6182475826
41.0067878975
1492.5210545371
280
129
882.6824610912
41.6176159079
1607.3648263627
240
130
780.4221453205
38.2341421401
1754.2865331634
280
131
932.6350373065
48.9205968834
1340.4109646799
260
132
1011.0413071322
47.634753274
1326.8933723011
280
133
1481.4405652622
41.2923464965
1506.9733232522
240
134
779.4198275894
41.2508621694
1691.8864427353
240
135
761.3587255121
45.6187900555
1655.0737351863
260
136
1086.1038329983
32.0183654467
1666.9975517871
240
137
1065.1921035013
42.092667728
1409.8976104506
260
138
1051.2869026705
38.4065539138
1831.6417860333
240
*
Figura 12.4 – A relação linear entre a inversa de volume (1/V) e pressão (P)
Gráf1
29.125
30.5625
31.9375
33.5
35.3125
36.78947
39.3125
41.11765
44.1875
46.6
50.3125
54.3125
58.25
61.3125
63.54545
66.57143
70
74.25
77.666
82.75
87.875
93.0625
100.4375
107.8125
117.5625
PRESSÃO
1/VOLUME
0.0208333333
0.0217391304
0.0227272727
0.0238095238
0.025
0.0263157895
0.0277777778
0.0294117647
0.03125
0.0333333333
0.0357142857
0.0384615385
0.0416666667
0.0434782609
0.0454545455
0.0476190476
0.05
0.0526315789
0.0555555556
0.0588235294
0.0625
0.0666666667
0.0714285714
0.0769230769
0.0833333333
Utilize a Opção "Regressão" na Barra de Menu.
Dica inicial:
PRESSÃO
PRESSÃO
Tabela 1.1 Neter et al., 1996 p. 21
DATA
weight
intervalo
dmes
t
t2
dano
dout
dnov
ddez
djan
dfev
dmar
dabril
dmaio
djun
t4/100000
t3/10000
dsam
t3
t4
c+
c-
x
VOLUME
PRESSÃO
1
958.541076315
26.4614437683
1834.2011041241
260
572
157
1
23
Produto
Custo
N_trim
Trimestre
PIB
Tam_Lote
Horas_T
10/28/02
91.7
0
28
1
1
300
1
0
0
0
0
0
0
0
0
0.00001
0.0001
2
1
1
0
-0.0207758074
73.9742241926
48
29.125
2
1101.3762926807
49.9453245639
1455.0252027802
280
570
161
2
59
1
193
1
1970-1
2872.8
Mes
balanço
letrasAAA
letras3-4
80
399
10/29/02
92.4
0
29
2
4
301
1
0
0
0
0
0
0
0
0
0.00016
0.0008
3
8
16
0.0094767
-0.0012991074
74.0144767
46
30.5625
3
1319.8233151427
32.7441649561
1500.3843751983
240
645
168
3
36
2
226
2
1970-2
2860.3
1
360.071
5.94
5.31
30
121
10/31/02
91.4
1
31
3
9
303
1
0
0
0
0
0
0
0
0
0.00081
0.0027
5
27
81
0
-0.0090967438
73.9872023636
44
31.9375
4
1707.6484008242
35.3986616674
1431.1808096536
260
645
186
4
99
3
240
3
1970-3
2896.6
2
361.217
6.00
5.60
50
221
11/1/02
91.9
0
1
4
16
304
0
1
0
0
0
0
0
0
0
0.00256
0.0064
6
64
256
0
-0.0106325433
73.9934642005
42
33.5
5
826.9155100463
44.9997879614
1517.4638330463
240
645
183
5
36
4
244
4
1970-4
2873.7
3
358.774
6.08
5.49
90
376
11/4/02
91.2
2
4
5
25
307
0
1
0
0
0
0
0
0
0
0.00625
0.0125
2
125
625
0.0025771368
0
74.0075771368
40
35.3125
6
919.2243052018
47.0577016231
1549.5936092193
260
671
184
6
74
5
257
5
1971-1
2942.9
4
360.271
6.17
5.80
70
361
11/5/02
91.1
0
5
6
36
308
0
1
0
0
0
0
0
0
0
0.01296
0.0216
3
216
1296
0.0022442543
0
74.0046671175
38
36.78947
7
1283.7731843454
49.3861217465
1348.7908214884
260
675
180
7
30
6
260
6
1971-2
2947.4
5
360.139
6.14
5.61
60
224
11/7/02
91
1
7
7
49
310
0
1
0
0
0
0
0
0
0
0.02401
0.0343
5
343
2401
0.0059903419
0
74.0087460876
36
39.3125
8
802.103872715
51.8782736536
1554.1375584362
260
670
175
8
54
7
274
7
1971-3
2966
6
362.164
6.09
5.28
120
546
11/8/02
91.4
0
8
8
64
311
0
1
0
0
0
0
0
0
0
0.04096
0.0512
6
512
4096
0.0069477596
0
74.0059574177
34
41.11765
9
1280.0995124188
44.7843400353
1422.7047737804
260
710
193
9
17
8
297
8
1971-4
2980.8
7
362.901
5.87
5.19
80
352
11/11/02
91.9
2
11
9
81
314
0
1
0
0
0
0
0
0
0
0.06561
0.0729
2
729
6561
0
-0.0087184998
73.9862815002
32
44.1875
10
935.3835631457
45.8151272242
1513.4722313305
260
656
184
10
36
9
350
9
1972-1
3037.3
8
361.878
5.84
5.18
100
353
11/12/02
92.7
0
12
10
100
315
0
1
0
0
0
0
0
0
0
0.1
0.1
3
1000
10000
0
-0.0148758852
73.9888426146
30
46.6
11
982.0033259159
42.7760393095
1838.8940967852
280
640
179
11
89
10
420
10
1972-2
3089.7
9
360.922
5.99
5.30
50
157
11/14/02
92
1
14
11
121
317
0
1
0
0
0
0
0
0
0
0.14641
0.1331
5
1331
14641
0.0019399448
-0.0029359404
74.0069399448
28
50.3125
12
748.7274743737
43.8944108383
1401.9062215666
260
599
164
12
77
11
1972-3
3125.8
10
361.307
6.12
5.23
40
160
11/16/02
91.8
1
16
12
144
319
0
1
0
0
0
0
0
0
0
0.20736
0.1728
7
1728
20736
0.000166309
0
74.0032263642
26
54.3125
13
793.6162754588
45.9063495428
1654.0785206089
280
569
154
13
86
12
1972-4
3175.5
11
362.290
6.42
5.64
70
252
11/18/02
92.7
1
18
13
169
321
0
1
0
0
0
0
0
0
0
0.28561
0.2197
2
2197
28561
0
-0.0043983772
73.9906016228
24
58.25
14
1193.514914675
32.5756355879
1524.4284592554
280
564
157
14
33
13
1973-1
3253.3
12
367.382
6.48
5.62
90
389
11/19/02
93
0
19
14
196
322
0
1
0
0
0
0
0
0
0
0.38416
0.2744
3
2744
38416
0
-0.001807856
73.9975905212
23
61.3125
15
765.6070291466
36.9988778048
1461.573564633
280
573
164
15
90
14
1973-2
3267.6
13
371.031
6.52
5.67
20
113
11/21/02
91.7
1
21
15
225
324
0
1
0
0
0
0
0
0
0
0.50625
0.3375
5
3375
50625
0
0
74.0013153567
22
63.54545
16
1084.3290968835
35.4480927045
1281.1673893011
280
667
188
16
74
15
1973-3
3264.3
14
373.734
6.64
5.83
110
435
11/22/02
91.6
0
22
16
256
325
0
1
0
0
0
0
0
0
0
0.65536
0.4096
6
4096
65536
0.0005779765
0
74.0055779765
21
66.57143
17
996.4888018692
46.6192569648
1550.843596
260
700
191
17
7
16
1973-4
3289.1
15
373.463
6.75
5.53
100
420
11/25/02
92.2
2
25
17
289
328
0
1
0
0
0
0
0
0
0
0.83521
0.4913
2
4913
83521
0
0
74.00138715
20
70
18
883.5227813313
44.9017444326
1455.4452188022
240
637
180
18
54
17
1974-1
3259.4
16
375.518
6.73
5.76
30
212
11/26/02
92
0
26
18
324
329
0
1
0
0
0
0
0
0
0
1.04976
0.5832
3
5832
104976
0
-0.0041096126
73.9908903874
19
74.25
19
590.6135705606
45.9109652284
1635.3805600957
260
650
172
19
98
18
1974-2
3267.6
17
374.804
6.89
6.09
50
268
11/28/02
91.4
1
28
19
361
331
0
1
0
0
0
0
0
0
0
1.30321
0.6859
5
6859
130321
0.0138484591
0
74.0188484591
18
77.666
20
1300.4111789121
37.1841589286
1196.4888850925
260
655
184
20
50
19
1974-3
3239.1
18
375.457
6.98
6.52
90
377
11/29/02
92
0
29
20
400
332
0
1
0
0
0
0
0
0
0
1.6
0.8
6
8000
160000
0.0137204404
0
74.0048719812
17
82.75
21
1050.8333790397
44.8825995691
1583.6159301798
240
665
179
21
86
20
1974-4
3226.4
19
375.423
6.98
6.68
110
421
11/30/02
91.7
0
30
21
441
333
0
1
0
0
0
0
0
0
0
1.94481
0.9261
7
9261
194481
0.0094428293
0
74.0007223889
16
87.875
22
1338.3788471991
36.4997982715
1610.0356712413
260
599
169
22
90
21
1975-1
3154
20
374.365
7.10
7.07
30
273
12/2/02
91.7
1
2
22
484
335
0
0
1
0
0
0
0
0
0
2.34256
1.0648
2
10648
234256
0.0127412408
0
74.0082984116
15
93.0625
23
453.5677172583
37.6864614837
1536.5323558071
240
605
160
23
65
22
1975-2
3190.4
21
372.314
7.19
7.12
90
468
12/3/02
91.7
0
3
23
529
336
0
0
1
0
0
0
0
0
0
2.79841
1.2167
3
12167
279841
0.0163613179
0
74.0086200771
14
100.4375
24
1021.2268418711
37.5212801928
1492.7739509076
280
24
20
23
1975-3
3249.9
22
373.765
7.29
7.25
40
244
12/4/02
91.5
0
4
24
576
337
0
0
1
0
0
0
0
0
0
3.31776
1.3824
4
13824
331776
0.0049960033
-0.0013653147
73.9936346853
13
107.8125
25
1036.7439516493
44.0067789087
1330.1136656664
240
25
17
24
1975-4
3292.5
23
372.776
7.65
7.85
80
342
12/9/02
93.9
4
9
25
625
342
0
0
1
0
0
0
0
0
0
3.90625
1.5625
2
15625
390625
0
-0.0055972316
73.9907680831
12
117.5625
26
1144.3424788097
34.6844127408
1523.7193944486
240
26
45
25
1976-1
3356.7
24
374.134
7.75
8.02
70
323
12/10/02
94
0
10
26
676
343
0
0
1
0
0
0
0
0
0
4.56976
1.7576
3
17576
456976
0.0061118879
0
74.0111118879
27
894.6862213769
45.0473090596
1615.1768174168
240
27
9
26
1976-2
3369.2
25
374.880
7.72
7.87
12/11/02
93.2
0
11
27
729
344
0
0
1
0
0
0
0
0
0
5.31441
1.9683
4
19683
531441
0
-0.0070117875
73.9879882125
28
883.4715807586
40.4072262527
1324.3446270863
280
28
72
27
1976-3
3381
26
376.735
7.67
7.14
12/12/02
93
0
12
28
784
345
0
0
1
0
0
0
0
0
0
6.14656
2.1952
5
21952
614656
0
-0.0176007086
73.9844110789
29
1130.5503527318
38.0125096499
1861.5732566686
260
29
33
28
1976-4
3416.3
27
374.841
7.66
7.20
12/14/02
92.6
1
14
29
841
347
0
0
1
0
0
0
0
0
0
7.07281
2.4389
7
24389
707281
0.002113249
-0.0054874596
74.007113249
30
1255.7770399916
31.0472979536
1532.4437223753
240
30
17
29
1977-1
3466.4
28
375.622
7.89
7.59
12/16/02
92.7
1
16
30
900
349
0
0
1
0
0
0
0
0
0
8.1
2.7
2
27000
810000
0.0034973106
0
74.0063840616
31
697.4665949336
43.6120184177
1819.4400051143
280
31
3
30
1977-2
3525
29
375.461
8.14
7.74
12/17/02
93
0
17
31
961
350
0
0
1
0
0
0
0
0
0
9.23521
2.9791
3
29791
923521
0.0205541943
0
74.0220568836
32
1648.2895565366
33.4715219752
1443.627472021
280
32
29
31
1977-3
3574.4
30
377.694
8.21
7.51
12/19/02
92.1
1
19
32
1024
352
0
0
1
0
0
0
0
0
0
10.48576
3.2768
5
32768
1048576
0.0299917405
0
74.0144375463
33
949.6742135155
37.2631485434
1603.7927290781
260
33
30
32
1977-4
3567.2
31
380.119
8.05
7.46
12/21/02
91.9
1
21
33
1089
354
0
0
1
0
0
0
0
0
0
11.85921
3.5937
7
35937
1185921
0.0380307795
0
74.013039039
34
1448.3374751442
39.1108211361
1696.0968347703
280
34
68
33
1978-1
3591.8
32
382.288
7.94
7.09
12/23/02
91.8
1
23
34
1156
356
0
0
1
0
0
0
0
0
0
13.36336
3.9304
2
39304
1336336
0.0341603833
0
74.0011296038
35
1002.40288098
39.5186556134
1382.5448983553
240
35
87
34
1978-2
3707
33
383.270
7.88
6.82
12/26/02
92.4
2
26
35
1225
359
0
0
1
0
0
0
0
0
0
15.00625
4.2875
5
42875
1500625
0.029179892
0
74.0000195087
36
1394.703421264
42.1223399926
1219.7423908801
260
36
44
35
1978-3
3735.6
34
387.978
7.79
6.22
12/27/02
92.3
0
27
36
1296
360
0
0
1
0
0
0
0
0
0
16.79616
4.6656
6
46656
1679616
0.0287169063
0
74.0045370143
37
1204.6822022142
43.5497350837
1600.5224703476
260
36
1978-4
3784.3
35
394.041
7.41
5.61
1/9/03
95
12
9
37
1369
8
0
0
0
1
0
0
0
0
0
18.74161
5.0653
5
50653
1874161
0.0234617589
0
73.9997448526
38
1030.9137481761
31.6281467449
1452.2447069467
260
37
1979-1
3807.5
36
403.423
7.18
5.48
1/15/03
92.9
5
15
38
1444
14
0
0
0
1
0
0
0
0
0
20.85136
5.4872
4
54872
2085136
0.0079150083
-0.0055467507
73.9894532493
39
729.720165841
46.0853381001
1675.3139713401
260
38
1979-2
3814.6
37
412.727
7.15
4.78
1/27/03
92.4
11
27
39
1521
26
0
0
0
1
0
0
0
0
0
23.13441
5.9319
2
59319
2313441
0
-0.0182948122
73.9822519385
40
1188.4925701081
39.8272699031
1519.5451548279
240
39
1979-3
3830.8
38
423.417
7.27
4.14
1/30/03
92.4
2
30
40
1600
29
0
0
0
1
0
0
0
0
0
25.6
6.4
5
64000
2560000
0.0032833139
-0.0050114982
74.0082833139
41
975.2114161613
35.2853158902
1492.4407347862
240
40
1979-4
3732.6
39
429.948
7.37
4.64
2/1/03
92.2
1
1
41
1681
31
0
0
0
0
1
0
0
0
0
28.25761
6.8921
7
68921
2825761
0.0027255589
0
74.004442245
42
1202.0228715385
41.7280456177
1658.8632585481
260
41
1980-1
3733.5
40
437.821
7.54
5.52
2/3/03
92.5
1
3
42
1764
33
0
0
0
0
1
0
0
0
0
31.11696
7.4088
2
74088
3111696
0.0039046204
0
74.0061790615
43
969.4408746412
37.2119098857
1599.5478899313
260
42
1980-2
3808.5
41
441.703
7.58
5.95
2/4/03
92.4
0
4
43
1849
34
0
0
0
0
1
0
0
0
0
34.18801
7.9507
3
79507
3418801
0.0010393523
0
74.0021347319
44
1229.4222482204
46.0446268435
1226.2443685031
280
43
1980-3
3860.5
42
446.663
7.62
6.20
2/6/03
92.1
1
6
44
1936
36
0
0
0
0
1
0
0
0
0
37.48096
8.5184
5
85184
3748096
0
-0.0052693093
73.9897306907
45
1088.5151458432
45.8757223087
1600.0204292723
260
44
1980-4
3844.4
43
447.964
7.58
6.03
2/8/03
91.8
1
8
45
2025
38
0
0
0
0
1
0
0
0
0
41.00625
9.1125
7
91125
4100625
0.0073819518
0
74.0123819518
46
1167.2849891368
41.9239053017
1923.4170773998
240
45
1981-1
3864.5
44
449.118
7.48
5.60
2/10/03
91.4
1
10
46
2116
40
0
0
0
0
1
0
0
0
0
44.77456
9.7336
2
97336
4477456
0
0
73.9968878683
47
780.2982887454
36.6640757521
1383.8965211689
260
46
1981-2
3803.1
45
449.234
7.35
5.26
2/12/03
90.8
1
12
47
2209
42
0
0
0
0
1
0
0
0
0
48.79681
10.3823
4
103823
4879681
0
-0.0033992177
73.9916007823
48
1121.1978900098
42.9782540878
1581.1475047158
240
47
1981-3
3756.1
46
454.162
7.19
4.96
2/13/03
91.8
0
13
48
2304
43
0
0
0
0
1
0
0
0
0
53.08416
11.0592
5
110592
5308416
0
-0.0066104996
73.991788718
49
1676.2068677138
47.1735257734
1296.7224771855
260
48
1981-4
3771.1
47
456.692
7.19
5.28
2/15/03
91.4
1
15
49
2401
45
0
0
0
0
1
0
0
0
0
57.64801
11.7649
7
117649
5764801
0
-0.005900427
73.9957100727
50
712.358224623
41.4332727005
1218.6837390473
260
49
1982-1
3754.4
48
465.117
7.11
5.37
2/17/03
92.8
1
17
50
2500
47
0
0
0
0
1
0
0
0
0
62.5
12.5
2
125000
6250000
0
-0.0054340421
73.9954663849
51
992.7421527748
43.7438667277
1539.5896222471
260
50
1982-2
3759.6
49
470.408
7.16
5.53
2/19/03
91.8
1
19
51
2601
49
0
0
0
0
1
0
0
0
0
67.65201
13.2651
4
132651
6765201
0.0015623453
0
74.0065623453
52
708.081773714
45.0035737331
1359.9851096515
260
51
1982-3
3783.5
50
475.600
7.22
5.72
2/21/03
92.8
1
21
52
2704
51
0
0
0
0
1
0
0
0
0
73.11616
14.0608
6
140608
7311616
0
0
73.9966444307
53
731.1548839509
44.397770681
1534.8678099726
240
52
1982-4
3886.5
51
475.857
7.36
6.04
2/24/03
91.8
2
24
53
2809
54
0
0
0
0
1
0
0
0
0
78.90481
14.8877
2
148877
7890481
0
0
73.9985494924
54
1011.0472252193
38.9240222931
1473.2779087935
240
53
1983-1
3944.4
52
480.259
7.34
5.66
2/26/03
91.4
1
26
54
2916
56
0
0
0
0
1
0
0
0
0
85.03056
15.7464
4
157464
8503056
0
-0.0010086563
73.9939913437
55
653.0243164064
39.5520738594
1588.1447022039
260
54
1983-2
4012.1
53
483.432
7.30
5.75
2/28/03
92.4
1
28
55
3025
58
0
0
0
0
1
0
0
0
0
91.50625
16.6375
6
166375
9150625
0
0
73.9984543365
56
1044.8657562704
31.2489101916
1593.4649051487
260
55
1983-3
1089.5
54
488.536
7.30
5.82
3/3/03
92
2
3
56
3136
61
0
0
0
0
0
1
0
0
0
98.34496
17.5616
2
175616
9834496
0
-0.0173353709
73.9776646291
57
903.653142236
42.6801558306
1547.8275978821
260
56
1983-4
4144
55
493.182
7.27
5.90
3/6/03
90.4
2
6
57
3249
64
0
0
0
0
0
1
0
0
0
105.56001
18.5193
5
185193
10556001
0
-0.013670782
73.9986645889
58
1026.0000179777
38.0265727118
1683.2842144722
240
57
1984-1
4166.4
56
494.242
7.30
6.11
3/8/03
91.3
1
8
58
3364
66
0
0
0
0
0
1
0
0
0
113.16496
19.5112
7
195112
11316496
0
-0.0219627742
73.9867080078
59
1042.6331315187
41.1540123523
1545.4790551885
240
58
1984-2
4194.2
57
493.484
7.31
6.05
3/10/03
91.4
1
10
59
3481
68
0
0
0
0
0
1
0
0
0
121.17361
20.5379
2
205379
12117361
0
-0.0153969767
74.0015657974
60
1124.7005651142
41.4400484361
1440.0647539005
260
59
1984-3
4221.8
58
498.186
7.26
5.98
3/12/03
91.7
1
12
60
3600
70
0
0
0
0
0
1
0
0
0
129.6
21.6
4
216000
12960000
0.0000302333
-0.0053667434
74.0050302333
61
1295.0732847087
48.7281932792
1490.6247580839
280
60
1984-4
4254.8
59
500.064
7.24
6.00
3/14/03
91.4
1
14
61
3721
72
0
0
0
0
0
1
0
0
0
138.45841
22.6981
6
226981
13845841
0.0082010808
0
74.0131708475
62
1319.4058895941
34.5988292893
1499.9942019713
260
61
1985-1
4309
60
506.684
7.25
6.24
3/15/03
91.4
0
15
62
3844
73
0
0
0
0
0
1
0
0
0
147.76336
23.8328
7
238328
14776336
0
-0.0011929541
73.9938070459
63
886.8782832586
32.6788632365
1564.0596908852
240
62
1985-2
4333.5
3/17/03
91.4
1
17
63
3969
75
0
0
0
0
0
1
0
0
0
157.52961
25.0047
2
250047
15752961
0
-0.003672593
73.992520361
64
1072.0146687929
49.1823949333
1494.6458615341
240
63
1985-3
4390.5
3/19/03
91
1
19
64
4096
77
0
0
0
0
0
1
0
0
0
167.77216
26.2144
4
262144
16777216
0
0
74.0014636498
65
1003.6565182452
38.5332124197
1486.8272198
240
64
1985-4
4387.7
3/21/03
91.7
1
21
65
4225
79
0
0
0
0
0
1
0
0
0
178.50625
27.4625
6
274625
17850625
0
0
73.9976856998
66
1079.1995899665
44.2208739615
1513.2418449539
260
65
1986-1
4412.6
3/24/03
91.6
2
24
66
4356
82
0
0
0
0
0
1
0
0
0
189.74736
28.7496
2
287496
18974736
0
0
73.9979168933
67
800.6747877879
33.7149027573
1633.0176928605
240
66
1986-2
4427.1
3/26/03
91.5
1
26
67
4489
84
0
0
0
0
0
1
0
0
0
201.51121
30.0763
4
300763
20151121
0.0107720024
0
74.0157720024
68
1142.1874761389
38.1725352427
1494.014387994
280
67
1986-3
4460
3/28/03
91.1
1
28
68
4624
86
0
0
0
0
0
1
0
0
0
213.81376
31.4432
6
314432
21381376
0.0061488515
0
74.0003768491
69
1240.9905245839
34.7485889606
1522.6160636885
240
68
1986-4
4515.3
3/31/03
93.3
2
31
69
4761
89
0
0
0
0
0
1
0
0
0
226.67121
32.8509
2
328509
22667121
0
0
73.9985402155
70
973.2945821809
40.1478554168
1604.1868245011
280
69
1987-1
4559.3
4/2/03
91.1
1
2
70
4900
91
0
0
0
0
0
0
1
0
0
240.1
34.3
4
343000
24010000
0.0133032171
0
74.0183032171
71
1062.2727130474
41.0317819488
1423.4898950817
280
70
1987-2
4625.5
4/4/03
91.3
1
4
71
5041
93
0
0
0
0
0
0
1
0
0
254.11681
35.7911
6
357911
25411681
0.0019958713
-0.0013073458
73.9936926542
72
951.2265747651
37.1275087773
1506.0430807025
240
71
1987-3
4655.3
4/7/03
91.8
2
7
72
5184
96
0
0
0
0
0
0
1
0
0
268.73856
37.3248
2
373248
26873856
0.0097072421
0
74.0127113708
73
1343.1415674084
43.0548790164
1950.2435331233
280
72
1987-4
4704.8
4/8/03
91.8
0
8
73
5329
97
0
0
0
0
0
0
1
0
0
283.98241
38.9017
3
389017
28398241
0.0045538558
0
73.9998466137
74
966.4401132829
38.6335524227
1554.8730554328
240
73
1988-1
4734.5
4/10/03
90.8
1
10
74
5476
99
0
0
0
0
0
0
1
0
0
299.86576
40.5224
5
405224
29986576
0
0
73.9993558276
75
1163.8294235843
47.7790218711
1545.1188952866
240
74
1988-2
4779.7
4/29/03
92
18
29
75
5625
118
0
0
0
0
0
0
1
0
0
316.40625
42.1875
3
421875
31640625
0.0111015578
0
74.0161015578
76
1647.3119556984
40.6746518011
1709.8825007124
260
75
1988-3
4809.8
4/30/03
90.9
0
30
76
5776
119
0
0
0
0
0
0
1
0
0
333.62176
43.8976
4
438976
33362176
0.0097278723
0
74.0036263145
77
1074.4715884618
45.0155676945
1816.193109029
280
76
1988-4
4832.4
5/2/03
91.8
1
2
77
5929
121
0
0
0
0
0
0
0
1
0
351.53041
45.6533
6
456533
35153041
0.0090984605
0
74.0043705882
78
1169.5604983878
38.6005718711
1481.276289418
260
77
1989-1
4845.6
5/5/03
90.5
2
5
78
6084
124
0
0
0
0
0
0
0
1
0
370.15056
47.4552
2
474552
37015056
0.001747212
0
73.9976487516
79
1231.3310081616
41.3569206203
1696.1507223314
260
78
1989-2
4859.7
5/13/03
91
7
13
79
6241
132
0
0
0
0
0
0
0
1
0
389.50081
49.3039
3
493039
38950081
0.0035804845
0
74.0068332724
80
1488.785751789
40.9740233509
1792.3038664448
260
79
1989-3
4880.8
5/15/03
90.4
1
15
80
6400
134
0
0
0
0
0
0
0
1
0
409.6
51.2
5
512000
40960000
0
0
73.9993136498
81
798.8942095187
42.5242343327
1749.2183739378
260
80
1989-4
4900.3
5/26/03
89.9
10
26
81
6561
145
0
0
0
0
0
0
0
1
0
430.46721
53.1441
2
531441
43046721
0
-0.002360768
73.992639232
82
1277.5237420185
33.260314568
1502.7482656151
260
81
1990-1
4903.3
5/27/03
89.6
0
27
82
6724
146
0
0
0
0
0
0
0
1
0
452.12176
55.1368
3
551368
45212176
0
-0.0083360953
73.9890246727
83
1297.5423399978
42.6207317205
1593.0054966375
260
82
1990-2
4855.1
5/30/03
90.4
2
30
83
6889
149
0
0
0
0
0
0
0
1
0
474.58321
57.1787
6
571787
47458321
0
-0.0012990887
74.0020370067
84
1399.7547560932
46.0295633375
1635.2942717858
240
83
1990-3
4824
5/31/03
89.5
0
31
84
7056
150
0
0
0
0
0
0
0
1
0
497.87136
59.2704
7
592704
49787136
0
-0.0061124683
73.9901866204
85
1002.1591734669
40.3654122338
1492.8656961856
240
84
1990-4
4840.7
6/4/03
91.1
3
4
85
7225
154
0
0
0
0
0
0
0
0
1
522.00625
61.4125
4
614125
52200625
0.0143957931
0
74.0193957931
86
1128.9840361854
42.8756517167
1558.7316435485
260
85
1991-1
4862.7
6/6/03
90.1
1
6
86
7396
156
0
0
0
0
0
0
0
0
1
547.00816
63.6056
6
636056
54700816
0.0081236373
0
73.9987278443
87
1154.4585234872
34.4504452287
1460.8616008118
240
86
1991-2
4868
0
-0.0108763214
73.9841236786
88
1197.7001121202
39.2689481587
1548.5284772367
280
87
1991-3
0
-0.0092294692
73.9966468522
89
1050.8102501397
45.1430902204
1432.3134716178
280
88
1991-4
0.004572318
0
74.009572318
90
822.4557339957
34.3891225485
1384.792487137
240
0
0
73.9961702997
91
1088.037814602
44.0507018184
1532.0562776324
260
0
-0.0015386416
73.9934613584
92
862.8632186662
43.3096853258
1608.7781811293
280
0
-0.0102024808
73.9863361609
93
1017.5953715168
35.6788656164
1557.7666128265
260
0
-0.0020413273
74.0031611535
94
1087.3247593871
32.0873506198
1496.023575477
280
0
0
73.9983629095
95
1047.7991785222
46.9085899668
1566.3424088998
240
0.0007125362
0
74.0057125362
96
1255.8141818124
37.1975967128
1029.5002008788
260
0
-0.0013737389
73.9936262611
97
919.4175735131
47.5559228208
1772.7310857153
240
0
0
73.9965382244
98
1035.4532295002
38.4683995535
1793.4621079476
280
0
0
74.0028593831
99
500.9588197616
38.5204340192
1475.9668298793
240
0
0
73.9966897121
100
1599.022174659
38.2268150234
1495.0362052914
240
0
0
74.0021222149
101
1257.7390542582
47.6544438343
1636.4184072372
260
102
1060.8373153025
43.3565015656
1503.3451215131
260
103
835.7055763689
55.3529981617
1492.0040067991
240
104
1260.0053388404
43.9553128772
1559.4260427533
260
105
1066.5222490473
40.4594426173
1600.3788838716
280
106
1054.9257226415
37.2311002239
1493.1069964987
280
107
922.7245037572
39.9080046109
1310.5841996221
260
108
1077.2643432658
40.6395453056
1562.3417690804
280
109
634.1266637071
42.8248109629
1520.6682670978
280
110
669.9503554534
42.6102043194
1354.6270489896
240
111
1099.7576683706
38.1659925652
1790.7868292823
260
112
1126.2576170827
47.520179679
1525.9761918642
260
113
841.144052041
45.9503918237
1463.0065303791
240
114
1411.3902465077
40.0900797659
1511.3075202535
260
115
1007.9536062761
35.5148382469
1422.7439957394
260
116
916.4248482278
33.6528865874
1683.6481260398
260
117
1093.4793407294
35.7203897338
1623.6039111063
240
118
730.2055783923
43.9762653614
1476.8150473756
260
119
1127.2292514234
42.1798257421
1668.1974026724
240
120
1194.7613026989
43.3445303416
1566.8744633003
260
121
1118.9910979873
43.7428549149
1744.1611286486
260
122
1423.1468677365
33.3252183837
1561.0929760114
240
123
1229.5581199076
46.7349446908
1549.1817786496
240
124
1265.9847485422
43.7992776925
1612.7873474616
260
125
1063.1293909994
43.5354787542
1536.7687107428
280
126
1012.2299095109
46.4223058871
1523.7773747358
280
127
1084.6532062395
35.9498268254
1385.5922740404
240
128
1244.6182475826
41.0067878975
1492.5210545371
280
129
882.6824610912
41.6176159079
1607.3648263627
240
130
780.4221453205
38.2341421401
1754.2865331634
280
131
932.6350373065
48.9205968834
1340.4109646799
260
132
1011.0413071322
47.634753274
1326.8933723011
280
133
1481.4405652622
41.2923464965
1506.9733232522
240
134
779.4198275894
41.2508621694
1691.8864427353
240
135
761.3587255121
45.6187900555
1655.0737351863
260
136
1086.1038329983
32.0183654467
1666.9975517871
240
137
1065.1921035013
42.092667728
1409.8976104506
260
138
1051.2869026705
38.4065539138
1831.6417860333
240
Informações gerais
Utilize a Opção "Regressão" na Barra de Menu.
Dica inicial:
PRESSÃO
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
PRESSÃO
Tabela 1.1 Neter et al., 1996 p. 21
DATA
weight
intervalo
dmes
t
t2
dano
dout
dnov
ddez
djan
dfev
dmar
dabril
dmaio
djun
t4/100000
t3/10000
dsam
t3
t4
c+
c-
x
VOLUME
PRESSÃO
1
958.541076315
26.4614437683
1834.2011041241
260
572
157
1
23
Produto
Custo
N_trim
Trimestre
PIB
Tam_Lote
Horas_T
10/28/02
91.7
0
28
1
1
300
1
0
0
0
0
0
0
0
0
0.00001
0.0001
2
1
1
0
-0.0207758074
73.9742241926
48
29.125
2
1101.3762926807
49.9453245639
1455.0252027802
280
570
161
2
59
1
193
1
1970-1
2872.8
Mes
balanço
letrasAAA
letras3-4
80
399
10/29/02
92.4
0
29
2
4
301
1
0
0
0
0
0
0
0
0
0.00016
0.0008
3
8
16
0.0094767
-0.0012991074
74.0144767
46
30.5625
3
1319.8233151427
32.7441649561
1500.3843751983
240
645
168
3
36
2
226
2
1970-2
2860.3
1
360.071
5.94
5.31
30
121
10/31/02
91.4
1
31
3
9
303
1
0
0
0
0
0
0
0
0
0.00081
0.0027
5
27
81
0
-0.0090967438
73.9872023636
44
31.9375
4
1707.6484008242
35.3986616674
1431.1808096536
260
645
186
4
99
3
240
3
1970-3
2896.6
2
361.217
6.00
5.60
50
221
11/1/02
91.9
0
1
4
16
304
0
1
0
0
0
0
0
0
0
0.00256
0.0064
6
64
256
0
-0.0106325433
73.9934642005
42
33.5
5
826.9155100463
44.9997879614
1517.4638330463
240
645
183
5
36
4
244
4
1970-4
2873.7
3
358.774
6.08
5.49
90
376
11/4/02
91.2
2
4
5
25
307
0
1
0
0
0
0
0
0
0
0.00625
0.0125
2
125
625
0.0025771368
0
74.0075771368
40
35.3125
6
919.2243052018
47.0577016231
1549.5936092193
260
671
184
6
74
5
257
5
1971-1
2942.9
4
360.271
6.17
5.80
70
361
11/5/02
91.1
0
5
6
36
308
0
1
0
0
0
0
0
0
0
0.01296
0.0216
3
216
1296
0.0022442543
0
74.0046671175
38
36.78947
7
1283.7731843454
49.3861217465
1348.7908214884
260
675
180
7
30
6
260
6
1971-2
2947.4
5
360.139
6.14
5.61
60
224
11/7/02
91
1
7
7
49
310
0
1
0
0
0
0
0
0
0
0.02401
0.0343
5
343
2401
0.0059903419
0
74.0087460876
36
39.3125
8
802.103872715
51.8782736536
1554.1375584362
260