Annexe n°2: Conditions de Gauss-Markov
TEST DE NORMALITE DES ERREURS
. quietly reg consult assurance dspc umed prim sec,robust
. predict l,resid
. sktest l
Skewness/Kurtosis tests for Normality
joint
Variable | Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2
+
l | 1.000 0.708 0.14 0.9325
Jacques Bera
. reg consult assurance dspc umed prim sec,robust
Linear regression Number of obs = 64
F( 5, 58) = 18.32
Prob > F = 0.0000
R-squared = 0.6765
Root MSE = 110.31
---
| Robust
consult | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+
---
assurance | 15.98919 3.523631 4.54 0.000 8.935876 23.04251
dspc | -.1682786 .0668738 -2.52 0.015 -.302141 -.0344162
4.94 0.000 256.9893 606.8234
1.21 0.232 -20.08993 81.22013
0.75 0.454 -45.96563 101.4678
-0.47 0.638 -4426.574 2735.212
|
umed |
|
431.9063
|
87.38348
|
|
prim |
|
30.5651
|
25.30578
|
|
sec |
|
27.75108
|
36.82673
|
|
_cons |
|
-845.681
|
1788.91
|
---
. predict res,resid
. su res,detail
Residuals
|
1%
5%
|
Percentiles
-246.2142
-163.7113
|
Smallest -246.2142 -214.6897
|
|
|
|
10%
|
-140.9988
|
-183.2607
|
Obs
|
64
|
|
25%
|
-72.91444
|
-163.7113
|
Sum of Wgt.
|
64
|
|
50%
|
0
|
|
Mean
|
0
|
|
|
Largest
|
Std. Dev.
|
105.8464
|
|
75%
|
72.91444
|
163.7113
|
|
|
|
90%
|
140.9988
|
183.2607
|
Variance
|
11203.47
|
|
95%
|
163.7113
|
214.6897
|
Skewness
|
0
|
|
99%
|
246.2142
|
246.2142
|
Kurtosis
|
2.642944
|
***JB=64/6[(0.128)/4]=0.341 qui est inferieur à 5.99 donc
on accepte l'hypothese nulle H0 de normalité des residus***
label var res "residus"
. graph7 res,xlabel ylabel bin(7) normal freq
TEST DE FORME FONCTIONNELLE (RAMSEY RESET)
Analyse de l'incidence du Seguro Popular et de son impact sur
l'utilisation des services de santé au Mexique
2009
. quietly reg consult assurance dspc umed prim sec,robust
. ovtest
Ramsey RESET test using powers of the fitted values of consult
Ho: model has no omitted variables
F(3, 55) = 1.35
Prob > F = 0.2680
|
reg consult
|
assurance dspc umed prim sec
|
|
|
|
Source
|
| SS
|
df
|
MS
|
Number of obs
|
= 64
|
|
+
|
|
|
F( 5, 58)
|
= 24.25
|
|
Model
|
| 1475761.07
|
5
|
295152.215
|
Prob > F
|
= 0.0000
|
|
Residual
|
| 705818.516
|
58
|
12169.2848
|
R-squared
|
= 0.6765
|
|
+
|
|
|
Adj R-squared
|
= 0.6486
|
|
Total
|
| 2181579.59
|
63
|
34628.2475
|
Root MSE
|
= 110.31
|
|
---
consult |
|
Coef. Std.
|
Err.
|
t
|
P>|t| [95% Conf.
|
Interval]
|
---
|
+
|
|
|
|
|
|
|
assurance
|
| 15.98919
|
3.80252
|
4.20
|
0.000
|
8.377619
|
23.60076
|
|
dspc
|
| -.1682786
|
.0856318
|
-1.97
|
0.054
|
-.3396893
|
.0031321
|
|
umed
|
| 431.9063
|
81.82656
|
5.28
|
0.000
|
268.1127
|
595.7
|
|
prim
|
| 30.5651
|
28.67511
|
1.07
|
0.291
|
-26.83437
|
87.96457
|
|
sec
|
| 27.75108
|
48.72145
|
0.57
|
0.571
|
-69.77549
|
125.2777
|
|
_cons
|
| -845.681
|
2160.785
|
-0.39
|
0.697
|
-5170.962
|
3479.6
|
---
. predict n
(option xb assumed; fitted values)
. gen n1=n^2
. gen n2=n^3
. gen
n3=n^4
|
reg consult
Source |
+
|
assurance dspc umed prim sec
SS df MS
|
|
Model
|
|
|
1591354.42
|
8
|
198919.303
|
|
Residual
|
|
|
590225.167
|
55
|
10731.3667
|
|
+
|
|
|
|
|
|
Total
|
|
|
2181579.59
|
63
|
34628.2475
|
|
|
|
|
|
|
Consult |
|
|
Coef. Std.
|
Err.
|
t
|
.
|
n1 n2 n3
Number of obs
|
=
|
64
|
|
F( 8, 55)
|
=
|
18.54
|
|
Prob > F
|
=
|
0.0000
|
|
R-squared
|
=
|
0.7295
|
|
Adj R-squared
|
=
|
0.6901
|
|
Root MSE
|
=
|
103.59
|
---
P>|t| [95% Conf. Interval]
|
---
|
|
|
|
|
|
|
|
assurance |
|
-1484.908
|
7107.014
|
-0.21
|
0.835
|
-15727.68
|
12757.87
|
|
dspc |
|
15.66445
|
74.79871
|
0.21
|
0.835
|
-134.2355
|
165.5644
|
|
umed |
|
-40035.64
|
191975.9
|
-0.21
|
0.836
|
-424764
|
344692.7
|
|
prim |
|
-2822.219
|
13585.53
|
-0.21
|
0.836
|
-30048.22
|
24403.78
|
|
sec |
|
-2571.639
|
12334.96
|
-0.21
|
0.836
|
-27291.46
|
22148.18
|
|
n1 |
|
.0365265
|
.258383
|
0.14
|
0.888
|
-.4812846
|
.5543376
|
|
n2 |
|
-4.79e-06
|
.0000665
|
-0.07
|
0.943
|
-.0001381
|
.0001285
|
|
n3 |
|
2.05e-11
|
6.40e-09
|
0.00
|
0.997
|
-1.28e-08
|
1.28e-08
|
|
_cons |
|
158017.5
|
661512.7
|
0.24
|
0.812
|
-1167684
|
1483718
|
TEST D'HETEROSCEDASTICITE
. reg consult assurance dspc umed prim sec
Source | SS df MS Number of obs = 64
+ F( 5, 58) = 24.25
|
295152.215
|
Prob > F
|
=
|
0.0000
|
|
12169.2848
|
R-squared
|
=
|
0.6765
|
|
Adj R-squared
|
=
|
0.6486
|
|
34628.2475
|
Root MSE
|
=
|
110.31
|
Model | 1475761.07 5
Residual | 705818.516 58
+
Total | 2181579.59 63
---
consult | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
---
|
+
|
|
|
|
|
|
|
assurance
|
| 15.98919
|
3.80252
|
4.20
|
0.000
|
8.377619
|
23.60076
|
|
dspc
|
| -.1682786
|
.0856318
|
-1.97
|
0.054
|
-.3396893
|
.0031321
|
|
umed
|
| 431.9063
|
81.82656
|
5.28
|
0.000
|
268.1127
|
595.7
|
|
prim
|
| 30.5651
|
28.67511
|
1.07
|
0.291
|
-26.83437
|
87.96457
|
|
sec
|
| 27.75108
|
48.72145
|
0.57
|
0.571
|
-69.77549
|
125.2777
|
|
_cons
|
| -845.681
|
2160.785
|
-0.39
|
0.697
|
-5170.962
|
3479.6
|
---
. predict l,resid
. gen assc=assurance^2
. gen dspcc=dspc^2
. gen umedc=umed^2
. gen primc=prim^2
. gen secc=sec^2
. gen lc=l^2
. gen m1=assurance*dspc
. gen m2=assurance*umed
. gen
m3=assurance*prim
. gen m4=assurance*sec . gen m5=dspc*umed
. gen m6=dspc*prim
. gen m7=dspc*sec
. gen m8=umed*prim
. gen m9=umed*sec . gen m10=prim*sec
. reg lc assurance dspc umed prim sec assc dspcc umedc primc secc
m1 m2
m3 m4 m5
> m6 m7 m8 m9 m10
Source | SS df MS
+
Model | 3.9329e+09 20 196647470
Residual | 8.8558e+09 43 205949367
+
Total | 1.2789e+10 63 202996384
Number of obs
|
=
|
64
|
|
F( 20, 43)
|
=
|
0.95
|
|
Prob > F
|
=
|
0.5289
|
|
R-squared
|
=
|
0.3075
|
|
Adj R-squared
|
=
|
0.0145
|
|
Root MSE
|
=
|
14351
|
---
lc | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---
|
+
|
|
|
|
|
|
|
assurance
|
| -63905.25
|
153166.9
|
-0.42
|
0.679
|
-372795.7
|
244985.2
|
|
dspc
|
| 12708.64
|
5602.225
|
2.27
|
0.028
|
1410.676
|
24006.6
|
|
umed
|
| 658941.9
|
4205224
|
0.16
|
0.876
|
-7821701
|
9139585
|
|
prim
|
| 3830256
|
1320961
|
2.90
|
0.006
|
1166285
|
6494227
|
|
sec
|
| 5057261
|
2034583
|
2.49
|
0.017
|
954133.5
|
9160389
|
|
assc
|
| -157.8679
|
200.9934
|
-0.79
|
0.437
|
-563.2098
|
247.4739
|
|
dspcc
|
| -.2588577
|
.1555726
|
-1.66
|
0.103
|
-.5725997
|
.0548842
|
|
umedc
|
| -15548.77
|
100339.8
|
-0.15
|
0.878
|
-217903.3
|
186805.8
|
|
primc
|
| -27233.15
|
9707.94
|
-2.81
|
0.008
|
-46811.08
|
-7655.221
|
|
secc
|
| -46833.25
|
26170.13
|
-1.79
|
0.081
|
-99610.33
|
5943.842
|
0.34 0.739 -14.42261 20.17337
1.31 0.198 -6843.359 32093.94
0.11 0.910 -3994.02 4473.155
0.45 0.654 -5309.912 8376.94
-0.64 0.526 -549.4181 285.0415
-2.17 0.036 -352.8566 -12.56346
-2.02 0.050 -431.4458 -.4926688
0.10 0.918 -100031.6 110912.7
-0.50 0.621 -258081.9 155909.4
-2.82 0.007 -115902.7 -19253.79
-2.84 0.007 -2.37e+08 -4.00e+07
|
m1 |
|
2.87538
|
8.577405
|
|
m2 |
|
12625.29
|
9653.755
|
|
m3 |
|
239.5673
|
2099.273
|
|
m4 |
|
1533.514
|
3393.391
|
|
m5 |
|
-132.1883
|
206.8882
|
|
m6 |
|
-182.71
|
84.36913
|
|
m7 |
|
-215.9692
|
106.8465
|
|
m8 |
|
5440.542
|
52299.59
|
|
m9 |
|
-51086.29
|
102641.2
|
|
m10 |
|
-67578.24
|
23962.23
|
|
_ cons |
|
-1.38e+08
|
4.88e+07
|
reg consult assurance dspc umed prim sec,robust
|
Number of obs
|
=
|
64
|
|
F( 5, 58)
|
=
|
18.32
|
|
Prob > F
|
=
|
0.0000
|
|
R-squared
|
=
|
0.6765
|
|
Root MSE
|
=
|
110.31
|
Linear regression
| Robust
|
consult |
---
|
Coef.
+
|
Std. Err.
|
t
|
P>|t|
|
[95% Conf.
|
Interval]
|
|
assurance
|
| 15.98919
|
3.523631
|
4.54
|
0.000
|
8.935876
|
23.04251
|
|
dspc
|
| -.1682786
|
.0668738
|
-2.52
|
0.015
|
-.302141
|
-.0344162
|
|
umed
|
| 431.9063
|
87.38348
|
4.94
|
0.000
|
256.9893
|
606.8234
|
|
prim
|
| 30.5651
|
25.30578
|
1.21
|
0.232
|
-20.08993
|
81.22013
|
|
sec
|
| 27.75108
|
36.82673
|
0.75
|
0.454
|
-45.96563
|
101.4678
|
|
_cons
|
| -845.681
|
1788.91
|
-0.47
|
0.638
|
-4426.574
|
2735.212
|
TEST D'AUTOCORRELATION
. predict h,resid
. gen he=h[_n-1]
(1 missing value generated)
|
=
|
63
|
|
=
|
1.53
|
|
=
|
0.1844
|
|
=
|
0.1411
|
|
=
|
0.0490
|
|
=
|
102.24
|
.reg h he assurance dspc umed prim sec
Source | SS df MS Number of obs
+ F( 6, 56)
Model | 96124.6983 6 16020.783 Prob > F
Residual | 585314.075 56 10452.0371 R-squared
+ Adj R-squared
Total | 681438.773 62 10990.948 Root MSE
---
h | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---
|
+
|
|
|
|
|
|
|
he
|
| -.3740779
|
.1242449
|
-3.01
|
0.004
|
-.6229704
|
-.1251855
|
|
assurance
|
| -.5785915
|
3.5672
|
-0.16
|
0.872
|
-7.724553
|
6.567369
|
|
dspc
|
| .0293717
|
.0799206
|
0.37
|
0.715
|
-.1307286
|
.1894719
|
|
umed
|
| -4.586678
|
76.13426
|
-0.06
|
0.952
|
-157.1019
|
147.9286
|
|
prim
|
| 5.387261
|
26.67895
|
0.20
|
0.841
|
-48.05709
|
58.83162
|
|
sec
|
| 7.705531
|
45.32575
|
0.17
|
0.866
|
-83.09286
|
98.50392
|
|
_cons
|
| -377.8631
|
2011.348
|
-0.19
|
0.852
|
-4407.077
|
3651.351
|
---
TEST D'ENDOGENEITE
|
dspc umed prim sec,robust
Number of obs F( 5, 58)
Prob > F R-squared
|
= = = =
|
64 18.32 0.0000 0.6765
|
. reg consult assurance
Linear regression
Root MSE = 110.31
---
| Robust
78
Analyse de l'incidence du Seguro Popular et de son impact sur
l'utilisation des services de santé au Mexique
2009
consult | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+
|
|
|
|
|
|
|
|
assurance |
|
15.98919
|
3.523631
|
4.54
|
0.000
|
8.935876
|
23.04251
|
|
dspc |
|
-.1682786
|
.0668738
|
-2.52
|
0.015
|
-.302141
|
-.0344162
|
|
umed |
|
431.9063
|
87.38348
|
4.94
|
0.000
|
256.9893
|
606.8234
|
|
prim |
|
30.5651
|
25.30578
|
1.21
|
0.232
|
-20.08993
|
81.22013
|
|
sec |
|
27.75108
|
36.82673
|
0.75
|
0.454
|
-45.96563
|
101.4678
|
|
_cons |
|
-845.681
|
1788.91
|
-0.47
|
0.638
|
-4426.574
|
2735.212
|
---
. reg sec revmin assurance dspc umed prim,robust
Linear regression Number of obs = 64
F( 5, 58) = 224.04
Prob > F = 0.0000
R-squared = 0.9474
Root MSE = .27428
---
| Robust
sec | Coef. Std. Err. t P>|t| [95% Conf. Interval]
|
+
|
|
|
|
|
|
|
revmin
|
| .0246799
|
.0075521
|
3.27
|
0.002
|
.0095628
|
.039797
|
|
assurance
|
| .0144096
|
.0097327
|
1.48
|
0.144
|
-.0050725
|
.0338916
|
|
dspc
|
| -.0008455
|
.000189
|
-4.47
|
0.000
|
-.0012239
|
-.0004671
|
|
umed
|
| .4882662
|
.1165126
|
4.19
|
0.000
|
.255041
|
.7214914
|
|
prim
|
| -.4139183
|
.0497857
|
-8.31
|
0.000
|
-.5135752
|
-.3142614
|
|
_cons
|
| 38.05473
|
2.324409
|
16.37
|
0.000
|
33.40192
|
42.70754
|
---
---
---
. predict u,resid
. reg consult assurance dspc umed prim sec u,robust
Linear regression Number of obs = 64
F( 6, 57) = 16.90
Prob > F = 0.0000
R-squared = 0.6867
Root MSE = 109.5
---
| Robust
consult | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---
|
+
|
|
|
|
|
|
assurance
|
| 14.78966
|
4.029954
|
3.67
|
0.001 6.719815
|
22.8595
|
|
dspc
|
| -.0366757
|
.1449738
|
-0.25
|
0.801 -.3269808
|
.2536294
|
|
umed
|
| 333.9981
|
136.0065
|
2.46
|
0.017 61.6497
|
606.3465
|
|
prim
|
| 104.624
|
71.65284
|
1.46
|
0.150 -38.85836
|
248.1063
|
|
sec
|
| 185.2295
|
151.9048
|
1.22
|
0.228 -118.9546
|
489.4137
|
|
u
|
| -185.0229
|
172.6449
|
-1.07
|
0.288 -530.7383
|
160.6924
|
|
_cons
|
| -7288.883
|
6148.376
|
-1.19
|
0.241 -19600.79
|
5023.028
|
---
Comme le coefficient du résidu n'est pas
significatif on ne peut pas faire la régression par les doubles moindres
carré on fait une régression MCO
Analyse de l'incidence du Seguro Popular et de son
impact sur l'utilisation des services de santé au Mexique
2009
| 
