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Joaquim J.S. Ramalho
ECONOMETRIA I
Resoluções dos Exercícios Práticos - Stata
Joaquim J.S. Ramalho
Inserção de comandos
Selecção de comandos no menu▪ Útil quando não se conhece o nome do comando
Introdução manual de comandos▪ Mais rápida
Execução de comandos gravados num ficheiro do▪ Ideal para processos repetitivos
▪ Implementação de métodos não disponíveis no Stata
Stata
2017/2018 Econometria I 2
Joaquim J.S. Ramalho
Stata – Janelas Principais
2017/2018 Econometria I 3
Inserção manual de comandos
Histórico de comandos
Resultados
Lista de variáveis
Joaquim J.S. Ramalho
File
Open – abre ficheiro de dados em formato dta
Save – grava ficheiro de dados em formato dta
Log – os resultados que aparecem na janela de resultados são simultaneamente gravados num ficheiro smcl (apenas pode ser aberto no Stata) ou log (ficheiro de texto que pode ser lido por qualquer software)▪ Begin – inícia a gravação
▪ Close – termina a gravação
▪ Suspend – suspende temporariamente a gravação
▪ Resume – retoma a gravação
Stata – Menus Principais
2017/2018 Econometria I 4
Joaquim J.S. Ramalho
Window
Data Editor – abre folha tipo excel para introdução, alteração ou visualização de dados
Help
Search – se não se souber o nome do comando
Stata command – se se souber o nome do comando
Stata – Menus Principais (cont.)
2017/2018 Econometria I 5
Joaquim J.S. Ramalho
Stata – Principais Botões
2017/2018 Econometria I 6
Open
Save
Log
Data Editor
Interrompe a execução de um comando
Joaquim J.S. Ramalho
. summarize X
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
X | 10 566 229.6955 300 1100
Exercício 1.1 – a
2017/2018 Econometria I 7
Joaquim J.S. Ramalho
. summarize X, d
X
-------------------------------------------------------------
Percentiles Smallest
1% 300 300
5% 300 350
10% 325 440 Obs 10
25% 440 450 Sum of Wgt. 10
50% 505 Mean 566
Largest Std. Dev. 229.6955
75% 670 640
90% 900 670 Variance 52760
95% 1100 700 Skewness 1.189377
99% 1100 1100 Kurtosis 3.967482
Exercício 1.1 – b
2017/2018 Econometria I 8
Joaquim J.S. Ramalho
. clear
. summarize X Y, d
X
-------------------------------------------------------------
Percentiles Smallest
1% 4.7 4.7
5% 4.7 5.2
10% 4.7 8.4 Obs 8
25% 6.8 9.3 Sum of Wgt. 8
50% 9.8 Mean 9.8375
Largest Std. Dev. 3.811988
75% 12.7 10.3
90% 15.4 11.3 Variance 14.53125
95% 15.4 14.1 Skewness .0394896
99% 15.4 15.4 Kurtosis 1.898667
Exercício 1.2 – a
2017/2018 Econometria I 9
Joaquim J.S. Ramalho
Y
-------------------------------------------------------------
Percentiles Smallest
1% 2.1 2.1
5% 2.1 3.5
10% 2.1 4.5 Obs 8
25% 4 5.1 Sum of Wgt. 8
50% 6.35 Mean 7.1875
Largest Std. Dev. 4.068849
75% 10.75 7.6
90% 13.2 9.5 Variance 16.55554
95% 13.2 12 Skewness .2968191
99% 13.2 13.2 Kurtosis 1.666582
Exercício 1.2 – a (cont.)
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Joaquim J.S. Ramalho
. cor X Y, c
(obs=8)
| X Y
-------------+------------------
X | 14.5313
Y | 12.9634 16.5555
. cor X Y
(obs=8)
| X Y
-------------+------------------
X | 1.0000
Y | 0.8358 1.0000
Exercício 1.2 – b
2017/2018 Econometria I 11
Joaquim J.S. Ramalho
. gen Xnew=10*X
. summarize Xnew, d
Xnew
-------------------------------------------------------------
Percentiles Smallest
1% 47 47
5% 47 52
10% 47 84 Obs 8
25% 68 93 Sum of Wgt. 8
50% 98 Mean 98.375
Largest Std. Dev. 38.11988
75% 127 103
90% 154 113 Variance 1453.125
95% 154 141 Skewness .0394897
99% 154 154 Kurtosis 1.898667
Exercício 1.2 – c
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Joaquim J.S. Ramalho
. cor Xnew Y, c
(obs=8)
| Xnew Y
-------------+------------------
Xnew | 1453.13
Y | 129.634 16.5555
. cor Xne Y
(obs=8)
| Xnew Y
-------------+------------------
Xnew | 1.0000
Y | 0.8358 1.0000
Exercício 1.2 – c (cont.)
2017/2018 Econometria I 13
Joaquim J.S. Ramalho
. regress Y X
Source | SS df MS Number of obs = 10
---------+------------------------------ F( 1, 8) = 374.92
Model | 26.0100006 1 26.0100006 Prob > F = 0.0000
Residual | .555000229 8 .069375029 R-squared = 0.9791
---------+------------------------------ Adj R-squared = 0.9765
Total | 26.5650009 9 2.95166676 Root MSE = .26339
------------------------------------------------------------------------------
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
X | 1.7 .0877971 19.363 0.000 1.497539 1.902461
_cons | 1.26 .3353575 3.757 0.006 .4866642 2.033336
------------------------------------------------------------------------------
. display 1.7*3
5.1
Exercício 2.4 – a
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Joaquim J.S. Ramalho
. gen yhat=1.26+1.7*X
ou
. predict yhat2
(option xb assumed; fitted values)
. scatter yhat Y X, connect(li)
Exercício 2.4 – b
2017/2018 Econometria I 15
46
81
0
2 3 4 5X
yhat Y
Joaquim J.S. Ramalho
c)
. gen uhat= Y-yhat
ou
. predict uhat2, resid
. summarize uhat
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
uhat | 10 -4.77e-08 .2483279 -.3600006 .3400002
e)
. display 1.26+1.7*5.2
10.1
Exercício 2.4 – c, e
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Joaquim J.S. Ramalho
. regress sono trab
Source | SS df MS Number of obs = 706
-------------+------------------------------ F( 1, 704) = 81.09
Model | 14381717.2 1 14381717.2 Prob > F = 0.0000
Residual | 124858119 704 177355.282 R-squared = 0.1033
-------------+------------------------------ Adj R-squared = 0.1020
Total | 139239836 705 197503.313 Root MSE = 421.14
------------------------------------------------------------------------------
sono | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
trab | -.1507458 .0167403 -9.00 0.000 -.1836126 -.117879
_cons | 3586.377 38.91243 92.17 0.000 3509.979 3662.775
------------------------------------------------------------------------------
Exercício 2.5 – a
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Joaquim J.S. Ramalho
b)
. predict yhat
(option xb assumed; fitted values)
. scatter yhat sono trab, connect(li)
c)
. display -0.1507458*120
-18.089496
Exercício 2.5 – b, c
2017/2018 Econometria I 18
100
02
00
03
00
04
00
05
00
0
0 2000 4000 6000min/sem
Fitted values min/sem
Joaquim J.S. Ramalho
. regress preco area quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 2, 85) = 72.95
Model | 579971.198 2 289985.599 Prob > F = 0.0000
Residual | 337883.308 85 3975.09774 R-squared = 0.6319
---------+------------------------------ Adj R-squared = 0.6232
Total | 917854.506 87 10550.0518 Root MSE = 63.048
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
area | 1.383606 .1489435 9.289 0.000 1.087467 1.679746
quartos | 15.12134 9.488598 1.594 0.115 -3.744537 33.98721
_cons | -19.2855 31.04753 -0.621 0.536 -81.0163 42.4453
------------------------------------------------------------------------------
Exercício 3.4 – a
2017/2018 Econometria I 19
Joaquim J.S. Ramalho
c)
. display 15.12134+1.383606*13
33.108218
d)
. display -19.2855+1.383606*226+15.12134*4
353.89482
e)
. display 300-353.89482
-53.89482
Exercício 3.4 – c, d, e
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Joaquim J.S. Ramalho
. regress Y X1
Source | SS df MS Number of obs = 10
---------+------------------------------ F( 1, 8) = 0.10
Model | 28.5136879 1 28.5136879 Prob > F = 0.7599
Residual | 2281.48631 8 285.185789 R-squared = 0.0123
---------+------------------------------ Adj R-squared = -0.1111
Total | 2310.00 9 256.666667 Root MSE = 16.887
------------------------------------------------------------------------------
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
X1 | 3.520209 11.13283 0.316 0.760 -22.15215 29.19256
_cons | 91.12125 19.3436 4.711 0.002 46.51484 135.7277
------------------------------------------------------------------------------
Exercício 3.5 – a
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. regress Y X1 X2
Source | SS df MS Number of obs = 10
---------+------------------------------ F( 2, 7) = 4.57
Model | 1307.77127 2 653.885636 Prob > F = 0.0538
Residual | 1002.22873 7 143.175533 R-squared = 0.5661
---------+------------------------------ Adj R-squared = 0.4422
Total | 2310.00 9 256.666667 Root MSE = 11.966
------------------------------------------------------------------------------
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
X1 | -11.34417 9.324809 -1.217 0.263 -33.39384 10.7055
X2 | .9856754 .3297534 2.989 0.020 .2059324 1.765418
_cons | 77.50342 14.44323 5.366 0.001 43.35061 111.6562
------------------------------------------------------------------------------
Exercício 3.5 – b
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Joaquim J.S. Ramalho
. summarize Y X1 X2
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
Y | 10 97 16.02082 70 120
X1 | 10 1.67 .5056349 1 2.5
X2 | 10 39 14.29841 20 60
. display -11.34417*1.67+.9856754*39+77.50342
96.999997
Exercício 3.5 – c
2017/2018 Econometria I 23
Joaquim J.S. Ramalho
. gen X2=X^2
. regress Y X X2
Source | SS df MS Number of obs = 12
---------+------------------------------ F( 2, 9) = 3.55
Model | 14.5231959 2 7.26159794 Prob > F = 0.0729
Residual | 18.3934708 9 2.04371898 R-squared = 0.4412
---------+------------------------------ Adj R-squared = 0.3170
Total | 32.9166667 11 2.99242424 Root MSE = 1.4296
------------------------------------------------------------------------------
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
X | 5.77921 2.184333 2.646 0.027 .8379048 10.72051
X2 | -1.12457 .4221503 -2.664 0.026 -2.079541 -.1696001
_cons | -2.92268 2.374032 -1.231 0.249 -8.293114 2.447754
------------------------------------------------------------------------------
Exercício 3.7 – a
2017/2018 Econometria I 24
Joaquim J.S. Ramalho
. gen LC=log(C)
. gen LQ=log(Q)
. regress LC LQ
Source | SS df MS Number of obs = 5
---------+------------------------------ F( 1, 3) = 482.89
Model | 2.75827995 1 2.75827995 Prob > F = 0.0002
Residual | .017136067 3 .005712022 R-squared = 0.9938
---------+------------------------------ Adj R-squared = 0.9918
Total | 2.77541602 4 .693854005 Root MSE = .07558
------------------------------------------------------------------------------
LC | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
LQ | 1.993872 .0907346 21.975 0.000 1.705114 2.28263
_cons | .6770666 .1291162 5.244 0.014 .2661613 1.087972
------------------------------------------------------------------------------
. display exp(0.677066408)
1.9680957
Exercício 3.8 – b
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Joaquim J.S. Ramalho
. regress sal educ exper antig
Source | SS df MS Number of obs = 526
---------+------------------------------ F( 3, 522) = 76.87
Model | 2194.1116 3 731.370532 Prob > F = 0.0000
Residual | 4966.30269 522 9.51398984 R-squared = 0.3064
---------+------------------------------ Adj R-squared = 0.3024
Total | 7160.41429 525 13.6388844 Root MSE = 3.0845
------------------------------------------------------------------------------
sal | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
educ | .5989651 .0512835 11.679 0.000 .4982176 .6997126
exper | .0223395 .0120568 1.853 0.064 -.0013464 .0460254
antig | .1692687 .0216446 7.820 0.000 .1267474 .2117899
_cons | -2.872735 .7289643 -3.941 0.000 -4.304799 -1.440671
------------------------------------------------------------------------------
Exercício 3.9 – a
2017/2018 Econometria I 26
Joaquim J.S. Ramalho
. predict uhat, resid
. histogram uhat, bin(15) normal
Exercício 3.9 – a (cont.)
2017/2018 Econometria I 27
0
.05
.1.1
5.2
Den
sity
-10 -5 0 5 10 15Residuals
Joaquim J.S. Ramalho
. gen lsal=log(sal)
. regress lsal educ exper antig
Source | SS df MS Number of obs = 526
---------+------------------------------ F( 3, 522) = 80.39
Model | 46.8741776 3 15.6247259 Prob > F = 0.0000
Residual | 101.455574 522 .194359337 R-squared = 0.3160
---------+------------------------------ Adj R-squared = 0.3121
Total | 148.329751 525 .28253286 Root MSE = .44086
------------------------------------------------------------------------------
lsal | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
educ | .092029 .0073299 12.555 0.000 .0776292 .1064288
exper | .0041211 .0017233 2.391 0.017 .0007357 .0075065
antig | .0220672 .0030936 7.133 0.000 .0159897 .0281448
_cons | .2843595 .1041904 2.729 0.007 .0796756 .4890435
------------------------------------------------------------------------------
Exercício 3.9 – b
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Joaquim J.S. Ramalho
. predict vhat, resid
. histogram vhat, bin(15) normal
Exercício 3.9 – b (cont.)
2017/2018 Econometria I 29
0.2
.4.6
.81
Den
sity
-2 -1 0 1 2Residuals
Joaquim J.S. Ramalho
. gen lY = log(Y)
. gen lX1 = log(X1)
. regress lY lX1 X2
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 2, 7) = 4.62
Model | .149383709 2 .074691854 Prob > F = 0.0527
Residual | .113277545 7 .016182506 R-squared = 0.5687
-------------+------------------------------ Adj R-squared = 0.4455
Total | .262661254 9 .029184584 Root MSE = .12721
------------------------------------------------------------------------------
lY | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lX1 | -.1995016 .15211 -1.31 0.231 -.5591844 .1601813
X2 | .0103668 .0034219 3.03 0.019 .0022752 .0184584
_cons | 4.250993 .1225426 34.69 0.000 3.961225 4.54076
------------------------------------------------------------------------------
Exercício 3.10 – b
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Joaquim J.S. Ramalho
. gen Yc = 2*Y
. gen X1d = 10*X1
. gen lYc = log(Yc)
. gen lX1d = log(X1d)
. regress lYc lX1d X2
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 2, 7) = 4.62
Model | .14938371 2 .074691855 Prob > F = 0.0527
Residual | .113277543 7 .016182506 R-squared = 0.5687
-------------+------------------------------ Adj R-squared = 0.4455
Total | .262661254 9 .029184584 Root MSE = .12721
------------------------------------------------------------------------------
lYc | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lX1d | -.1995016 .1521099 -1.31 0.231 -.5591844 .1601813
X2 | .0103668 .0034219 3.03 0.019 .0022752 .0184584
_cons | 5.403509 .3754146 14.39 0.000 4.515795 6.291224
------------------------------------------------------------------------------
Exercício 3.10 – b (cont.)
2017/2018 Econometria I 31
Joaquim J.S. Ramalho
. regress Y X1 X2
Source | SS df MS Number of obs = 5
-------------+------------------------------ F( 2, 2) = 17.90
Model | 11.3650794 2 5.68253968 Prob > F = 0.0529
Residual | .634920635 2 .317460317 R-squared = 0.9471
-------------+------------------------------ Adj R-squared = 0.8942
Total | 12 4 3 Root MSE = .56344
------------------------------------------------------------------------------
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
X1 | 1.174603 .2007795 5.85 0.028 .3107186 2.038488
X2 | -.3968254 .2007795 -1.98 0.187 -1.26071 .4670592
_cons | 3.825397 .322187 11.87 0.007 2.439138 5.211656
------------------------------------------------------------------------------
Exercício 3.11 – a
2017/2018 Econometria I 32
Joaquim J.S. Ramalho
. sum
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
X1 | 5 1 1.414214 -1 2
X2 | 5 0 1.414214 -2 1
Y | 5 5 1.732051 2 6
. gen zy=(Y-5)/1.732051
. gen z1=(X1-1)/1.414214
. gen z2=X2/1.414214
Exercício 3.11 – b
2017/2018 Econometria I 33
Joaquim J.S. Ramalho
. regress zy z1 z2
Source | SS df MS Number of obs = 5
-------------+------------------------------ F( 2, 2) = 17.90
Model | 3.78835906 2 1.89417953 Prob > F = 0.0529
Residual | .211640178 2 .105820089 R-squared = 0.9471
-------------+------------------------------ Adj R-squared = 0.8942
Total | 3.99999924 4 .999999809 Root MSE = .3253
------------------------------------------------------------------------------
zy | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
z1 | .9590596 .1639358 5.85 0.028 .2537007 1.664419
z2 | -.3240066 .1639358 -1.98 0.187 -1.029366 .3813523
_cons | -1.19e-08 .1454786 -0.00 1.000 -.6259438 .6259438
------------------------------------------------------------------------------
Exercício 3.11 – b (cont.)
2017/2018 Econometria I 34
Joaquim J.S. Ramalho
. display 0.9590596*1.732051/1.414214
1.1746031
. display -0.3240066*1.732051/1.414214
-.39682534
. display 5-1.174603*1+0.3968254*0
3.825397
Exercício 3.11 – c
2017/2018 Econometria I 35
Joaquim J.S. Ramalho
. gen X11=10*X1
. regress Y X11 X2
Source | SS df MS Number of obs = 5
-------------+------------------------------ F( 2, 2) = 17.90
Model | 11.3650794 2 5.68253968 Prob > F = 0.0529
Residual | .634920635 2 .317460317 R-squared = 0.9471
-------------+------------------------------ Adj R-squared = 0.8942
Total | 12 4 3 Root MSE = .56344
------------------------------------------------------------------------------
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
X11 | .1174603 .020078 5.85 0.028 .0310719 .2038488
X2 | -.3968254 .2007795 -1.98 0.187 -1.26071 .4670592
_cons | 3.825397 .322187 11.87 0.007 2.439138 5.211656
------------------------------------------------------------------------------
Exercício 3.11 – d
2017/2018 Econometria I 36
Joaquim J.S. Ramalho
. sum Y X11 X2
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
Y | 5 5 1.732051 2 6
X11 | 5 10 14.14214 -10 20
X2 | 5 0 1.414214 -2 1
. gen z11=(X11-10)/14.14214
. regress zy z11 z2
Source | SS df MS Number of obs = 5
-------------+------------------------------ F( 2, 2) = 17.90
Model | 3.78835906 2 1.89417953 Prob > F = 0.0529
Residual | .211640178 2 .105820089 R-squared = 0.9471
-------------+------------------------------ Adj R-squared = 0.8942
Total | 3.99999924 4 .999999809 Root MSE = .3253
------------------------------------------------------------------------------
zy | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
z11 | .9590596 .1639358 5.85 0.028 .2537007 1.664419
z2 | -.3240066 .1639358 -1.98 0.187 -1.029366 .3813523
_cons | -1.19e-08 .1454786 -0.00 1.000 -.6259438 .6259438
------------------------------------------------------------------------------
Exercício 3.11 – d (cont.)
2017/2018 Econometria I 37
Joaquim J.S. Ramalho
. gen lpreco=log(preco)
. regress lpreco area quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 2, 85) = 60.81
Model | 4.71914298 2 2.35957149 Prob > F = 0.0000
Residual | 3.29846053 85 .038805418 R-squared = 0.5886
---------+------------------------------ Adj R-squared = 0.5789
Total | 8.01760352 87 .092156362 Root MSE = .19699
------------------------------------------------------------------------------
lpreco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
area | .0040895 .0004654 8.788 0.000 .0031643 .0050148
quartos | .0285935 .0296466 0.964 0.338 -.0303518 .0875388
_cons | 4.76599 .0970062 49.131 0.000 4.573116 4.958864
------------------------------------------------------------------------------
Exercício 4.2 – a
2017/2018 Econometria I 38
Joaquim J.S. Ramalho
. estat vce, cov
Covariance matrix of coefficients of regress model
e(V) | area quartos _cons
-------------+------------------------------------
area | 2.166e-07
quartos | -7.341e-06 .00087892
_cons | -.00001432 -.00176255 .00941019
. display sqrt(14^2*0.0004654^2+0.0296466^2+2*14*(-7.341e-06))
. 02675492
--- ou ---
Exercício 4.2 – b
2017/2018 Econometria I 39
Joaquim J.S. Ramalho
. gen dif=area-14*quartos
. regress lpreco dif quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 2, 85) = 60.81
Model | 4.71914298 2 2.35957149 Prob > F = 0.0000
Residual | 3.29846053 85 .038805418 R-squared = 0.5886
---------+------------------------------ Adj R-squared = 0.5789
Total | 8.01760352 87 .092156362 Root MSE = .19699
------------------------------------------------------------------------------
lpreco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
dif | .0040895 .0004654 8.788 0.000 .0031643 .0050148
quartos | .0858472 .0267546 3.209 0.002 .0326519 .1390424
_cons | 4.76599 .0970062 49.131 0.000 4.573116 4.958864
------------------------------------------------------------------------------
Exercício 4.2 – b (cont.)
2017/2018 Econometria I 40
Joaquim J.S. Ramalho
. regress preco lote area quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 3, 84) = 57.43
Model | 617018.847 3 205672.949 Prob > F = 0.0000
Residual | 300835.658 84 3581.37688 R-squared = 0.6722
---------+------------------------------ Adj R-squared = 0.6605
Total | 917854.506 87 10550.0518 Root MSE = 59.845
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lote | .0222365 .0069137 3.216 0.002 .0084878 .0359852
area | 1.322524 .1426449 9.271 0.000 1.038859 1.606189
quartos | 13.7864 9.015998 1.529 0.130 -4.142902 31.7157
_cons | -21.72645 29.47964 -0.737 0.463 -80.34993 36.89704
------------------------------------------------------------------------------
. display -21.72645+.0222365*1000+1.322524*230+13.7864*4
359.83617
Exercício 4.10 - a
2017/2018 Econometria I 41
Joaquim J.S. Ramalho
. gen lo=lote-1000
. gen ar=area-230
. gen qu=quartos-4
. regress preco lo ar qu
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 3, 84) = 57.43
Model | 617018.847 3 205672.949 Prob > F = 0.0000
Residual | 300835.658 84 3581.37688 R-squared = 0.6722
---------+------------------------------ Adj R-squared = 0.6605
Total | 917854.506 87 10550.0518 Root MSE = 59.845
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lo | .0222365 .0069137 3.216 0.002 .0084878 .0359852
ar | 1.322524 .1426449 9.271 0.000 1.038859 1.606189
qu | 13.7864 9.015998 1.529 0.130 -4.142902 31.7157
_cons | 359.8361 8.216905 43.792 0.000 343.4959 376.1763
------------------------------------------------------------------------------
Exercício 4.10 - b
2017/2018 Econometria I 42
Joaquim J.S. Ramalho
. regress peso cigs ordn rend educm educp
Source | SS df MS Number of obs = 605
---------+------------------------------ F( 5, 599) = 4.51
Model | 7.30566668 5 1.46113334 Prob > F = 0.0005
Residual | 193.943433 599 .323778687 R-squared = 0.0363
---------+------------------------------ Adj R-squared = 0.0283
Total | 201.2491 604 .333193874 Root MSE = .56902
------------------------------------------------------------------------------
peso | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
cigs | -.0166765 .0045913 -3.632 0.000 -.0256935 -.0076595
ordn | .0377162 .0281633 1.339 0.181 -.0175946 .093027
rend | .0012149 .0014845 0.818 0.413 -.0017005 .0041303
educm | -.0083417 .0131635 -0.634 0.527 -.0341939 .0175105
educp | .0187163 .0117298 1.596 0.111 -.0043202 .0417528
_cons | 3.140262 .1528979 20.538 0.000 2.839981 3.440543
------------------------------------------------------------------------------
Exercício 5.1 - a
2017/2018 Econometria I 43
Joaquim J.S. Ramalho
. regress peso cigs ordn rend
Source | SS df MS Number of obs = 605
---------+------------------------------ F( 3, 601) = 6.63
Model | 6.44231307 3 2.14743769 Prob > F = 0.0002
Residual | 194.806787 601 .324137748 R-squared = 0.0320
---------+------------------------------ Adj R-squared = 0.0272
Total | 201.2491 604 .333193874 Root MSE = .56933
------------------------------------------------------------------------------
peso | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
cigs | -.0173886 .0045572 -3.816 0.000 -.0263386 -.0084385
ordn | .0361859 .0279447 1.295 0.196 -.0186952 .0910671
rend | .0020474 .0013133 1.559 0.120 -.0005317 .0046265
_cons | 3.254679 .0689307 47.217 0.000 3.119304 3.390053
------------------------------------------------------------------------------
. display ((0.0363-0.0320)/(1-0.0363))*((605-6)/2)
1.3363599
. display invFtail(2,599,0.05)
3.0107647
. display Ftail(2,599,1.3363599)
.2635829
Exercício 5.1 - a (cont.)
2017/2018 Econometria I 44
Joaquim J.S. Ramalho
. predict vhat, resid
. regress vhat cigs ordn rend educm educp
Source | SS df MS Number of obs = 605
---------+------------------------------ F( 5, 599) = 0.53
Model | .86335366 5 .172670732 Prob > F = 0.7511
Residual | 193.943436 599 .323778691 R-squared = 0.0044
---------+------------------------------ Adj R-squared = -0.0039
Total | 194.80679 604 .322527797 Root MSE = .56902
------------------------------------------------------------------------------
vhat | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
cigs | .0007121 .0045913 0.155 0.877 -.0083049 .009729
ordn | .0015302 .0281633 0.054 0.957 -.0537805 .056841
rend | -.0008325 .0014845 -0.561 0.575 -.0037479 .0020829
educm | -.0083417 .0131635 -0.634 0.527 -.0341939 .0175105
educp | .0187163 .0117298 1.596 0.111 -.0043202 .0417528
_cons | -.1144165 .1528979 -0.748 0.455 -.4146975 .1858645
------------------------------------------------------------------------------
Exercício 5.1 - a (cont.)
2017/2018 Econometria I 45
Joaquim J.S. Ramalho
a (cont.). display 605*0.0044
2.662
. display invchi2tail(2,0.05)
5.9914645
. display chi2tail(2,2.662)
.26421292
b). display 605*0.0363
21.9615
. display invchi2tail(5,0.05)
11.070498
. display chi2tail(5,21.9615)
.0005325
Exercício 5.1 - a (cont.) + b
2017/2018 Econometria I 46
Joaquim J.S. Ramalho
(Modelo 1)
. regress preco lote area quartos
Source | SS df MS Number of obs = 88
-------------+------------------------------ F( 3, 84) = 57.43
Model | 617018.847 3 205672.949 Prob > F = 0.0000
Residual | 300835.658 84 3581.37688 R-squared = 0.6722
-------------+------------------------------ Adj R-squared = 0.6605
Total | 917854.506 87 10550.0518 Root MSE = 59.845
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lote | .0222365 .0069137 3.22 0.002 .0084878 .0359852
area | 1.322524 .1426449 9.27 0.000 1.038859 1.606189
quartos | 13.7864 9.015998 1.53 0.130 -4.142903 31.7157
_cons | -21.72645 29.47964 -0.74 0.463 -80.34994 36.89704
------------------------------------------------------------------------------
Exercício 6.3 – a
2017/2018 Econometria I 47
Joaquim J.S. Ramalho
(Modelo 2)
. regress preco lote
Source | SS df MS Number of obs = 88
-------------+------------------------------ F( 1, 86) = 11.79
Model | 110620.511 1 110620.511 Prob > F = 0.0009
Residual | 807233.995 86 9386.4418 R-squared = 0.1205
-------------+------------------------------ Adj R-squared = 0.1103
Total | 917854.506 87 10550.0518 Root MSE = 96.884
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lote | .0377265 .0109895 3.43 0.001 .01588 .0595729
_cons | 261.9334 13.83699 18.93 0.000 234.4264 289.4404
------------------------------------------------------------------------------
Exercício 6.3 – a (cont.)
2017/2018 Econometria I 48
Joaquim J.S. Ramalho
(Modelo 3)
. gen llote=log(lote)
. gen larea=log(area)
. regress preco llote larea quartos
Source | SS df MS Number of obs = 88
-------------+------------------------------ F( 3, 84) = 59.00
Model | 622466.689 3 207488.896 Prob > F = 0.0000
Residual | 295387.817 84 3516.52163 R-squared = 0.6782
-------------+------------------------------ Adj R-squared = 0.6667
Total | 917854.506 87 10550.0518 Root MSE = 59.3
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
llote | 61.46859 12.29808 5.00 0.000 37.01251 85.92467
larea | 225.4347 29.87263 7.55 0.000 166.0297 284.8397
quartos | 19.22659 8.850484 2.17 0.033 1.626428 36.82675
_cons | -1347.869 141.5272 -9.52 0.000 -1629.311 -1066.426
------------------------------------------------------------------------------
Exercício 6.3 – a (cont.)
2017/2018 Econometria I 49
Joaquim J.S. Ramalho
(Modelo 1) vs. (Modelo 2)
. display (0.6722-0.1205)/(1-0.6722)*(88-4)/2
70.687614
. display Ftail(2,84, 70.687614)
9.947e-19
(Modelo 1) vs. (Modelo 3) - R-squared
(Modelo 2) vs. (Modelo 3) - Adj R-squared
Exercício 6.3 – a (cont.)
2017/2018 Econometria I 50
Joaquim J.S. Ramalho
. predict yhat
(option xb assumed; fitted values)
. gen yhat2=yhat^2
. gen yhat3=yhat^3
Exercício 6.3 – b
2017/2018 Econometria I 51
Joaquim J.S. Ramalho
. regress preco llote larea quartos yhat2 yhat3
Source | SS df MS Number of obs = 88
-------------+------------------------------ F( 5, 82) = 54.38
Model | 705183.155 5 141036.631 Prob > F = 0.0000
Residual | 212671.35 82 2593.55305 R-squared = 0.7683
-------------+------------------------------ Adj R-squared = 0.7542
Total | 917854.506 87 10550.0518 Root MSE = 50.927
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
llote | 63.08395 106.0743 0.59 0.554 -147.9316 274.0995
larea | 270.4471 382.5531 0.71 0.482 -490.573 1031.467
quartos | 16.2466 33.20621 0.49 0.626 -49.81114 82.30433
yhat2 | -.0039443 .005176 -0.76 0.448 -.014241 .0063525
yhat3 | 7.00e-06 5.02e-06 1.40 0.166 -2.97e-06 .000017
_cons | -1439.169 2468.623 -0.58 0.562 -6350.047 3471.71
------------------------------------------------------------------------------
. display (0.7683-0.6782)/(1-0.7683)*(88-6)/2
15.943461
. display Ftail(2,82,15.943461)
1.416e-06
Exercício 6.3 – b (cont.)
2017/2018 Econometria I 52
. display invFtail(2,82,0.05)
3.1078913
Joaquim J.S. Ramalho
. regress preco llote larea quartos
Source | SS df MS Number of obs = 88
-------------+------------------------------ F( 3, 84) = 59.00
Model | 622466.689 3 207488.896 Prob > F = 0.0000
Residual | 295387.817 84 3516.52163 R-squared = 0.6782
-------------+------------------------------ Adj R-squared = 0.6667
Total | 917854.506 87 10550.0518 Root MSE = 59.3
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
llote | 61.46859 12.29808 5.00 0.000 37.01251 85.92467
larea | 225.4347 29.87263 7.55 0.000 166.0297 284.8397
quartos | 19.22659 8.850484 2.17 0.033 1.626428 36.82675
_cons | -1347.869 141.5272 -9.52 0.000 -1629.311 -1066.426
------------------------------------------------------------------------------
. predict uhat, resid
Exercício 6.3 – c
2017/2018 Econometria I 53
Joaquim J.S. Ramalho
. regress uhat llote larea quartos yhat2 yhat3
Source | SS df MS Number of obs = 88
-------------+------------------------------ F( 5, 82) = 6.38
Model | 82716.465 5 16543.293 Prob > F = 0.0000
Residual | 212671.35 82 2593.55305 R-squared = 0.2800
-------------+------------------------------ Adj R-squared = 0.2361
Total | 295387.816 87 3395.26225 Root MSE = 50.927
------------------------------------------------------------------------------
uhat | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
llote | 1.615355 106.0743 0.02 0.988 -209.4002 212.6309
larea | 45.01234 382.5531 0.12 0.907 -716.0077 806.0324
quartos | -2.979988 33.20621 -0.09 0.929 -69.03772 63.07775
yhat2 | -.0039443 .005176 -0.76 0.448 -.014241 .0063525
yhat3 | 7.00e-06 5.02e-06 1.40 0.166 -2.97e-06 .000017
_cons | -91.29995 2468.623 -0.04 0.971 -5002.178 4819.579
------------------------------------------------------------------------------
Exercício 6.3 – c (cont.)
2017/2018 Econometria I 54
Joaquim J.S. Ramalho
. display 88*0.28
24.64
. display invchi2tail(2,0.05)
5.9914645
. display chi2tail(2,24.64)
4.462e-06
Exercício 6.3 – c (cont.)
2017/2018 Econometria I 55
Joaquim J.S. Ramalho
. gen id2=idade^2
. regress sono trab educ idade id2 filpeq if masc==1
Source | SS df MS Number of obs = 400
---------+------------------------------ F( 5, 394) = 14.59
Model | 11806161.6 5 2361232.32 Prob > F = 0.0000
Residual | 63763979.0 394 161837.51 R-squared = 0.1562
---------+------------------------------ Adj R-squared = 0.1455
Total | 75570140.6 399 189398.849 Root MSE = 402.29
------------------------------------------------------------------------------
sono | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
trab | -.1821232 .0244855 -7.438 0.000 -.2302618 -.1339846
educ | -13.05238 7.414218 -1.760 0.079 -27.62876 1.523995
idade | 7.156591 14.32037 0.500 0.618 -20.99731 35.31049
id2 | -.0447674 .1684053 -0.266 0.791 -.3758528 .286318
filpeq | 60.38021 59.02278 1.023 0.307 -55.65877 176.4192
_cons | 3648.208 310.0393 11.767 0.000 3038.67 4257.747
------------------------------------------------------------------------------
Exercício 7.3 – a
2017/2018 Econometria I 56
Joaquim J.S. Ramalho
. regress sono trab educ idade id2 filpeq if masc==0
Source | SS df MS Number of obs = 306
---------+------------------------------ F( 5, 300) = 6.50
Model | 6201576.18 5 1240315.24 Prob > F = 0.0000
Residual | 57288575.9 300 190961.92 R-squared = 0.0977
---------+------------------------------ Adj R-squared = 0.0826
Total | 63490152.1 305 208164.433 Root MSE = 436.99
------------------------------------------------------------------------------
sono | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
trab | -.1399495 .0276594 -5.060 0.000 -.1943806 -.0855184
educ | -10.20514 9.588848 -1.064 0.288 -29.07506 8.664786
idade | -30.35657 18.53091 -1.638 0.102 -66.82361 6.110463
id2 | .3679406 .2233398 1.647 0.101 -.0715705 .8074516
filpeq | -118.2826 93.18757 -1.269 0.205 -301.6666 65.10153
_cons | 4238.729 384.8923 11.013 0.000 3481.299 4996.16
------------------------------------------------------------------------------
Exercício 7.3 – a (cont.)
2017/2018 Econometria I 57
Joaquim J.S. Ramalho
. gen mtrab= masc*trab
. gen meduc= masc*educ
. gen mid= masc*idade
. gen mid2= masc*id2
. gen mfilp= masc*filpeq
Exercício 7.3 – b
2017/2018 Econometria I 58
Joaquim J.S. Ramalho
. regress sono trab educ idade id2 filpeq masc mtrab meduc mid mid2 mfilp
Source | SS df MS Number of obs = 706
---------+------------------------------ F( 11, 694) = 9.48
Model | 18187280.8 11 1653389.17 Prob > F = 0.0000
Residual | 121052555 694 174427.313 R-squared = 0.1306
---------+------------------------------ Adj R-squared = 0.1168
Total | 139239836 705 197503.313 Root MSE = 417.64
------------------------------------------------------------------------------
sono | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
trab | -.1399495 .0264349 -5.294 0.000 -.1918514 -.0880476
educ | -10.20514 9.164321 -1.114 0.266 -28.19826 7.787983
idade | -30.35657 17.71049 -1.714 0.087 -65.12914 4.415998
id2 | .3679406 .2134519 1.724 0.085 -.0511483 .7870294
filpeq | -118.2826 89.06187 -1.328 0.185 -293.1456 56.58046
masc | -590.5211 488.7916 -1.208 0.227 -1550.209 369.1665
mtrab | -.0421737 .036674 -1.150 0.251 -.114179 .0298317
meduc | -2.847243 11.96795 -0.238 0.812 -26.34497 20.65048
mid | 37.51316 23.12332 1.622 0.105 -7.886887 82.91321
mid2 | -.4127079 .2759136 -1.496 0.135 -.9544333 .1290175
mfilp | 178.6628 108.1051 1.653 0.099 -33.5895 390.915
_cons | 4238.729 367.8519 11.523 0.000 3516.493 4960.965
------------------------------------------------------------------------------
Exercício 7.3 – b (cont.)
2017/2018 Econometria I 59
Joaquim J.S. Ramalho
. regress sono trab educ idade id2 filpeq
Source | SS df MS Number of obs = 706
---------+------------------------------ F( 5, 700) = 18.14
Model | 15972384.7 5 3194476.94 Prob > F = 0.0000
Residual | 123267451 700 176096.359 R-squared = 0.1147
---------+------------------------------ Adj R-squared = 0.1084
Total | 139239836 705 197503.313 Root MSE = 419.64
------------------------------------------------------------------------------
sono | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
trab | -.1460463 .0168809 -8.652 0.000 -.1791896 -.1129031
educ | -11.13772 5.890168 -1.891 0.059 -22.70223 .4267912
idade | -8.123949 11.37049 -0.714 0.475 -30.4483 14.2004
id2 | .126287 .135186 0.934 0.351 -.1391317 .3917057
filpeq | 17.15441 50.00839 0.343 0.732 -81.02999 115.3388
_cons | 3825.375 240.2585 15.922 0.000 3353.661 4297.088
------------------------------------------------------------------------------
Exercício 7.3 – c
2017/2018 Econometria I 60
Joaquim J.S. Ramalho
. display ((123267451-(63763979+57288575.9))/(63763979+57288575.9))*(694/6)
2.1163506
. display (0.1306-0.1147)/(1-0.1306)*(694/6)
2.1116259
. display invFtail(6,694,0.1)
1.7826172
Exercício 7.3 – c (cont.)
2017/2018 Econometria I 61
Joaquim J.S. Ramalho
. regress sono trab educ idade id2 filpeq masc
Source | SS df MS Number of obs = 706
---------+------------------------------ F( 6, 699) = 16.30
Model | 17092058.6 6 2848676.43 Prob > F = 0.0000
Residual | 122147777 699 174746.462 R-squared = 0.1228
---------+------------------------------ Adj R-squared = 0.1152
Total | 139239836 705 197503.313 Root MSE = 418.03
------------------------------------------------------------------------------
sono | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
trab | -.1634235 .0181634 -8.997 0.000 -.1990848 -.1277623
educ | -11.71327 5.871952 -1.995 0.046 -23.24205 -.1844949
idade | -8.697402 11.32909 -0.768 0.443 -30.94053 13.54572
id2 | .1284415 .1346696 0.954 0.341 -.1359638 .3928469
filpeq | -.0228006 50.27641 0.000 1.000 -98.73367 98.68807
masc | 87.75455 34.66794 2.531 0.012 19.68878 155.8203
_cons | 3840.852 239.4139 16.043 0.000 3370.795 4310.909
------------------------------------------------------------------------------
Exercício 7.3 – d
2017/2018 Econometria I 62
Joaquim J.S. Ramalho
d) (cont.)
. display (0.1306-0.1228)/(1-0.1306)*(694/5)
1.2452726
. display invFtail(5,694,0.05)
2.2270118
f)
. display 3840.852-0.1634235*2400-11.71327*12-8.697402*30+0.1284415*900-.0228006
3162.7288
Exercício 7.3 – d (cont.), f
2017/2018 Econometria I 63
Joaquim J.S. Ramalho
. regress preco lote area quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 3, 84) = 57.43
Model | 617018.847 3 205672.949 Prob > F = 0.0000
Residual | 300835.658 84 3581.37688 R-squared = 0.6722
---------+------------------------------ Adj R-squared = 0.6605
Total | 917854.506 87 10550.0518 Root MSE = 59.845
------------------------------------------------------------------------------
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lote | .0222365 .0069137 3.216 0.002 .0084878 .0359852
area | 1.322524 .1426449 9.271 0.000 1.038859 1.606189
quartos | 13.7864 9.015998 1.529 0.130 -4.142902 31.7157
_cons | -21.72645 29.47964 -0.737 0.463 -80.34993 36.89704
------------------------------------------------------------------------------
Exercício 8.2 – a
2017/2018 Econometria I 64
Joaquim J.S. Ramalho
. regress preco lote area quartos, robust
Regression with robust standard errors Number of obs = 88
F( 3, 84) = 23.68
Prob > F = 0.0000
R-squared = 0.6722
Root MSE = 59.845
------------------------------------------------------------------------------
| Robust
preco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lote | .0222365 .0135092 1.646 0.103 -.004628 .049101
area | 1.322524 .1911281 6.920 0.000 .9424446 1.702603
quartos | 13.7864 8.500484 1.622 0.109 -3.117745 30.69054
_cons | -21.72645 37.15716 -0.585 0.560 -95.61754 52.16464
------------------------------------------------------------------------------
Exercício 8.2 – a (cont.)
2017/2018 Econometria I 65
Joaquim J.S. Ramalho
. gen lpreco=ln(preco)
. gen llote=ln(lote)
. gen larea=ln(area)
. regress lpreco llote larea quartos
Source | SS df MS Number of obs = 88
-------------+------------------------------ F( 3, 84) = 50.55
Model | 5.15967627 3 1.71989209 Prob > F = 0.0000
Residual | 2.85792725 84 .034022943 R-squared = 0.6435
-------------+------------------------------ Adj R-squared = 0.6308
Total | 8.01760352 87 .092156362 Root MSE = .18445
------------------------------------------------------------------------------
lpreco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
llote | .1679747 .0382531 4.39 0.000 .0919042 .2440452
larea | .7019095 .0929186 7.55 0.000 .5171306 .8866884
quartos | .0365371 .0275294 1.33 0.188 -.0182081 .0912823
_cons | .7585933 .4402196 1.72 0.089 -.1168315 1.634018
------------------------------------------------------------------------------
Exercício 8.2 – b
2017/2018 Econometria I 66
Joaquim J.S. Ramalho
. regress lpreco llote larea quartos, robust
Linear regression Number of obs = 88
F( 3, 84) = 49.52
Prob > F = 0.0000
R-squared = 0.6435
Root MSE = .18445
------------------------------------------------------------------------------
| Robust
lpreco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
llote | .1679747 .0415668 4.04 0.000 .0853146 .2506348
larea | .7019095 .1037882 6.76 0.000 .4955153 .9083037
quartos | .0365371 .0306545 1.19 0.237 -.0244228 .097497
_cons | .7585933 .5261796 1.44 0.153 -.2877724 1.804959
------------------------------------------------------------------------------
Exercício 8.2 – b (cont.)
2017/2018 Econometria I 67
Joaquim J.S. Ramalho
. gen id2=idade^2
. regress sono trab educ idade id2 filpeq masc
Source | SS df MS Number of obs = 706
---------+------------------------------ F( 6, 699) = 16.30
Model | 17092058.6 6 2848676.43 Prob > F = 0.0000
Residual | 122147777 699 174746.462 R-squared = 0.1228
---------+------------------------------ Adj R-squared = 0.1152
Total | 139239836 705 197503.313 Root MSE = 418.03
------------------------------------------------------------------------------
sono | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
trab | -.1634235 .0181634 -8.997 0.000 -.1990848 -.1277623
educ | -11.71327 5.871952 -1.995 0.046 -23.24205 -.1844949
idade | -8.697402 11.32909 -0.768 0.443 -30.94053 13.54572
id2 | .1284415 .1346696 0.954 0.341 -.1359638 .3928469
filpeq | -.0228006 50.27641 0.000 1.000 -98.73367 98.68807
masc | 87.75455 34.66794 2.531 0.012 19.68878 155.8203
_cons | 3840.852 239.4139 16.043 0.000 3370.795 4310.909
------------------------------------------------------------------------------
Exercício 8.3 – b
2017/2018 Econometria I 68
Joaquim J.S. Ramalho
. predict util, resid
. gen util2=util^2
. regress util2 masc
Source | SS df MS Number of obs = 706
---------+------------------------------ F( 1, 704) = 1.12
Model | 1.4430e+11 1 1.4430e+11 Prob > F = 0.2909
Residual | 9.0942e+13 704 1.2918e+11 R-squared = 0.0016
---------+------------------------------ Adj R-squared = 0.0002
Total | 9.1086e+13 705 1.2920e+11 Root MSE = 3.6e+05
------------------------------------------------------------------------------
util2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
masc | -28849.63 27296.51 -1.057 0.291 -82441.94 24742.69
_cons | 189359.2 20546.36 9.216 0.000 149019.8 229698.7
------------------------------------------------------------------------------
Exercício 8.3 – b (cont.)
2017/2018 Econometria I 69
Joaquim J.S. Ramalho
. gen Yh=Y/sqrt(X)
. gen X0h=1/sqrt(X)
. gen X1h=X/sqrt(X)
. regress Yh X0h X1h, nocons
Source | SS df MS Number of obs = 9
---------+------------------------------ F( 2, 7) = 122.81
Model | 17.9623069 2 8.98115347 Prob > F = 0.0000
Residual | .511899221 7 .07312846 R-squared = 0.9723
---------+------------------------------ Adj R-squared = 0.9644
Total | 18.4742062 9 2.05268957 Root MSE = .27042
------------------------------------------------------------------------------
Yh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
X0h | .6149646 .2961876 2.076 0.077 -.0854079 1.315337
X1h | .4797121 .0645436 7.432 0.000 .3270907 .6323335
------------------------------------------------------------------------------
Exercício 8.4 – b
2017/2018 Econometria I 70
Joaquim J.S. Ramalho
. gen lpreco=log(preco)
. gen llote=log(lote)
. gen larea=log(area)
. regress lpreco llote larea quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 3, 84) = 50.55
Model | 5.15967627 3 1.71989209 Prob > F = 0.0000
Residual | 2.85792725 84 .034022943 R-squared = 0.6435
---------+------------------------------ Adj R-squared = 0.6308
Total | 8.01760352 87 .092156362 Root MSE = .18445
------------------------------------------------------------------------------
lpreco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
llote | .1679747 .0382531 4.391 0.000 .0919042 .2440452
larea | .7019095 .0929186 7.554 0.000 .5171306 .8866884
quartos | .0365371 .0275294 1.327 0.188 -.0182081 .0912823
_cons | .7585933 .4402196 1.723 0.089 -.1168315 1.634018
------------------------------------------------------------------------------
Exercício 8.5 – a
2017/2018 Econometria I 71
Joaquim J.S. Ramalho
. gen uhat2=uhat^2
. regress uhat2 llote larea quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 3, 84) = 1.40
Model | .022400626 3 .007466875 Prob > F = 0.2487
Residual | .44822913 84 .005336061 R-squared = 0.0476
---------+------------------------------ Adj R-squared = 0.0136
Total | .470629755 87 .005409537 Root MSE = .07305
------------------------------------------------------------------------------
uhat2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
llote | -.0069405 .0151492 -0.458 0.648 -.0370665 .0231854
larea | -.0623878 .0367983 -1.695 0.094 -.1355651 .0107896
quartos | .0168984 .0109024 1.550 0.125 -.0047821 .038579
_cons | .3416968 .1743387 1.960 0.053 -.0049948 .6883884
------------------------------------------------------------------------------
Exercício 8.5 – a (cont.)
2017/2018 Econometria I 72
Joaquim J.S. Ramalho
. display invFtail(3,84,.05)
2.7132332
. display 88*0.0476
4.1888
. display invchi2tail(3,.05)
7.8147277
. display chi2tail(3,4.1888)
.24178563
Exercício 8.5 – a (cont.)
2017/2018 Econometria I 73
Joaquim J.S. Ramalho
. gen ll2=llote^2
. gen la2=larea^2
. gen qu2=quartos^2
. gen llla= llote*larea
. gen llqu= llote*quartos
. gen laqu= larea*quartos
Exercício 8.5 – b
2017/2018 Econometria I 74
Joaquim J.S. Ramalho
. regress uhat2 llote larea quartos ll2 la2 qu2 llla llqu laqu
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 9, 78) = 1.05
Model | .051031949 9 .005670217 Prob > F = 0.4060
Residual | .419597806 78 .005379459 R-squared = 0.1084
---------+------------------------------ Adj R-squared = 0.0056
Total | .470629755 87 .005409537 Root MSE = .07334
-----------------------------------------------------------------------------
uhat2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
llote | -.8787222 .481022 -1.827 0.072 -1.836363 .078919
larea | -1.275723 1.136708 -1.122 0.265 -3.538734 .9872888
quartos | .2267013 .2015069 1.125 0.264 -.1744682 .6278707
ll2 | .0236562 .0162613 1.455 0.150 -.0087176 .0560301
la2 | .0395875 .1230645 0.322 0.749 -.2054151 .2845901
qu2 | -.005083 .0090609 -0.561 0.576 -.0231218 .0129559
llla | .1216009 .0721513 1.685 0.096 -.0220413 .2652431
llqu | -.0255157 .0320444 -0.796 0.428 -.0893113 .0382799
laqu | -.0010719 .0482751 -0.022 0.982 -.0971801 .0950363
_cons | 6.056804 3.191556 1.898 0.061 -.297095 12.4107
------------------------------------------------------------------------------
Exercício 8.5 – b (cont.)
2017/2018 Econometria I 75
Joaquim J.S. Ramalho
. display invFtail(9,78,0.05)
2.0022447
. display 88*0.1084
9.5392
. display invchi2tail(9,0.05)
16.918978
. display chi2tail(9,9.5392)
.38905938
Exercício 8.5 – b (cont.)
2017/2018 Econometria I 76
Joaquim J.S. Ramalho
. regress lpreco llote larea quartos
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 3, 84) = 50.55
Model | 5.15967627 3 1.71989209 Prob > F = 0.0000
Residual | 2.85792725 84 .034022943 R-squared = 0.6435
---------+------------------------------ Adj R-squared = 0.6308
Total | 8.01760352 87 .092156362 Root MSE = .18445
------------------------------------------------------------------------------
lpreco | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
llote | .1679747 .0382531 4.391 0.000 .0919042 .2440452
larea | .7019095 .0929186 7.554 0.000 .5171306 .8866884
quartos | .0365371 .0275294 1.327 0.188 -.0182081 .0912823
_cons | .7585933 .4402196 1.723 0.089 -.1168315 1.634018
------------------------------------------------------------------------------
. predict yhat
(option xb assumed; fitted values)
. gen yhat2=yhat^2
Exercício 8.5 – c
2017/2018 Econometria I 77
Joaquim J.S. Ramalho
. regress uhat2 yhat yhat2
Source | SS df MS Number of obs = 88
---------+------------------------------ F( 2, 85) = 1.70
Model | .01807784 2 .00903892 Prob > F = 0.1892
Residual | .452551915 85 .00532414 R-squared = 0.0384
---------+------------------------------ Adj R-squared = 0.0158
Total | .470629755 87 .005409537 Root MSE = .07297
------------------------------------------------------------------------------
uhat2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
yhat | -1.699499 1.165166 -1.459 0.148 -4.01616 .6171621
yhat2 | .1443385 .1011488 1.427 0.157 -.0567724 .3454495
_cons | 5.017344 3.350334 1.498 0.138 -1.644018 11.67871
------------------------------------------------------------------------------
. display invFtail(2,85,0.05)
3.1038384
. display 88*0.0384
3.3792
. display invchi2tail(2,0.05)
5.9914645
. display chi2tail(2,3.3792)
.18459335
Exercício 8.5 – c (cont.)
2017/2018 Econometria I 78
Joaquim J.S. Ramalho
. regress Y X1 X2 X3
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 3, 6) = 2.91
Model | 1369.14446 3 456.381488 Prob > F = 0.1230
Residual | 940.855535 6 156.809256 R-squared = 0.5927
-------------+------------------------------ Adj R-squared = 0.3891
Total | 2310 9 256.666667 Root MSE = 12.522
------------------------------------------------------------------------------
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
X1 | -11.37792 9.758836 -1.17 0.288 -35.25693 12.5011
X2 | 1.3758 .712711 1.93 0.102 -.3681412 3.119741
X3 | -3.970404 6.346455 -0.63 0.555 -19.49962 11.55881
_cons | 77.43246 15.11569 5.12 0.002 40.44569 114.4192
------------------------------------------------------------------------------
Exercício 9.1 - a
2017/2018 Econometria I 79
Joaquim J.S. Ramalho
. regress X1 X2 X3
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 2, 7) = 1.39
Model | .654447026 2 .327223513 Prob > F = 0.3100
Residual | 1.64655293 7 .235221847 R-squared = 0.2844
-------------+------------------------------ Adj R-squared = 0.0800
Total | 2.30099996 9 .255666662 Root MSE = .485
------------------------------------------------------------------------------
X1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
X2 | .0192113 .0266315 0.72 0.494 -.0437622 .0821848
X3 | -.0035945 .2457975 -0.01 0.989 -.5848133 .5776243
_cons | .9344181 .466909 2.00 0.085 -.1696462 2.038482
------------------------------------------------------------------------------
. display 1/(1-0.2844)
1.3974287
Exercício 9.1 - b
2017/2018 Econometria I 80
Joaquim J.S. Ramalho
. regress X2 X1 X3
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 2, 7) = 17.36
Model | 1531.29421 2 765.647107 Prob > F = 0.0019
Residual | 308.705787 7 44.1008267 R-squared = 0.8322
-------------+------------------------------ Adj R-squared = 0.7843
Total | 1840 9 204.444444 Root MSE = 6.6408
------------------------------------------------------------------------------
X2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
X1 | 3.601853 4.993035 0.72 0.494 -8.204798 15.4085
X3 | 7.791191 1.629656 4.78 0.002 3.937666 11.64472
_cons | 3.378381 7.913791 0.43 0.682 -15.33476 22.09152
------------------------------------------------------------------------------
. display 1/(1-0.8322)
5.9594756
Exercício 9.1 – b (cont.)
2017/2018 Econometria I 81
Joaquim J.S. Ramalho
. regress X3 X1 X2
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 2, 7) = 15.92
Model | 17.7067765 2 8.85338827 Prob > F = 0.0025
Residual | 3.89322345 7 .556174779 R-squared = 0.8198
-------------+------------------------------ Adj R-squared = 0.7683
Total | 21.6 9 2.4 Root MSE = .74577
------------------------------------------------------------------------------
X3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
X1 | -.008499 .5811807 -0.01 0.989 -1.382773 1.365775
X2 | .0982581 .0205523 4.78 0.002 .0496596 .1468566
_cons | -.0178728 .900193 -0.02 0.985 -2.146491 2.110745
------------------------------------------------------------------------------
. display 1/(1-0.8198)
5.5493896
Exercício 9.1 – b (cont.)
2017/2018 Econometria I 82
Joaquim J.S. Ramalho
. summarize
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
x1 | 11 9 3.316625 4 14
x2 | 11 9 3.316625 4 14
x3 | 11 9 3.316625 4 14
x4 | 11 9 3.316625 8 19
y1 | 11 7.500909 2.031568 4.26 10.84
-------------+--------------------------------------------------------
y2 | 11 7.500909 2.031657 3.1 9.26
y3 | 11 7.5 2.030424 5.39 12.74
y4 | 11 7.500909 2.030579 5.25 12.5
Exercício 9.2 - a
2017/2018 Econometria I 83
Joaquim J.S. Ramalho
. regress y1 x1
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 1, 9) = 17.99
Model | 27.5100011 1 27.5100011 Prob > F = 0.0022
Residual | 13.7626904 9 1.52918783 R-squared = 0.6665
-------------+------------------------------ Adj R-squared = 0.6295
Total | 41.2726916 10 4.12726916 Root MSE = 1.2366
------------------------------------------------------------------------------
y1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .5000909 .1179055 4.24 0.002 .2333701 .7668117
_cons | 3.000091 1.124747 2.67 0.026 .4557369 5.544445
------------------------------------------------------------------------------
. predict yhat1
(option xb assumed; fitted values)
Exercício 9.2 - b
2017/2018 Econometria I 84
Joaquim J.S. Ramalho
. regress y2 x2
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 1, 9) = 17.97
Model | 27.5000024 1 27.5000024 Prob > F = 0.0022
Residual | 13.776294 9 1.53069933 R-squared = 0.6662
-------------+------------------------------ Adj R-squared = 0.6292
Total | 41.2762964 10 4.12762964 Root MSE = 1.2372
------------------------------------------------------------------------------
y2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x2 | .5 .1179638 4.24 0.002 .2331475 .7668526
_cons | 3.000909 1.125303 2.67 0.026 .4552978 5.54652
------------------------------------------------------------------------------
. predict yhat2
(option xb assumed; fitted values)
Exercício 9.2 – b (cont.)
2017/2018 Econometria I 85
Joaquim J.S. Ramalho
. regress y3 x3
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 1, 9) = 17.97
Model | 27.4700075 1 27.4700075 Prob > F = 0.0022
Residual | 13.7561905 9 1.52846561 R-squared = 0.6663
-------------+------------------------------ Adj R-squared = 0.6292
Total | 41.2261979 10 4.12261979 Root MSE = 1.2363
------------------------------------------------------------------------------
y3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x3 | .4997273 .1178777 4.24 0.002 .2330695 .7663851
_cons | 3.002455 1.124481 2.67 0.026 .4587014 5.546208
------------------------------------------------------------------------------
. predict yhat3
(option xb assumed; fitted values)
Exercício 9.2 – b (cont.)
2017/2018 Econometria I 86
Joaquim J.S. Ramalho
. regress y4 x4
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 1, 9) = 18.00
Model | 27.4900007 1 27.4900007 Prob > F = 0.0022
Residual | 13.7424908 9 1.52694342 R-squared = 0.6667
-------------+------------------------------ Adj R-squared = 0.6297
Total | 41.2324915 10 4.12324915 Root MSE = 1.2357
------------------------------------------------------------------------------
y4 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x4 | .4999091 .1178189 4.24 0.002 .2333841 .7664341
_cons | 3.001727 1.123921 2.67 0.026 .4592411 5.544213
------------------------------------------------------------------------------
. predict yhat4
(option xb assumed; fitted values)
Exercício 9.2 – b (cont.)
2017/2018 Econometria I 87
Joaquim J.S. Ramalho
. scatter yhat1 y1 x1, connect(li)
Exercício 9.2 – c
2017/2018 Econometria I 88
46
81
01
2
4 6 8 10 12 14x1
Fitted values y1
Joaquim J.S. Ramalho
. scatter yhat2 y2 x2, connect(li)
Exercício 9.2 – c (cont.)
2017/2018 Econometria I 89
24
68
10
4 6 8 10 12 14x2
Fitted values y2
Joaquim J.S. Ramalho
. scatter yhat3 y3 x3, connect(li)
Exercício 9.2 – c (cont.)
2017/2018 Econometria I 90
46
81
01
2
4 6 8 10 12 14x3
Fitted values y3
Joaquim J.S. Ramalho
. scatter yhat4 y4 x4, connect(li)
Exercício 9.2 – c (cont.)
2017/2018 Econometria I 91
68
10
12
14
5 10 15 20x4
Fitted values y4
Joaquim J.S. Ramalho
. gen x22=x2^2
. regress y2 x2 x22
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 2, 8) = .
Model | 41.276274 2 20.638137 Prob > F = 0.0000
Residual | .000022378 8 2.7973e-06 R-squared = 1.0000
-------------+------------------------------ Adj R-squared = 1.0000
Total | 41.2762964 10 4.12762964 Root MSE = .00167
------------------------------------------------------------------------------
y2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x2 | 2.780839 .0010401 2673.72 0.000 2.778441 2.783238
x22 | -.1267133 .0000571 -2219.22 0.000 -.126845 -.1265816
_cons | -5.995735 .00433 -1384.70 0.000 -6.00572 -5.98575
------------------------------------------------------------------------------
Exercício 9.2 - d
2017/2018 Econometria I 92
Joaquim J.S. Ramalho
. regress y3 x3 if y3<10
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 1, 8) = .
Model | 11.0227641 1 11.0227641 Prob > F = 0.0000
Residual | .000075971 8 9.4963e-06 R-squared = 1.0000
-------------+------------------------------ Adj R-squared = 1.0000
Total | 11.0228401 9 1.22476001 Root MSE = .00308
------------------------------------------------------------------------------
y3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x3 | .3453896 .0003206 1077.38 0.000 .3446503 .3461289
_cons | 4.005649 .0029242 1369.84 0.000 3.998906 4.012392
------------------------------------------------------------------------------
Exercício 9.2 - e
2017/2018 Econometria I 93