Índice de ejercicios resueltos
Chapter 4 - Multiple Regression Analysis: Inference
*Ejercicio C4.1
vote1.cvs
insheet using
"C:\Users\Nerys\Documents\Biblioteca\Econometria, libos ebooks\Solucion a
ejercicios de econometria\Base de datos wooldridge\vote1.csv ", comma
clear
i.
*un cambio en una unidad porcentual en el gasto
incide en B1 en el cambio del porcentaje de votos obtenidos.
ii.
*H0; _b[expendA]=1
iii.
. gen lexpenda=ln( expenda)
. regress votea
lexpenda lexpendb prtystra
Source | SS
df MS Number of obs = 173
-------------+------------------------------ F(
3, 169) = 215.15
Model |
38402.1673 3 12800.7224 Prob > F =
0.0000
Residual |
10055.0813 169 59.4975224 R-squared =
0.7925
-------------+------------------------------ Adj R-squared = 0.7888
Total |
48457.2486 172 281.728189 Root MSE
= 7.7135
------------------------------------------------------------------------------
votea | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
lexpenda
| 6.081334 .3821187
15.91 0.000 5.326994
6.835675
lexpendb
| -6.615268 .3788756
-17.46 0.000 -7.363206
-5.867329
prtystra
| .1520142 .0620267
2.45 0.015 .0295674
.2744611
_cons
| 45.08597 3.92679
11.48 0.000 37.33409
52.83785
------------------------------------------------------------------------------
*3.1. Si afecta. (P>|t|=0.000, por tanto se
rechaza la H0; B=0)
*3.2. Si afecta. (P>|t|=0.000, por tanto se
rechaza la H0; B=0)
*3.3. No, no se puede usar, es necesario modificar
la forma en como se ha construido el estadístico t, el que el software testea
por default es con un valor teórico igual a cero, en este caso sería igual a 1.
iv.
. scalar tvalue=(_b[lexpenda]-1)/_se[lexpenda]
. scalar pvalue=ttail(169, tvalue)
. display
"T-value: " tvalue ", P-value: " pvalue
T-value: 13.297791,
P-value: 2.249e-28
*Ejercicio C4.2 lawsch85.cvs
insheet using
"C:\Users\Nerys\Documents\Biblioteca\Econometria, libos ebooks\Solucion a
ejercicios de econometria\Base de datos wooldridge\lawsch85.csv ", comma
clear
i.
. gen lsalary=ln(salary)
. gen lcost=ln(cost)
. gen llibvol=ln( libvol)
. regress lsalary
lsat gpa llibvol lcost rank
Source | SS
df MS Number of obs = 136
-------------+------------------------------ F(
5, 130) = 138.23
Model
| 8.73362207 5
1.74672441 Prob >
F =
0.0000
Residual |
1.64272974 130 .012636383 R-squared =
0.8417
-------------+------------------------------ Adj R-squared = 0.8356
Total |
10.3763518 135 .076861865 Root MSE =
.11241
------------------------------------------------------------------------------
lsalary | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
lsat
| .0046965 .0040105
1.17 0.244 -.0032378
.0126308
gpa
| .2475239 .090037
2.75 0.007 .0693964
.4256514
llibvol
| .0949932 .0332543
2.86 0.005 .0292035 .160783
lcost
| .0375538 .0321061
1.17 0.244 -.0259642
.1010718
rank
| -.0033246 .0003485
-9.54 0.000 -.004014 -.0026352
_cons
| 8.343226 .5325192
15.67 0.000 7.2897
9.396752
------------------------------------------------------------------------------
*siendo el t=-9.54 y como se puede usar la tabla de
la normal (95% signifiancia=-1.645), por tanto cae en la región de rechazo y se
rechaza ho (P>|t| también muestra evidencia en contra de h0).
ii.
*Individualmente: gpa es significativa (t=0.007),
sin embargo lsat no (t=0.244)
*de manera conjunta lo podemos testear con la prueba
F, comparando el modelo anterior con uno donde se omitan estas dos variables.
estimates store mz24,
title(Model No_Rest)
regress
lsalary lsat gpa llibvol lcost rank
estimates store mz26,
title(Model Rest)
regress
lsalary llibvol lcost rank
estout mz26 mz24, cells(b(star
fmt(3)) se(par fmt(3))) legend label varlabels(_cons constant) stats(N r2 rss)title(Models
of votes)
Models of votes
----------------------------------------------------
Model Rest Model No_R~t
b/se b/se
----------------------------------------------------
LSAT 0.005
(0.004)
GPA 0.248**
(0.090)
llibvol 0.095** 0.129***
(0.033) (0.033)
lcost 0.038 0.027
(0.032) (0.030)
rank -0.003*** -0.004***
(0.000) (0.000)
constant 8.343*** 9.880***
(0.533) (0.343)
----------------------------------------------------
N 136.000 141.000
r2 0.842 0.822
rss 1.643 1.909
----------------------------------------------------
* p<0.05, **
p<0.01, *** p<0.001
. scalar F=((1.909-1.643)/2)/(1.643/(136-5-1))
. display F
10.523433
. display
invF(2,130,.95)
3.0658391
*por tanto, F, rechaza que ambas en conjunto sean no
significativas
iii. *Coregir el modelo 3, no considera valores
perdidos
eststo clear
estimates store mz24,
title(Model No_Rest)
regress
lsalary lsat gpa llibvol lcost rank
estimates store mz26,
title(Model Rest)
regress
lsalary llibvol lcost rank
estimates store mlo27,
title(Model No_Rest2)
regress
lsalary lsat gpa llibvol lcost rank clsize faculty
estout mlo27 mz26 mz24,
cells(b(star fmt(3)) se(par fmt(3))) legend label varlabels(_cons constant)
stats(N r2 rss) title(Models of votes3)
Models of votes3
--------------------------------------------------------------------
Model No_R~2 Model Rest Model No_R~t
b/se b/se b/se
--------------------------------------------------------------------
llibvol 0.129*** 0.095** 0.055
(0.033)
(0.033) (0.040)
lcost 0.027 0.038 0.030
(0.030) (0.032) (0.035)
rank -0.004*** -0.003*** -0.003***
(0.000) (0.000) (0.000)
LSAT
0.005 0.006
(0.004) (0.004)
GPA 0.248** 0.266**
(0.090) (0.093)
clsize
0.000
(0.000)
faculty
0.000
(0.000)
constant 9.880*** 8.343*** 8.416***
(0.343) (0.533) (0.552)
--------------------------------------------------------------------
N 141.000 136.000 131.000
r2 0.822 0.842 0.844
rss 1.909 1.643 1.573
--------------------------------------------------------------------
* p<0.05, **
p<0.01, *** p<0.001
*Ejercicio C4.3 hprice1.cvs
insheet using
"C:\Users\Nerys\Documents\Biblioteca\Econometria, libos ebooks\Solucion a
ejercicios de econometria\Base de datos wooldridge\hprice1.csv ", comma
clear
i.
. regress lprice
sqrft bdrms
Source | SS
df MS Number of obs = 88
-------------+------------------------------ F(
2, 85) = 60.73
Model |
4.71671294 2 2.35835647 Prob > F =
0.0000
Residual |
3.30088996 85 .038833999 R-squared =
0.5883
-------------+------------------------------ Adj R-squared = 0.5786
Total |
8.0176029 87 .092156355 Root MSE =
.19706
------------------------------------------------------------------------------
lprice | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
sqrft
| .0003794 .0000432
8.78 0.000 .0002935
.0004654
bdrms
| .0288844 .0296433
0.97 0.333 -.0300544
.0878231
_cons
| 4.766028 .0970445
49.11 0.000 4.573077
4.958978
------------------------------------------------------------------------------
scalar theta1=(150*_b[sqrft])+_b[bdrms]
. display theta1
.08580125
ii.
* _b[bdrms]’=theta1-(150*_b[sqrft])
*********
*Ejercicio C4.4 bwght.cvs
insheet using
"C:\Users\Nerys\Documents\Biblioteca\Econometria, libos ebooks\Solucion a
ejercicios de econometria\Base de datos wooldridge\bwght.csv ", comma
clear
eststo clear
estimates store mz1,
title(Model No_Rest)
regress bwght cigs parity faminc motheduc
fatheduc
estimates store mz2,
title(Model Rest)
regress bwght cigs parity faminc
estout mz1 mz2, cells(b(star
fmt(3)) se(par fmt(3))) legend label varlabels(_cons constant) stats(N r2 rss) title(Models.
Education de los padres y el peso al nacer)
Models. Education de los padres y el peso al nacer
----------------------------------------------------
Model No_R~t Model Rest
b/se b/se
----------------------------------------------------
cigs -0.477*** -0.596***
(0.092)
(0.110)
parity 1.616** 1.788**
(0.604) (0.659)
faminc 0.098*** 0.056
(0.029) (0.037)
motheduc -0.370
(0.320)
fatheduc 0.472
(0.283)
constant 114.214*** 114.524***
(1.469) (3.728)
----------------------------------------------------
N 1388.000 1191.000
r2 0.035 0.039
rss 554615.199 464041.135
----------------------------------------------------
* p<0.05, ** p<0.01, *** p<0.001
*Ejercicio C4.4 mlb1.cvs
insheet using
"C:\Users\Nerys\Documents\Biblioteca\Econometria, libos ebooks\Solucion a
ejercicios de econometria\Base de datos wooldridge\mlb1.csv ", comma clear
eststo clear
estimates store mz3,
title(Model 1)
regress lsalary years gamesyr bavg hrunsyr rbisyr
estimates store mz4,
title(Model 2)
regress lsalary years gamesyr bavg hrunsyr
estout mz3 mz4, cells(b(star
fmt(3)) p se(par fmt(3))) legend label varlabels(_cons constant) stats(N r2
rss) title(Models. Salirio de las grandes ligas)
Models. Salirio de las grandes ligas
----------------------------------------------------
Model 1 Model 2
b/p/se b/p/se
----------------------------------------------------
years 0.068*** 0.069***
0.000 0.000
(0.012) (0.012)
gamesyr 0.016*** 0.013***
0.000 0.000
(0.002) (0.003)
bavg 0.001 0.001
0.184 0.376
(0.001) (0.001)
hrunsyr 0.036*** 0.014
0.000 0.369
(0.007) (0.016)
rbisyr
0.011
0.134
(0.007)
constant 11.021*** 11.192***
0.000 0.000
(0.266) (0.289)
----------------------------------------------------
N 353.000 353.000
r2 0.625 0.628
rss 184.375 183.186
----------------------------------------------------
*pasa a ser significativo a no. Y la magnitud del
coeficiente se reduce.
iii.
estimates store mzl5,
title(Model 3)
regress lsalary years gamesyr bavg hrunsyr runsyr fldperc sbasesyr
estout mz4 mz3 mzl5,
cells(b(star fmt(3)) p se(par fmt(3))) legend label varlabels(_cons constant)
stats(N r2 rss) title(Models. Salirio de las grandes ligas)
Models. Salirio de las grandes ligas
--------------------------------------------------------------------
Model 2
Model 1 Model 3
b/p/se b/p/se b/p/se
--------------------------------------------------------------------
years 0.069*** 0.068*** 0.070***
0.000 0.000 0.000
(0.012) (0.012) (0.012)
gamesyr 0.013*** 0.016*** 0.008**
0.000 0.000 0.003
(0.003) (0.002) (0.003)
bavg 0.001 0.001 0.001
0.376 0.184 0.632
(0.001) (0.001) (0.001)
hrunsyr 0.014 0.036*** 0.023**
0.369 0.000 0.008
(0.016) (0.007) (0.009)
rbisyr 0.011
0.134
(0.007)
runsyr 0.017***
0.001
(0.005)
fldperc
0.001
0.606
(0.002)
sbasesyr
-0.006
0.216
(0.005)
constant 11.192*** 11.021*** 10.408***
0.000 0.000 0.000
(0.289) (0.266) (2.003)
--------------------------------------------------------------------
N 353.000 353.000 353.000
r2 0.628 0.625 0.639
rss 183.186 184.375 177.665
--------------------------------------------------------------------
* p<0.05, **
p<0.01, *** p<0.001
*individualmente solo
runsyr es significativo
iii.
para la significancia conjunta se necesita la prueba
F, entre los dos ultimos modelos.
*Ejercicio C4.6 wage2.cvs
insheet using
"C:\Users\Nerys\Documents\Biblioteca\Econometria, libos ebooks\Solucion a
ejercicios de econometria\Base de datos wooldridge\wage2.csv ", comma
clear
i.
. regress lwage educ exper tenure
. *H0; _b[exper] = _b[tenure]
. testparm exper
tenure, equal
( 1) -
exper + tenure = 0
F(
1, 931) = 0.17
Prob > F = 0.6805
. test exper =tenure
( 1)
exper - tenure = 0
F(
1, 931) = 0.17
Prob > F = 0.6805
*Ejercicio C4.7 twoyear.cvs
insheet using
"C:\Users\Nerys\Documents\Biblioteca\Econometria, libos ebooks\Solucion a
ejercicios de econometria\Base de datos wooldridge\twoyear.csv ", comma
clear
i.
. summ phsrank
Variable | Obs Mean
Std. Dev. Min Max
-------------+--------------------------------------------------------
phsrank
| 6763 56.15703
24.27296 0 99
ii.
. regress lwage jc totcoll exper phsrank
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
4, 6758) = 483.85
Model |
358.050584 4 89.512646 Prob > F =
0.0000
Residual |
1250.24551 6758 .185002295 R-squared =
0.2226
-------------+------------------------------ Adj R-squared = 0.2222
Total |
1608.29609 6762 .237843255 Root MSE =
.43012
------------------------------------------------------------------------------
lwage | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
jc
| -.0093108 .0069693
-1.34 0.182 -.0229728
.0043512
totcoll
| .0754757 .0025588
29.50 0.000 .0704595
.0804918
exper
| .0049396 .0001575
31.36 0.000 .0046308
.0052483
phsrank
| .0003032 .0002389 1.27
0.204 -.0001651 .0007716
_cons
| 1.458747 .0236211
61.76 0.000 1.412442
1.505052
------------------------------------------------------------------------------
. display _b[phsrank]*10
.00303232
iii.
eststo clear
estimates store mzl3,
title(Model 1)
regress
lwage jc totcoll exper
estimates store mzl4,
title(Model 2)
regress
lwage jc totcoll exper phsrank
estout mzl3 mzl4, cells(b(star
fmt(3)) p se(par fmt(3))) legend label varlabels(_cons constant) stats(N r2
rss) title(Models. Salario y bachillerato)
Models. Salario y bachillerato
----------------------------------------------------
Model 1 Model 2
b/p/se b/p/se
----------------------------------------------------
jc -0.009 -0.010
0.182
0.142
(0.007) (0.007)
totcoll 0.075*** 0.077***
0.000 0.000
(0.003) (0.002)
exper 0.005*** 0.005***
0.000 0.000
(0.000) (0.000)
phsrank 0.000
0.204
(0.000)
constant 1.459*** 1.472***
0.000 0.000
(0.024) (0.021)
----------------------------------------------------
N 6763.000 6763.000
r2 0.223 0.222
rss 1250.246 1250.544
----------------------------------------------------
* p<0.05, **
p<0.01, *** p<0.001
