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C3.8
(i)
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
prpblck | 409 .1134864 .1824165 0 .9816579
income | 409 47053.78 13179.29 15919 136529
storage display value
variable name type format label variable label
----------------------------------------------------------------------------
prpblck float %9.0g proportion black, zipcode
income float %9.0g median family income, zipcode
rata-rata prpblck 0.1135 proporsi black dan income sebesar $47053.78
(ii)
Source | SS df MS Number of obs = 401
-------------+------------------------------ F( 2, 398) = 13.66
Model | .202552215 2 .101276107 Prob > F = 0.0000
Residual | 2.95146493 398 .007415741 R-squared = 0.0642
-------------+------------------------------ Adj R-squared = 0.0595
Total | 3.15401715 400 .007885043 Root MSE = .08611
------------------------------------------------------------------------------
psoda | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prpblck | .1149882 .0260006 4.42 0.000 .0638724 .1661039
income | 1.60e-06 3.62e-07 4.43 0.000 8.91e-07 2.31e-06
_cons | .9563196 .018992 50.35 0.000 .9189824 .9936568
------------------------------------------------------------------------------
Usual Form
Psoda = .0956 + .115 prpblck + 0.0000016 income
(.019) (.026) (0.000000036)
n=401, R2=0.064, adj R2=0.059
Economically large? Tidak. karena pengaruh prpblck dan income tidak jauh berbeda jika mereka
dalam 1 skala yang sama. Income disini adalah puluh ribuan (rata-rata 47053.78). Jika dibuat
menjadi 0.47053, koefisien income dapat menjadi 0.16
(iii)
Source | SS df MS Number of obs = 401
-------------+------------------------------ F( 1, 399) = 7.34
Model | .057010466 1 .057010466 Prob > F = 0.0070
Residual | 3.09700668 399 .007761922 R-squared = 0.0181
-------------+------------------------------ Adj R-squared = 0.0156
Total | 3.15401715 400 .007885043 Root MSE = .0881
------------------------------------------------------------------------------
psoda | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prpblck | .0649269 .023957 2.71 0.007 .0178292 .1120245
_cons | 1.037399 .0051905 199.87 0.000 1.027195 1.047603
------------------------------------------------------------------------------
Ternyata, dengan mengkontrol pendapatan, efek proporsi orang hitam terhadap harga soda
meningkat. berarti ada diskriminasi orang hitam yang lebih besar saat mengkontrol
pendapatan.
(iv)
Source | SS df MS Number of obs = 401
-------------+------------------------------ F( 2, 398) = 14.54
Model | .196020672 2 .098010336 Prob > F = 0.0000
Residual | 2.68272938 398 .006740526 R-squared = 0.0681
-------------+------------------------------ Adj R-squared = 0.0634
Total | 2.87875005 400 .007196875 Root MSE = .0821
------------------------------------------------------------------------------
lpsoda | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prpblck | .1215803 .0257457 4.72 0.000 .0709657 .1721948
lincome | .0765114 .0165969 4.61 0.000 .0438829 .1091399
_cons | -.793768 .1794337 -4.42 0.000 -1.146524 -.4410117
------------------------------------------------------------------------------
Jika proporsi orang hitam meningkat 20%, maka terjadi peningkatan .02431% harga soda
(v)
Source | SS df MS Number of obs = 401
-------------+------------------------------ F( 3, 397) = 12.60
Model | .250340622 3 .083446874 Prob > F = 0.0000
Residual | 2.62840943 397 .006620679 R-squared = 0.0870
-------------+------------------------------ Adj R-squared = 0.0801
Total | 2.87875005 400 .007196875 Root MSE = .08137
------------------------------------------------------------------------------
lpsoda | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prpblck | .0728072 .0306756 2.37 0.018 .0125003 .1331141
lincome | .1369553 .0267554 5.12 0.000 .0843552 .1895553
prppov | .38036 .1327903 2.86 0.004 .1192999 .6414201
_cons | -1.463333 .2937111 -4.98 0.000 -2.040756 -.8859092
------------------------------------------------------------------------------
Setelah memasukkan variabel prppov, terjadi penurunan dampak prpblck terhadap %harga
soda.
(vi)
(obs=409)
| prppov lincome
-------------+------------------
prppov | 1.0000
lincome | -0.8385 1.0000
iya. Karena semakin tinggi rata-rata pendapatan keluarga, semakin rendah proporsi kemiskinan
(vii)
Walau prppov dan lincome memiliki hubungan kuat yang negatif, mereka tetap perlu
dimasukkan kedalam regresi karena keduanya adalah variabel-variabel yang penting untuk
mengkontrol dampak proporsi penduduk hitam terhadap harga soda.
C8.5
(i) By regressing sprdcvr on an intercept only we obtain μˆ ≈ .515 se ≈ .021). The asymptotic t
statistic for H0: μ = .5 is (.515 − .5)/.021 ≈ .71, which is not significant at the 10% level, or even
the 20% level.
(ii) 35 games were played on a neutral court.
(iii) Estimasi LPM :
sprdcvr = .490 + .035 favhome + .118 neutral − .023 fav25 + .018 und25
(.045) (.050) (.095) (.050) (.092)
n = 553, R2 = .0034.
The variable neutral has by far the largest effect – if the game is played on a neutral court, the
probability that the spread is covered is estimated to be about .12 higher – and, except for the
intercept, its t statistic is the only t statistic greater than one in absolute value (about 1.24).
(iv) Under H0: β0= β1= β2= β3 = 0 the response probability does not depend on any explanatory
variables, which means neither the mean nor the variance depends on the explanatory
variables. [See equation (8.38).]
(v) Ftest: Prob>F = .76 tidak tolak h0.
(vi) Based on these variables, it is not possible to predict whether the spread will be covered.
The explanatory power is very low, and the explanatory variables are jointly very insignificant.
The coefficient on neutral may indicate something is going on with games played on a neutral
court, but we would not want to bet money on it unless it could be confirmed with a separate,
larger sample.
C8.7
(i) The heteroskedasticity-robust standard error for white β ≈ .129 is about .026, which is
notably higher than the nonrobust standard error (about .020). The heteroskedasticity-robust
95% confidence interval is about .078 to .179, while the nonrobust CI is, of course, narrower,
about .090 to .168. The robust CI still excludes the value zero by some margin.
(ii) tidak ada fitted value yang kurang dari nol, tetapi ada 231 yang lebih besar dari 1. Unless we
do something to those fitted values, we cannot directly apply WLS, as ˆi h will be negative in
231 cases.
C11.4
Source | SS df MS Number of obs = 55
-------------+------------------------------ F( 1, 53) = 8.26
Model | 42.4133575 1 42.4133575 Prob > F = 0.0058
Residual | 272.275016 53 5.13726445 R-squared = 0.1348
-------------+------------------------------ Adj R-squared = 0.1185
Total | 314.688374 54 5.82756247 Root MSE = 2.2666
------------------------------------------------------------------------------
cinf | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cunem | -.8328101 .2898415 -2.87 0.006 -1.414159 -.2514616
_cons | -.0721421 .3058418 -0.24 0.814 -.6855832 .5412989
------------------------------------------------------------------------------
Usual form:
cinf = -.0721421 - .8328101 cunem
(.306) (.289)
n= 55, R2=0.1348, Adj R-squared = 0.1185 discuss: sign: setelah menggunakan turunan pertama dari unem, koefisien tetap negatif, berarti peningkatan penggangguran akan menurunkan inflasi size: besar dari koefisien cunem meningkat dibandingkan unem. Signifikansi: dengan signifikansi 95%, cunem juga signifikan seperti unem
Model yang lebih baik
1. Bisa hanya analisis adj R2
Model yang menggunakan cunem memiliki adj r2 yang lebih tinggi (0.1185) daripada
yang mengguankan unem (0.088)
2. Lebih baik jika kalian melakukan tes spesifikasi
WALD TEST
Source | SS df MS Number of obs = 55
-------------+------------------------------ F( 2, 52) = 5.68
Model | 56.4448973 2 28.2224487 Prob > F = 0.0059
Residual | 258.243476 52 4.9662207 R-squared = 0.1794
-------------+------------------------------ Adj R-squared = 0.1478
Total | 314.688374 54 5.82756247 Root MSE = 2.2285
------------------------------------------------------------------------------
cinf | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cunem | -.6623503 .3024816 -2.19 0.033 -1.269324 -.0553765
unem | -.3602916 .2143455 -1.68 0.099 -.7904073 .0698242
_cons | 1.96291 1.247483 1.57 0.122 -.5403486 4.466169
------------------------------------------------------------------------------
( 1) unem = 0
F( 1, 52) = 2.83
Prob > F = 0.0988
H0= unem tidak signifikan
H1= unem signifikan
Hasil: tidak tolak h0 karena Prob > F lebih besar dari alfa (5%)
SELECTION CRITERIA
Source | SS df MS Number of obs = 55
-------------+------------------------------ F( 1, 53) = 8.26
Model | 42.4133575 1 42.4133575 Prob > F = 0.0058
Residual | 272.275016 53 5.13726445 R-squared = 0.1348
-------------+------------------------------ Adj R-squared = 0.1185
Total | 314.688374 54 5.82756247 Root MSE = 2.2666
------------------------------------------------------------------------------
cinf | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cunem | -.8328101 .2898415 -2.87 0.006 -1.414159 -.2514616
_cons | -.0721421 .3058418 -0.24 0.814 -.6855832 .5412989
------------------------------------------------------------------------------
. estat ic
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 55 -126.0085 -122.0273 2 248.0546 252.0693
-----------------------------------------------------------------------------
Note: N=Obs used in calculating BIC; see [R] BIC note
Source | SS df MS Number of obs = 55
-------------+------------------------------ F( 1, 53) = 6.13
Model | 32.6324798 1 32.6324798 Prob > F = 0.0165
Residual | 282.055894 53 5.32180932 R-squared = 0.1037
-------------+------------------------------ Adj R-squared = 0.0868
Total | 314.688374 54 5.82756247 Root MSE = 2.3069
------------------------------------------------------------------------------
cinf | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
unem | -.5176487 .209045 -2.48 0.017 -.9369398 -.0983576
_cons | 2.828202 1.224871 2.31 0.025 .3714212 5.284982
------------------------------------------------------------------------------
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 55 -126.0085 -122.9979 2 249.9957 254.0104
-----------------------------------------------------------------------------
Note: N=Obs used in calculating BIC; see [R] BIC note
Dari AIC dan BIC diatas, dapat dilihat regresi dengan cunem lebih baik
11.7
11.7 (i) We plug the first equation into the second to get
and, rearranging,
dimana (ii) An OLS regression of yt on yt-1 and xt produces consistent, asymptotically normal
estimators of the βj. Under E(et|xt,yt-1,xt-1, … ) = E(at|xt,yt-1,xt-1, … ) = 0 it follows that
E(ut|xt,yt-1,xt-1, … ) = 0, which means that the model is dynamically complete [see equation
(11.37)]. Therefore, the errors are serially uncorrelated. If the homoskedasticity assumption
Var(ut|xt,yt-1) = σ2
holds, then the usual standard errors, t statistics and F statistics are
asymptotically valid.
(iii) karena dan maka
