Ch. 3 stata - sociologiaの日記

C1
(i)
$bwght=\beta_0+\beta_1 bigs+\beta_2 faminc+u,$
$\beta_2$ はプラスの方向を示すだろう．
(ii)
収入が多い人は健康にも気を使う可能性があるので，相関があるにしてもマイナスだろう．
(iii)

 reg bwght cigs

      Source |       SS       df       MS              Number of obs =    1388
-------------+------------------------------           F(  1,  1386) =   32.24
       Model |  13060.4194     1  13060.4194           Prob > F      =  0.0000
    Residual |    561551.3  1386  405.159668           R-squared     =  0.0227
-------------+------------------------------           Adj R-squared =  0.0220
       Total |   574611.72  1387  414.283864           Root MSE      =  20.129

------------------------------------------------------------------------------
       bwght |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        cigs |  -.5137721   .0904909    -5.68   0.000    -.6912861   -.3362581
       _cons |   119.7719   .5723407   209.27   0.000     118.6492    120.8946
------------------------------------------------------------------------------
 reg bwght cigs faminc

      Source |       SS       df       MS              Number of obs =    1388
-------------+------------------------------           F(  2,  1385) =   21.27
       Model |  17126.2088     2  8563.10442           Prob > F      =  0.0000
    Residual |  557485.511  1385  402.516614           R-squared     =  0.0298
-------------+------------------------------           Adj R-squared =  0.0284
       Total |   574611.72  1387  414.283864           Root MSE      =  20.063

------------------------------------------------------------------------------
       bwght |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        cigs |  -.4634075   .0915768    -5.06   0.000    -.6430518   -.2837633
      faminc |   .0927647   .0291879     3.18   0.002     .0355075    .1500219
       _cons |   116.9741   1.048984   111.51   0.000     114.9164    119.0319
------------------------------------------------------------------------------

収入を含めても，たばこを吸うことの新生児の体重への効果はほぼ変化はない．

C2
$price=\beta_0+\beta_1 sqrft+\beta_2 bdrms +u,$
(i)

reg pric sqrft bdrms

      Source |       SS       df       MS              Number of obs =      88
-------------+------------------------------           F(  2,    85) =   72.96
       Model |  580009.152     2  290004.576           Prob > F      =  0.0000
    Residual |  337845.354    85  3974.65122           R-squared     =  0.6319
-------------+------------------------------           Adj R-squared =  0.6233
       Total |  917854.506    87  10550.0518           Root MSE      =  63.045

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       sqrft |   .1284362   .0138245     9.29   0.000     .1009495    .1559229
       bdrms |   15.19819   9.483517     1.60   0.113    -3.657582    34.05396
       _cons |    -19.315   31.04662    -0.62   0.536    -81.04399      42.414
------------------------------------------------------------------------------

$price=-19.315+.1284362*sqrft+15.19819*bdrms +u,$
$n=88,R^2=.632,$
(ii)
一部屋ベッドルームが増えると，15200$のアップ．
(iii)
一部屋ベッドルームが増えて，140スクエアフィート増えると，33181$のアップ．
(iv)
63.2%
(v)
予測は，354.6(in thousand dollars)．
(vi)
実際は，300(in thousand dollars)なので，残さは，43.05であり，十分には支払われていない．
C3
(i)
$log(salary)=\beta_0+\beta_1*log(sales)+\beta_2*log(mktval)+u$ を推定する．

reg lsalary lsales lmktval

      Source |       SS       df       MS              Number of obs =     177
-------------+------------------------------           F(  2,   174) =   37.13
       Model |  19.3365617     2  9.66828083           Prob > F      =  0.0000
    Residual |  45.3096514   174  .260400295           R-squared     =  0.2991
-------------+------------------------------           Adj R-squared =  0.2911
       Total |  64.6462131   176  .367308029           Root MSE      =  .51029

------------------------------------------------------------------------------
     lsalary |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lsales |   .1621283   .0396703     4.09   0.000     .0838315    .2404252
     lmktval |    .106708    .050124     2.13   0.035     .0077787    .2056372
       _cons |   4.620917   .2544083    18.16   0.000     4.118794    5.123041
------------------------------------------------------------------------------

$log(salary)=4.62+.162*log(sales)+.107*log(mktval)+u, n=177,R^2=0.3$ となる．
(ii)

 sum sales mktval profits

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       sales |       177    3529.463    6088.654         29      51300
      mktval |       177    3600.316    6442.276        387      45400
     profits |       177    207.8305    404.4543       -463       2700

$log{a} x$ と書く場合，xは正の実数をとる必要がある．profitsは負をとるため，対数変換には向かない．

 reg lsalary lsales lmktval profits

      Source |       SS       df       MS              Number of obs =     177
-------------+------------------------------           F(  3,   173) =   24.64
       Model |  19.3509799     3  6.45032663           Prob > F      =  0.0000
    Residual |  45.2952332   173  .261822157           R-squared     =  0.2993
-------------+------------------------------           Adj R-squared =  0.2872
       Total |  64.6462131   176  .367308029           Root MSE      =  .51169

------------------------------------------------------------------------------
     lsalary |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lsales |   .1613683   .0399101     4.04   0.000     .0825949    .2401416
     lmktval |   .0975286   .0636886     1.53   0.128    -.0281782    .2232354
     profits |   .0000357    .000152     0.23   0.815    -.0002643    .0003356
       _cons |   4.686924   .3797294    12.34   0.000     3.937425    5.436423
------------------------------------------------------------------------------

決定係数はそれほど高くない．
(iii)

 reg lsalary lsales lmktval profits ceoten

      Source |       SS       df       MS              Number of obs =     177
-------------+------------------------------           F(  4,   172) =   20.08
       Model |  20.5768102     4  5.14420254           Prob > F      =  0.0000
    Residual |  44.0694029   172  .256217459           R-squared     =  0.3183
-------------+------------------------------           Adj R-squared =  0.3024
       Total |  64.6462131   176  .367308029           Root MSE      =  .50618

------------------------------------------------------------------------------
     lsalary |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lsales |   .1622339   .0394826     4.11   0.000     .0843012    .2401667
     lmktval |   .1017598    .063033     1.61   0.108     -.022658    .2261775
     profits |   .0000291   .0001504     0.19   0.847    -.0002677    .0003258
      ceoten |   .0116847    .005342     2.19   0.030     .0011403     .022229
       _cons |    4.55778   .3802548    11.99   0.000     3.807213    5.308347
------------------------------------------------------------------------------

$log(salary)=4.56+.16*log(sales)+.102*log(mktval)+.00*profits+.012*ceoten, n=177, R^2=.318$ となる．
1年働くと，1.2%の収入増加となる．
(iv)

 cor lmktval profits
(obs=177)

             |  lmktval  profits
-------------+------------------
     lmktval |   1.0000
     profits |   0.7769   1.0000

相関は高いが，vifは高くないので，それほど問題はない．
C4
(i)

 sum atndrte priGPA ACT

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
     atndrte |       680    81.70956    17.04699       6.25        100
      priGPA |       680    2.586775    .5447141       .857       3.93
         ACT |       680    22.51029    3.490768         13         32

81.7%のクラスに平均的に出席しており，前学期のGPAは平均2.59，ACTのスコアは平均22.51である．
それぞれの最小値・最大値は，6.25%と100%，.857と3.93，13と32である．
(ii)
$atndrte=\beta_0+\beta_1priGPA+\beta_2ACT+u$ を推定する．

 reg atndrte priGPA ACT

      Source |       SS       df       MS              Number of obs =     680
-------------+------------------------------           F(  2,   677) =  138.65
       Model |  57336.7612     2  28668.3806           Prob > F      =  0.0000
    Residual |  139980.564   677  206.765974           R-squared     =  0.2906
-------------+------------------------------           Adj R-squared =  0.2885
       Total |  197317.325   679   290.59989           Root MSE      =  14.379

------------------------------------------------------------------------------
     atndrte |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      priGPA |   17.26059   1.083103    15.94   0.000     15.13395    19.38724
         ACT |  -1.716553    .169012   -10.16   0.000    -2.048404   -1.384702
       _cons |    75.7004   3.884108    19.49   0.000     68.07406    83.32675
------------------------------------------------------------------------------

$atndrte=75.7+17.26*priGPA+-1.72*ACT, R^2=0.291,n=680$ である．
GPAが0，かつACTのスコアが0の学生は，平均的に75.7%の出席率となる．あまり意味のある数字ではない．
(iii)
GPAがよい学生は，そうでない学生と比べ，より出席する傾向にある．ACTのスコアが良いと，そうでない学生と比べ，出席しにくくなる．
少し不思議な結果である．よりテストでうまくできていた学生は，出席しなくてもうまくやれると思っているということを反映しているのかもしれない．
(iv)
$atndrte=75.7+17.26*3.65+-1.72*(20)\approx104.3$ となり，出席率100%を超えてしまう．実際にサンプルのなかにこの値をとるサンプルがある．
(v)
$atndrte for A=75.7+17.26*3.1+-1.72*(21)\approx93.09,$
$atndrte for B=75.7+17.26*2.1+-1.72*(26)\approx67.23$ となり，差は25.86%程度となる．
C5