## Chapter 4 - Examples

```-------------------------------------------------------------------------------------
name:  SN
log:  Wooldridge\intro-econx\iexample4.smcl
log type:  smcl
opened on:   6 Jan 2019, 17:17:19

. **********************************************
. * Solomon Negash - Replicating Examples
. * Wooldridge (2016). Introductory Econometrics: A Modern Approach. 6ed.
. * STATA Program, version 15.1.

. * Chapter 4  - Multiple Regression Analysis: Inference
. * Computer Exercises (Examples)
. ******************** SETUP *********************

*example4.1. Wage equation
. u wage1.dta, clear

. reg lwage educ exper tenure

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
Total |  148.329751       525   .28253286   Root MSE        =    .44086

------------------------------------------------------------------------------
lwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |    .092029   .0073299    12.56   0.000     .0776292    .1064288
exper |   .0041211   .0017233     2.39   0.017     .0007357    .0075065
tenure |   .0220672   .0030936     7.13   0.000     .0159897    .0281448
_cons |   .2843595   .1041904     2.73   0.007     .0796756    .4890435
------------------------------------------------------------------------------

*example4.2. Student performance
. u meap93.dta, clear

. *Lin-lin model
. eststo: reg math10 totcomp staff enroll

Source |       SS           df       MS      Number of obs   =       408
-------------+----------------------------------   F(3, 404)       =      7.70
Model |  2422.93434         3  807.644779   Prob > F        =    0.0001
Residual |  42394.2462       404  104.936253   R-squared       =    0.0541
Total |  44817.1805       407  110.115923   Root MSE        =    10.244

------------------------------------------------------------------------------
math10 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
totcomp |   .0004586   .0001004     4.57   0.000     .0002613    .0006559
staff |   .0479199    .039814     1.20   0.229    -.0303487    .1261884
enroll |  -.0001976   .0002152    -0.92   0.359    -.0006207    .0002255
_cons |   2.274021   6.113794     0.37   0.710    -9.744801    14.29284
------------------------------------------------------------------------------
(est1 stored)
. *Lin-log model
. eststo: reg math10 ltotcomp lstaff lenroll

Source |       SS           df       MS      Number of obs   =       408
-------------+----------------------------------   F(3, 404)       =      9.42
Model |  2930.03493         3  976.678311   Prob > F        =    0.0000
Residual |  41887.1456       404  103.681053   R-squared       =    0.0654
Total |  44817.1805       407  110.115923   Root MSE        =    10.182

------------------------------------------------------------------------------
math10 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ltotcomp |     21.155   4.055549     5.22   0.000     13.18238    29.12761
lstaff |   3.980018    4.18966     0.95   0.343    -4.256239    12.21628
lenroll |  -1.268046    .693204    -1.83   0.068    -2.630784    .0946912
_cons |  -207.6648   48.70313    -4.26   0.000     -303.408   -111.9216
------------------------------------------------------------------------------
(est2 stored)

. estout *, cells(b(star fmt(3)) se(par fmt(2))) stats(r2_a N, fmt(%9.3f %9.0g) label
> s(R-squared))   legend label collabels(none) varlabels(_cons Constant)

----------------------------------------------------
est1            est2
----------------------------------------------------
salary + benefits           0.000***
(0.00)
staff per 1000 stu~s        0.048
(0.04)
school enrollment          -0.000
(0.00)
log(totcomp)                               21.155***
(4.06)
log(staff)                                  3.980
(4.19)
log(enroll)                                -1.268
(0.69)
Constant                    2.274        -207.665***
(6.11)         (48.70)
----------------------------------------------------
R-squared                   0.047           0.058
N                             408             408
----------------------------------------------------
* p<0.05, ** p<0.01, *** p<0.001

. est clear

*example4.3. Collage GPA
. u gpa1.dta, clear
. reg colGPA hsGPA ACT skipped

Source |       SS           df       MS      Number of obs   =       141
-------------+----------------------------------   F(3, 137)       =     13.92
Model |  4.53313314         3  1.51104438   Prob > F        =    0.0000
Residual |  14.8729663       137  .108561798   R-squared       =    0.2336
Total |  19.4060994       140  .138614996   Root MSE        =    .32949

------------------------------------------------------------------------------
colGPA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
hsGPA |   .4118162   .0936742     4.40   0.000     .2265819    .5970505
ACT |   .0147202   .0105649     1.39   0.166    -.0061711    .0356115
skipped |  -.0831131   .0259985    -3.20   0.002    -.1345234   -.0317028
_cons |   1.389554   .3315535     4.19   0.000     .7339295    2.045178
------------------------------------------------------------------------------

*example4.4. Campus crime & enrollment
. u campus.dta, clear
. reg lcrime lenroll

Source |       SS           df       MS      Number of obs   =        97
-------------+----------------------------------   F(1, 95)        =    133.79
Model |  107.083654         1  107.083654   Prob > F        =    0.0000
Residual |  76.0358244        95  .800377098   R-squared       =    0.5848
Total |  183.119479        96  1.90749457   Root MSE        =    .89464

------------------------------------------------------------------------------
lcrime |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lenroll |    1.26976    .109776    11.57   0.000     1.051827    1.487693
_cons |   -6.63137    1.03354    -6.42   0.000    -8.683206   -4.579533
------------------------------------------------------------------------------

*example4.5. Housing prices
. u hprice2.dta, clear
. g ldist=ln(dist)
. reg  lprice lnox ldist rooms stratio

Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(4, 501)       =    175.86
Model |  49.3987586         4  12.3496897   Prob > F        =    0.0000
Residual |  35.1834663       501   .07022648   R-squared       =    0.5840
Total |   84.582225       505  .167489554   Root MSE        =      .265

------------------------------------------------------------------------------
lprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnox |  -.9535388   .1167417    -8.17   0.000    -1.182902   -.7241751
ldist |  -.1343395   .0431032    -3.12   0.002    -.2190247   -.0496542
rooms |   .2545271   .0185303    13.74   0.000     .2181203    .2909338
stratio |  -.0524511   .0058971    -8.89   0.000    -.0640372    -.040865
_cons |   11.08386   .3181113    34.84   0.000     10.45887    11.70886
------------------------------------------------------------------------------

*example4.6. Participation rates in 401k plans
. u 401k.dta, clear
. reg prate mrate age totemp

Source |       SS           df       MS      Number of obs   =     1,534
-------------+----------------------------------   F(3, 1530)      =     56.38
Model |  42642.5383         3  14214.1794   Prob > F        =    0.0000
Residual |  385743.001     1,530  252.119609   R-squared       =    0.0995
Total |  428385.539     1,533  279.442622   Root MSE        =    15.878

------------------------------------------------------------------------------
prate |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mrate |   5.442221    .524419    10.38   0.000     4.413565    6.470878
age |   .2691979   .0451449     5.96   0.000     .1806455    .3577503
totemp |  -.0001291   .0000367    -3.52   0.000     -.000201   -.0000572
_cons |   80.29405   .7777274   103.24   0.000     78.76853    81.81958
------------------------------------------------------------------------------

*example4.7. Job training (only for the year 1987 and for nonunionized firms)
. u jtrain.dta, clear
. d year union

storage   display    value
variable name   type    format     label      variable label
-------------------------------------------------------------------------------------
year            int     %9.0g                 1987, 1988, or 1989
union           byte    %9.0g                 =1 if unionized

. reg lscrap hrsemp lsales lemploy if year==1987 & union==0

Source |       SS           df       MS      Number of obs   =        29
-------------+----------------------------------   F(3, 25)        =      2.97
Model |  16.8426986         3  5.61423287   Prob > F        =    0.0513
Residual |  47.3369125        25   1.8934765   R-squared       =    0.2624
Total |  64.1796111        28  2.29212897   Root MSE        =     1.376

------------------------------------------------------------------------------
lscrap |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
hrsemp |  -.0292689   .0228048    -1.28   0.211    -.0762364    .0176985
lsales |  -.9620269   .4525181    -2.13   0.044    -1.894005   -.0300484
lemploy |   .7614704   .4074328     1.87   0.073    -.0776532    1.600594
_cons |   12.45837    5.68677     2.19   0.038      .746249    24.17049
------------------------------------------------------------------------------

.
*example4.8.
. u rdchem.dta, clear
. reg lrd lsales profmarg

Source |       SS           df       MS      Number of obs   =        32
-------------+----------------------------------   F(2, 29)        =    162.23
Model |  85.5967531         2  42.7983766   Prob > F        =    0.0000
Residual |  7.65051127        29  .263810733   R-squared       =    0.9180
Total |  93.2472644        31  3.00797627   Root MSE        =    .51363

------------------------------------------------------------------------------
lrd |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lsales |    1.08422    .060195    18.01   0.000     .9611073    1.207333
profmarg |   .0216557   .0127826     1.69   0.101    -.0044877    .0477991
_cons |  -4.378273   .4680185    -9.35   0.000    -5.335479   -3.421068
------------------------------------------------------------------------------

*example4.9. Parent's education on birth weight
. u bwght.dta, clear
. reg bwght cigs parity faminc motheduc fatheduc

Source |       SS           df       MS      Number of obs   =     1,191
-------------+----------------------------------   F(5, 1185)      =      9.55
Model |  18705.5567         5  3741.11135   Prob > F        =    0.0000
Residual |  464041.135     1,185  391.595895   R-squared       =    0.0387
Total |  482746.692     1,190  405.669489   Root MSE        =    19.789

------------------------------------------------------------------------------
bwght |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
cigs |  -.5959362   .1103479    -5.40   0.000    -.8124352   -.3794373
parity |   1.787603   .6594055     2.71   0.007     .4938709    3.081336
faminc |   .0560414   .0365616     1.53   0.126    -.0156913    .1277742
motheduc |  -.3704503   .3198551    -1.16   0.247    -.9979957    .2570951
fatheduc |   .4723944   .2826433     1.67   0.095    -.0821426    1.026931
_cons |   114.5243   3.728453    30.72   0.000     107.2092    121.8394
------------------------------------------------------------------------------

. test motheduc fatheduc

( 1)  motheduc = 0
( 2)  fatheduc = 0

F(  2,  1185) =    1.44
Prob > F =    0.2380

. reg bwght cigs parity faminc

Source |       SS           df       MS      Number of obs   =     1,388
-------------+----------------------------------   F(3, 1384)      =     16.63
Model |  19996.5211         3  6665.50703   Prob > F        =    0.0000
Residual |  554615.199     1,384  400.733525   R-squared       =    0.0348
Total |   574611.72     1,387  414.283864   Root MSE        =    20.018

------------------------------------------------------------------------------
bwght |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
cigs |  -.4771537    .091518    -5.21   0.000    -.6566827   -.2976247
parity |   1.616372    .603955     2.68   0.008     .4316058    2.801138
faminc |   .0979201   .0291868     3.35   0.001      .040665    .1551752
_cons |   114.2143     1.4693    77.73   0.000     111.3321    117.0966
------------------------------------------------------------------------------

*Exaploring further 4.5.
. u attend, clear
. eststo: reg atndrte priGPA

Source |       SS           df       MS      Number of obs   =       680
-------------+----------------------------------   F(1, 678)       =    151.35
Model |  36008.3571         1  36008.3571   Prob > F        =    0.0000
Residual |  161308.968       678  237.918832   R-squared       =    0.1825
Total |  197317.325       679   290.59989   Root MSE        =    15.425

------------------------------------------------------------------------------
atndrte |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
priGPA |   13.36898   1.086703    12.30   0.000     11.23527    15.50268
_cons |   47.12702   2.872615    16.41   0.000     41.48673    52.76732
------------------------------------------------------------------------------
(est1 stored)

. eststo: 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
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
------------------------------------------------------------------------------
(est2 stored)

. estout *, cells(b(star fmt(3)) se(par fmt(2))) stats(r2_a N, fmt(%9.3f %9.0g) label
> s(R-squared))   legend label collabels(none) varlabels(_cons Constant)

----------------------------------------------------
est1            est2
----------------------------------------------------
cumulative GPA pri~m       13.369***       17.261***
(1.09)          (1.08)
ACT score                                  -1.717***
(0.17)
Constant                   47.127***       75.700***
(2.87)          (3.88)
----------------------------------------------------
R-squared                   0.181           0.288
N                             680             680
----------------------------------------------------
* p<0.05, ** p<0.01, *** p<0.001

. est clear

. u meap93.dta, clear
. d bensal

storage   display    value
variable name   type    format     label      variable label
-------------------------------------------------------------------------------------
bensal          float   %9.0g                 benefits/salary
. eststo: qui reg lsalary bensal
(est1 stored)
. eststo: qui reg lsalary bensal lenrol lstaff
(est2 stored)
. eststo: qui reg lsalary bensal lenrol lstaff droprate gradrate
(est3 stored)
. estout *, cells(b(star fmt(3)) se(par fmt(2))) stats(r2_a N, fmt(%9.3f %9.0g) label
> s(R-squared))    varlabels(_cons Constant) ti("Compare to Table 4.1 on the textbook
> ")

Compare to Table 4.1 in the textbook
------------------------------------------------------------
est1            est2            est3
b/se            b/se            b/se
------------------------------------------------------------
bensal             -0.825***       -0.605***       -0.589***
(0.20)          (0.17)          (0.16)
lenroll                             0.087***        0.088***
(0.01)          (0.01)
lstaff                             -0.222***       -0.218***
(0.05)          (0.05)
droprate                                           -0.000
(0.00)
(0.00)
Constant           10.523***       10.844***       10.738***
(0.04)          (0.25)          (0.26)
------------------------------------------------------------
R-squared           0.038           0.348           0.353
N                     408             408             408
------------------------------------------------------------

. est clear

. log close
name:  SN
log:  Wooldridge\intro-econx\iexample4.smcl
log type:  smcl
closed on:   6 Jan 2019, 17:17:20
-------------------------------------------------------------------------------------
```