## Verbeek 5ed. Chapter 2 - Linear Regression

### Examples

```----------------------------------------------------------------------------------------------------
name:  SN
log:  \5iexample2_s.smcl
log type:  smcl
opened on:   5 Jun 2020, 11:33:46
**********************************************
* Solomon Negash - Examples
* Verbeek(2017). A Giude To Modern Econometrics. 5ed.
* STATA Program, version 16.1.

* Chapter 2  - Introduction to Linear Regression
******************** **** *********************

*Figure 2.1 Simple linear regression: fitted line and observation points, hypothetical data
clear
set seed 123
set obs 100
g x = uniform()
g eps = runiform()
g y = x + .5 + eps
twoway (scatter y x) (lfit y x), title("Figure 2.1 Simple linear regression: fitted line and
observation points", size(*.8)) legend(off)

*Table 2.1 Individual Wages

use "Data/Wages1.dta", clear

reg wage male

Source |       SS           df       MS      Number of obs   =     3,294
-------------+----------------------------------   F(1, 3292)      =    107.93
Model |  1117.26971         1  1117.26971   Prob > F        =    0.0000
Residual |  34076.9173     3,292   10.351433   R-squared       =    0.0317
Total |   35194.187     3,293  10.6875758   Root MSE        =    3.2174

------------------------------------------------------------------------------
wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
male |   1.166097   .1122422    10.39   0.000     .9460258    1.386169
_cons |   5.146924   .0812248    63.37   0.000     4.987668     5.30618
------------------------------------------------------------------------------

* Table 2.2

reg wage male school exper

Source |       SS           df       MS      Number of obs   =     3,294
-------------+----------------------------------   F(3, 3290)      =    167.63
Model |  4666.31659         3  1555.43886   Prob > F        =    0.0000
Residual |  30527.8705     3,290  9.27898798   R-squared       =    0.1326
Total |   35194.187     3,293  10.6875758   Root MSE        =    3.0461

------------------------------------------------------------------------------
wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
male |   1.344369   .1076759    12.49   0.000      1.13325    1.555487
school |   .6387977   .0327958    19.48   0.000     .5744954       .7031
exper |   .1248255   .0237628     5.25   0.000     .0782342    .1714167
_cons |  -3.380018   .4649765    -7.27   0.000    -4.291691   -2.468346
------------------------------------------------------------------------------

test school=exper=0

( 1)  school - exper = 0
( 2)  school = 0

F(  2,  3290) =  191.24
Prob > F =    0.0000

*Table 2.3 CAPM regression (without intercept)

u "Data/Capm5.dta", clear

reg foodrf rmrf, nocons

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(1, 659)       =    948.26
Model |   7500.0027         1   7500.0027   Prob > F        =    0.0000
Residual |   5212.1658       659  7.90920454   R-squared       =    0.5900
Total |  12712.1685       660  19.2608614   Root MSE        =    2.8123

------------------------------------------------------------------------------
foodrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   .7548109   .0245117    30.79   0.000     .7066804    .8029414
------------------------------------------------------------------------------

reg durblrf rmrf, nocons

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(1, 659)       =   1584.65
Model |  14954.0435         1  14954.0435   Prob > F        =    0.0000
Residual |   6218.8779       659  9.43684052   R-squared       =    0.7063
Total |  21172.9214       660  32.0801839   Root MSE        =    3.0719

------------------------------------------------------------------------------
durblrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   1.065827   .0267745    39.81   0.000     1.013254    1.118401
------------------------------------------------------------------------------

reg cnstrrf rmrf, nocons

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(1, 659)       =   2262.26
Model |  18134.9986         1  18134.9986   Prob > F        =    0.0000
Residual |  5282.75449       659  8.01631941   R-squared       =    0.7744
Total |  23417.7531       660  35.4814441   Root MSE        =    2.8313

------------------------------------------------------------------------------
cnstrrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   1.173725   .0246771    47.56   0.000     1.125269     1.22218
------------------------------------------------------------------------------

*Table 2.4 CAPM regression (with intercept)

reg foodrf rmrf

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(1, 658)       =    926.56
Model |  7245.32113         1  7245.32113   Prob > F        =    0.0000
Residual |  5145.27877       658   7.8195726   R-squared       =    0.5847
Total |  12390.5999       659  18.8021243   Root MSE        =    2.7963

------------------------------------------------------------------------------
foodrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |    .746687   .0245302    30.44   0.000     .6985201    .7948539
_cons |   .3204065   .1095524     2.92   0.004     .1052921    .5355209
------------------------------------------------------------------------------

reg durblrf rmrf

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(1, 658)       =   1573.23
Model |  14846.5253         1  14846.5253   Prob > F        =    0.0000
Residual |  6209.53493       658  9.43698318   R-squared       =    0.7051
Total |  21056.0602       659  31.9515329   Root MSE        =     3.072

------------------------------------------------------------------------------
durblrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   1.068863    .026948    39.66   0.000     1.015949    1.121778
_cons |  -.1197493   .1203502    -1.00   0.320    -.3560661    .1165675
------------------------------------------------------------------------------

reg cnstrrf rmrf

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(1, 658)       =   2232.68
Model |  17923.4422         1  17923.4422   Prob > F        =    0.0000
Residual |  5282.27559       658  8.02777446   R-squared       =    0.7724
Total |  23205.7178       659  35.2135323   Root MSE        =    2.8333

------------------------------------------------------------------------------
cnstrrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   1.174412   .0248546    47.25   0.000     1.125608    1.223216
_cons |  -.0271114   .1110013    -0.24   0.807    -.2450708     .190848
------------------------------------------------------------------------------

*Table 2.5 CAPM regressions (with intercept and January dummy)

reg foodrf rmrf jan

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(2, 657)       =    469.94
Model |  7292.79687         2  3646.39843   Prob > F        =    0.0000
Residual |  5097.80303       657  7.75921314   R-squared       =    0.5886
Total |  12390.5999       659  18.8021243   Root MSE        =    2.7855

------------------------------------------------------------------------------
foodrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   .7489516   .0244525    30.63   0.000     .7009372    .7969661
jan |  -.9710764   .3925784    -2.47   0.014    -1.741936   -.2002168
_cons |   .4001843   .1137949     3.52   0.000     .1767388    .6236297
------------------------------------------------------------------------------

reg durblrf rmrf jan

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(2, 657)       =    785.48
Model |  14846.8533         2  7423.42665   Prob > F        =    0.0000
Residual |   6209.2069       657  9.45084764   R-squared       =    0.7051
Total |  21056.0602       659  31.9515329   Root MSE        =    3.0742

------------------------------------------------------------------------------
durblrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   1.068675   .0269867    39.60   0.000     1.015685    1.121666
jan |   .0807189   .4332643     0.19   0.852    -.7700308    .9314686
_cons |  -.1263806   .1255883    -1.01   0.315    -.3729835    .1202222
------------------------------------------------------------------------------

reg cnstrrf rmrf jan

Source |       SS           df       MS      Number of obs   =       660
-------------+----------------------------------   F(2, 657)       =   1119.70
Model |  17941.8761         2  8970.93804   Prob > F        =    0.0000
Residual |  5263.84168       657  8.01193559   R-squared       =    0.7732
Total |  23205.7178       659  35.2135323   Root MSE        =    2.8305

------------------------------------------------------------------------------
cnstrrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   1.173001   .0248475    47.21   0.000     1.124211    1.221791
jan |   .6050988   .3989204     1.52   0.130    -.1782139    1.388412
_cons |  -.0768226   .1156332    -0.66   0.507    -.3038778    .1502325
------------------------------------------------------------------------------

*Table 2.6 CAPM regression (with intercept) Madoff's returns

reg fslrf rmrf

Source |       SS           df       MS      Number of obs   =       215
-------------+----------------------------------   F(1, 213)       =     14.54
Model |  6.44404169         1  6.44404169   Prob > F        =    0.0002
Residual |  94.4286913       213  .443327189   R-squared       =    0.0639
Total |  100.872733       214  .471367911   Root MSE        =    .66583

------------------------------------------------------------------------------
fslrf |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rmrf |   .0408859    .010724     3.81   0.000     .0197471    .0620246
_cons |   .5049538   .0456993    11.05   0.000      .414873    .5950347
------------------------------------------------------------------------------

*Table 2.7 Alternative specifications with dummy variables

u "Data/Wages1.dta", clear

g female = 0

replace female=1 if male==0

reg wage male

Source |       SS           df       MS      Number of obs   =     3,294
-------------+----------------------------------   F(1, 3292)      =    107.93
Model |  1117.26971         1  1117.26971   Prob > F        =    0.0000
Residual |  34076.9173     3,292   10.351433   R-squared       =    0.0317
Total |   35194.187     3,293  10.6875758   Root MSE        =    3.2174

------------------------------------------------------------------------------
wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
male |   1.166097   .1122422    10.39   0.000     .9460258    1.386169
_cons |   5.146924   .0812248    63.37   0.000     4.987668     5.30618
------------------------------------------------------------------------------

reg wage female

Source |       SS           df       MS      Number of obs   =     3,294
-------------+----------------------------------   F(1, 3292)      =    107.93
Model |  1117.26971         1  1117.26971   Prob > F        =    0.0000
Residual |  34076.9173     3,292   10.351433   R-squared       =    0.0317
Total |   35194.187     3,293  10.6875758   Root MSE        =    3.2174

------------------------------------------------------------------------------
wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
female |  -1.166097   .1122422   -10.39   0.000    -1.386169   -.9460258
_cons |   6.313021    .077465    81.50   0.000     6.161137    6.464906
------------------------------------------------------------------------------

reg wage male female, nocons

Source |       SS           df       MS      Number of obs   =     3,294
-------------+----------------------------------   F(2, 3292)      =   5328.38
Model |  110312.663         2  55156.3313   Prob > F        =    0.0000
Residual |  34076.9173     3,292   10.351433   R-squared       =    0.7640
Total |   144389.58     3,294  43.8341166   Root MSE        =    3.2174

------------------------------------------------------------------------------
wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
male |   6.313021    .077465    81.50   0.000     6.161137    6.464906
female |   5.146924   .0812248    63.37   0.000     4.987668     5.30618
------------------------------------------------------------------------------

log close
name:  SN
log:  \5iexample2_s.smcl
log type:  smcl
closed on:   5 Jun 2020, 11:33:47
----------------------------------------------------------------------------------------------------

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