CLASSICAL LINEAR REGRESSION MODEL HANDOUT
Data
Dataset: Wage
The data file WAGE contains a cross-section of 935 males. The variables are as follows. WAGE
= monthly earnings in dollars (year 2007 dollars). HOURS = average hours worked per week. IQ
= IQ score. KWW = knowledge of world work score. EDU = years of education. EXPER = years
of work experience. TENURE = years with current employer. AGE = age in years. MARRIED =
dummy variable for marital status (1 if married, 0 otherwise). BLACK = dummy variable for
race (1 if black, 0 otherwise). SOUTH = dummy variable for region of country where worker
lives (1 if individual lives in south, 0 otherwise). URBAN = dummy variable for urban area (1 if
individual lives in Standard Metropolitan Statistical Area, 0 otherwise). SIBS = number of
siblings. BRTHORD = birth order. MEDUC = mother’s years of education. FEDUC = father’s
years of education. Note that missing observations are denoted by the number -999.
Descriptive Statistics
Note: When cutting and pasting Stata results use Courier New font.
summarize wage edu exper married iq tenure age black south urban
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------wage |
935
2414.017
1018.981
290
7757
edu |
935
13.46845
2.196654
9
18
exper |
935
11.56364
4.374586
1
23
married |
935
.8930481
.3092174
0
1
iq |
935
101.2824
15.05264
50
145
-------------+-------------------------------------------------------tenure |
935
7.234225
5.075206
0
22
age |
935
33.08021
3.107803
28
38
black |
935
.1283422
.3346495
0
1
south |
935
.3411765
.4743582
0
1
urban |
935
.7176471
.4503851
0
1
. correlate wage edu exper married iq tenure
(obs=935)
|
wage
edu
exper married
iq
tenure
-------------+-----------------------------------------------------wage |
1.0000
edu |
0.3271
1.0000
exper |
0.0022 -0.4556
1.0000
married |
0.1366 -0.0586
0.1063
1.0000
iq |
0.3091
0.5157 -0.2249 -0.0147
1.0000
tenure |
0.1283 -0.0362
0.2437
0.0726
0.0422
1.0000
Descriptive Statistics for Educational Subsamples
summarize wage edu exper married iq tenure if edu<12
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------wage |
88
1951.114
743.9319
504
4722
edu |
88
10.375
.6833403
9
11
exper |
88
15.05682
3.925624
1
23
married |
88
.9318182
.2535021
0
1
iq |
88
86.10227
12.13908
59
118
-------------+-------------------------------------------------------tenure |
88
6.829545
5.217613
0
16
summarize wage edu exper married iq tenure if edu==12
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------wage |
393
2173.929
817.4633
290
6300
edu |
393
12
0
12
12
exper |
393
13.14758
4.233443
1
22
married |
393
.8982188
.3027457
0
1
iq |
393
96.39695
13.32981
50
131
-------------+-------------------------------------------------------tenure |
393
7.862595
5.483412
0
22
summarize wage edu exper married iq tenure if edu>12
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------wage |
454
2711.573
1129.56
587
7757
edu |
454
15.33921
1.619256
13
18
exper |
454
9.515419
3.498152
1
21
married |
454
.8810573
.3240782
0
1
iq |
454
108.4537
12.96527
54
145
-------------+-------------------------------------------------------tenure |
454
6.768722
4.611799
0
18
Regression Results for Linear in Variables Functional Form
. regress wage edu exper married iq tenure
Source |
SS
df
MS
-------------+-----------------------------Model |
182312181
5 36462436.1
Residual |
787481197
929 847665.444
-------------+-----------------------------Total |
969793378
934 1038322.67
Number of obs
F( 5,
929)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
935
43.02
0.0000
0.1880
0.1836
920.69
-----------------------------------------------------------------------------wage |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------edu |
145.7489
17.54229
8.31
0.000
111.3217
180.176
exper |
35.03248
8.023559
4.37
0.000
19.28608
50.77889
married |
446.2199
98.11792
4.55
0.000
253.6614
638.7784
iq |
12.13539
2.342102
5.18
0.000
7.538965
16.73181
tenure |
17.18767
6.165825
2.79
0.005
5.087112
29.28823
_cons | -1706.033
300.7636
-5.67
0.000
-2296.288
-1115.778
------------------------------------------------------------------------------
Elasticity Estimates
. mfx, eyex
Elasticities after regress
y = Fitted values (predict)
= 2414.0171
-----------------------------------------------------------------------------variable |
ey/ex
Std. Err.
z
P>|z| [
95% C.I.
]
X
---------+-------------------------------------------------------------------edu |
.813172
.0984
8.26
0.000
.620317 1.00603
13.4684
exper |
.1678128
.03849
4.36
0.000
.092371 .243255
11.5636
married |
.1650758
.03636
4.54
0.000
.093819 .236333
.893048
iq |
.5091516
.09847
5.17
0.000
.316154 .702149
101.282
tenure |
.0515073
.01849
2.79
0.005
.01527 .087744
7.23422
Regression Results for Log Linear Functional Form
. regress lwage edu exper married iq tenure
Source |
SS
df
MS
-------------+-----------------------------Model | 33.6835747
5 6.73671494
Residual | 131.974611
929 .142060937
-------------+-----------------------------Total | 165.658185
934 .177364224
Number of obs
F( 5,
929)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
935
47.42
0.0000
0.2033
0.1990
.37691
-----------------------------------------------------------------------------lwage |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------edu |
.056293
.0071814
7.84
0.000
.0421993
.0703867
exper |
.0142331
.0032847
4.33
0.000
.0077869
.0206794
married |
.196096
.0401674
4.88
0.000
.1172667
.2749253
iq |
.0053931
.0009588
5.62
0.000
.0035115
.0072748
tenure |
.0117732
.0025242
4.66
0.000
.0068195
.0167269
_cons |
5.973971
.1231262
48.52
0.000
5.732333
6.215608
------------------------------------------------------------------------------
Elasticity Estimates
. mfx, dyex
Elasticities after regress
y = Fitted values (predict)
= 7.7032598
-----------------------------------------------------------------------------variable |
dy/ex
Std. Err.
z
P>|z| [
95% C.I.
]
X
---------+-------------------------------------------------------------------edu |
.7581793
.09672
7.84
0.000
.568606 .947753
13.4684
exper |
.1645866
.03798
4.33
0.000
.090142 .239031
11.5636
married |
.1751232
.03587
4.88
0.000
.104817
.24543
.893048
iq |
.5462301
.09711
5.62
0.000
.355898 .736562
101.282
tenure |
.08517
.01826
4.66
0.000
.04938
.12096
7.23422