Classical Linear Regression Model Handout
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 Number of obs = 935
------+------F( 5, 929) = 43.02
Model | 182312181 5 36462436.1 Prob > F = 0.0000
Residual | 787481197 929 847665.444 R-squared = 0.1880
------+------Adj R-squared = 0.1836
Total | 969793378 934 1038322.67 Root MSE = 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 Number of obs = 935
------+------F( 5, 929) = 47.42
Model | 33.6835747 5 6.73671494 Prob > F = 0.0000
Residual | 131.974611 929 .142060937 R-squared = 0.2033
------+------Adj R-squared = 0.1990
Total | 165.658185 934 .177364224 Root MSE = .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