Chapter 02 - The Simple Regression Model#
import stata_setup
stata_setup.config("C:/Program Files/Stata18/", "se" ,splash=False)
Example 2.3. CEO Salary & Return on Equity;#
\(salary = \beta_0 + \beta_1 roe + u\)
%%stata
use ceosal1.dta
regress salary roe
. use ceosal1.dta
. regress salary roe
Source | SS df MS Number of obs = 209
-------------+---------------------------------- F(1, 207) = 2.77
Model | 5166419.04 1 5166419.04 Prob > F = 0.0978
Residual | 386566563 207 1867471.32 R-squared = 0.0132
-------------+---------------------------------- Adj R-squared = 0.0084
Total | 391732982 208 1883331.64 Root MSE = 1366.6
------------------------------------------------------------------------------
salary | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
roe |
18.50119 11.12325 1.66 0.098 -3.428196 40.43057
_cons | 963.1913 213.2403 4.52 0.000 542.7902 1383.592
------------------------------------------------------------------------------
.
Example 2.4#
%%stata
u wage1.dta, clear
sum wage educ
reg wage educ
. u wage1.dta, clear
. sum wage educ
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
wage | 526 5.896103 3.693086 .53 24.98
educ | 526 12.56274 2.769022 0 18
. reg wage educ
Source | SS df MS Number of obs = 526
-------------+---------------------------------- F(1, 524) = 103.36
Model | 1179.73204 1 1179.73204 Prob > F = 0.0000
Residual | 5980.68225 524 11.4135158 R-squared = 0.1648
-------------+---------------------------------- Adj R-squared = 0.1632
Total | 7160.41429 525 13.6388844 Root MSE = 3.3784
------------------------------------------------------------------------------
wage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .5413593 .053248 10.17 0.000 .4367534 .6459651
_cons | -.9048516 .6849678 -1.32 0.187 -2.250472 .4407687
------------------------------------------------------------------------------
.
Example 2.5#
%%stata
u vote1.dta, clear
reg voteA shareA
. u vote1.dta, clear
. reg voteA shareA
Source | SS df MS Number of obs = 173
-------------+---------------------------------- F(1, 171) = 1017.66
Model | 41486.2307 1 41486.2307 Prob > F = 0.0000
Residual | 6971.01783 171 40.7661862 R-squared = 0.8561
-------------+---------------------------------- Adj R-squared = 0.8553
Total | 48457.2486 172 281.728189 Root MSE = 6.3848
------------------------------------------------------------------------------
voteA | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
shareA | .4638269 .0145397 31.90 0.000 .4351266 .4925272
_cons | 26.81221 .8872146 30.22 0.000 25.06091 28.56352
------------------------------------------------------------------------------
.
Example 2.6#
Table 2.2
%%stata
use ceosal1.dta, clear
regress salary roe
esttab, r2
predict salaryhat, xb
predict uhat, residual
list roe salary salaryhat uhat in 1/15, table separator(15)
. use ceosal1.dta, clear
. regress salary roe
Source | SS df MS Number of obs = 209
-------------+---------------------------------- F(1, 207) = 2.77
Model | 5166419.04 1 5166419.04 Prob > F = 0.0978
Residual | 386566563 207 1867471.32 R-squared = 0.0132
-------------+---------------------------------- Adj R-squared = 0.0084
Total | 391732982 208 1883331.64 Root MSE = 1366.6
------------------------------------------------------------------------------
salary | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
roe | 18.50119 11.12325 1.66 0.098 -3.428196 40.43057
_cons | 963.1913 213.2403 4.52 0.000 542.7902 1383.592
------------------------------------------------------------------------------
. esttab, r2
----------------------------
(1)
salary
----------------------------
roe 18.50
(1.66)
_cons 963.2***
(4.52)
----------------------------
N 209
R-sq 0.013
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. predict salaryhat, xb
. predict uhat, residual
. list roe salary salaryhat uhat in 1/15, table separator(15)
+--------------------------------------+
| roe salary salary~t uhat |
|--------------------------------------|
1. | 14.1 1095 1224.058 -129.0581 |
2. | 10.9 1001 1164.854 -163.8543 |
3. | 23.5 1122 1397.969 -275.9692 |
4. | 5.9 578 1072.348 -494.3483 |
5. | 13.8 1368 1218.508 149.4923 |
6. | 20 1145 1333.215 -188.2151 |
7. | 16.4 1078 1266.611 -188.6108 |
8. | 16.3 1094 1264.761 -170.7607 |
9. | 10.5 1237 1157.454 79.5462 |
10. | 26.3 833 1449.773 -616.7725 |
11. | 25.9 567 1442.372 -875.3721 |
12. | 26.8 933 1459.023 -526.0231 |
13. | 14.8 1339 1237.009 101.9911 |
14. | 22.3 937 1375.768 -438.7678 |
15. | 56.3 2011 2004.808 6.191886 |
+--------------------------------------+
.
Example 2.7 Wage & Education#
%%stata
u wage1.dta, clear
sum wage
qui reg wage educ
esttab, r2
display as text "if educ=12.56, then wage_hat = " as result -.90 + .54*12.56
. u wage1.dta, clear
. sum wage
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
wage | 526 5.896103 3.693086 .53 24.98
. qui reg wage educ
. esttab, r2
----------------------------
(1)
wage
----------------------------
educ 0.541***
(10.17)
_cons -0.905
(-1.32)
----------------------------
N 526
R-sq 0.165
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. display as text "if educ=12.56, then wage_hat = " as result -.90 + .54*12.56
if educ=12.56, then wage_hat = 5.8824
.
Example 2.8. CEO Salary - R-squared#
%%stata
use ceosal1.dta, clear
qui regress salary roe
esttab, r2
. use ceosal1.dta, clear
. qui regress salary roe
. esttab, r2
----------------------------
(1)
salary
----------------------------
roe 18.50
(1.66)
_cons 963.2***
(4.52)
----------------------------
N 209
R-sq 0.013
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
.
Example 2.9 Voting outcome - R-squared. See ## Example 2.5 for details.#
%%stata
u vote1.dta, clear
qui reg voteA shareA
esttab, r2
. u vote1.dta, clear
. qui reg voteA shareA
. esttab, r2
----------------------------
(1)
voteA
----------------------------
shareA 0.464***
(31.90)
_cons 26.81***
(30.22)
----------------------------
N 173
R-sq 0.856
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
.
Example 2.3 in session2.4 Units of measurement & functional form#
%%stata
use ceosal1.dta, clear
g salardol=1000*salary
eststo: regress salardol roe
eststo: regress salary roe
esttab, r2
est clear
. use ceosal1.dta, clear
. g salardol=1000*salary
. eststo: regress salardol roe
Source | SS df MS Number of obs = 209
-------------+---------------------------------- F(1, 207) = 2.77
Model | 5.1664e+12 1 5.1664e+12 Prob > F = 0.0978
Residual | 3.8657e+14 207 1.8675e+12 R-squared = 0.0132
-------------+---------------------------------- Adj R-squared = 0.0084
Total | 3.9173e+14 208 1.8833e+12 Root MSE = 1.4e+06
------------------------------------------------------------------------------
salardol | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
roe | 18501.19 11123.25 1.66 0.098 -3428.196 40430.57
_cons | 963191.3 213240.3 4.52 0.000 542790.2 1383592
------------------------------------------------------------------------------
(est1 stored)
. eststo: regress salary roe
Source | SS df MS Number of obs = 209
-------------+---------------------------------- F(1, 207) = 2.77
Model | 5166419.04 1 5166419.04 Prob > F = 0.0978
Residual | 386566563 207 1867471.32 R-squared = 0.0132
-------------+---------------------------------- Adj R-squared = 0.0084
Total | 391732982 208 1883331.64 Root MSE = 1366.6
------------------------------------------------------------------------------
salary | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
roe | 18.50119 11.12325 1.66 0.098 -3.428196 40.43057
_cons | 963.1913 213.2403 4.52 0.000 542.7902 1383.592
------------------------------------------------------------------------------
(est2 stored)
. esttab, r2
--------------------------------------------
(1) (2)
salardol salary
--------------------------------------------
roe 18501.2 18.50
(1.66) (1.66)
_cons 963191.3*** 963.2***
(4.52) (4.52)
--------------------------------------------
N 209 209
R-sq 0.013 0.013
--------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
.
Example 2.10 A log wage equation (log-lin model; semi-elasticity )#
%%stata
u wage1.dta, clear
sum wage lwage educ
reg lwage educ
esttab, r2
. u wage1.dta, clear
. sum wage lwage educ
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
wage | 526 5.896103 3.693086 .53 24.98
lwage | 526 1.623268 .5315382 -.6348783 3.218076
educ | 526 12.56274 2.769022 0 18
. reg lwage educ
Source | SS df MS Number of obs = 526
-------------+---------------------------------- F(1, 524) = 119.58
Model | 27.5606288 1 27.5606288 Prob > F = 0.0000
Residual | 120.769123 524 .230475425 R-squared = 0.1858
-------------+---------------------------------- Adj R-squared = 0.1843
Total | 148.329751 525 .28253286 Root MSE = .48008
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .0827444 .0075667 10.94 0.000 .0678796 .0976091
_cons | .5837727 .0973358 6.00 0.000 .3925563 .7749891
------------------------------------------------------------------------------
. esttab, r2
----------------------------
(1)
lwage
----------------------------
educ 0.0827***
(10.94)
_cons 0.584***
(6.00)
----------------------------
N 526
R-sq 0.186
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
.
Example 2.11 Ceo Salary & Fim Sales (log-log model; elasticity)#
%%stata
use ceosal1.dta, clear
regress lsalary lsales
esttab, r2
. use ceosal1.dta, clear
. regress lsalary lsales
Source | SS df MS Number of obs = 209
-------------+---------------------------------- F(1, 207) = 55.30
Model | 14.0661688 1 14.0661688 Prob > F = 0.0000
Residual | 52.6559944 207 .254376785 R-squared = 0.2108
-------------+---------------------------------- Adj R-squared = 0.2070
Total | 66.7221632 208 .320779631 Root MSE = .50436
------------------------------------------------------------------------------
lsalary | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lsales | .2566717 .0345167 7.44 0.000 .1886224 .3247209
_cons | 4.821997 .2883396 16.72 0.000 4.253538 5.390455
------------------------------------------------------------------------------
. esttab, r2
----------------------------
(1)
lsalary
----------------------------
lsales 0.257***
(7.44)
_cons 4.822***
(16.72)
----------------------------
N 209
R-sq 0.211
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
.
Example 2.12 Student math performance#
%%stata
u meap93.dta, clear
reg math10 lnchprg
esttab, r2
.
. u meap93.dta, clear
. reg math10 lnchprg
Source | SS df MS Number of obs = 408
-------------+---------------------------------- F(1, 406) = 83.77
Model | 7665.26597 1 7665.26597 Prob > F = 0.0000
Residual | 37151.9145 406 91.5071786 R-squared = 0.1710
-------------+---------------------------------- Adj R-squared = 0.1690
Total | 44817.1805 407 110.115923 Root MSE = 9.5659
------------------------------------------------------------------------------
math10 | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lnchprg | -.3188643 .0348393 -9.15 0.000 -.3873523 -.2503763
_cons | 32.14271 .9975824 32.22 0.000 30.18164 34.10378
------------------------------------------------------------------------------
. esttab, r2
----------------------------
(1)
math10
----------------------------
lnchprg -0.319***
(-9.15)
_cons 32.14***
(32.22)
----------------------------
N 408
R-sq 0.171
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
.