___ ____ ____ ____ ____ tm
/__ / ____/ / ____/
___/ / /___/ / /___/ 5.0 Copyright 1984-1997
Statistics/Data Analysis Stata Corporation
. * program to illustrate effects of ill-conditioning on OLS
. * x1 is a trend; x2 is a trend + eps, where eps(0,sigma^2).
. * Note the regression results as sigma -> 0.
. *
. * CFB ec761 Fall 1997
. *
. set obs 100
obs was 0, now 100
. gen x1=_n/100.0
. program define conditio
1. local i = 0
2. while `i'<`1' {
3. scalar sigma=10.0^-`i'
4. dis " "
5. dis "*** sigma = " sigma " ***"
6. gen eps=sigma*invnorm(uniform())
7. gen eps2=invnorm(uniform())
8. gen x2=x1+eps
9. gen y=2.0+10.0*x1+10.0*x2+eps2
10. correlate x1 x2
11. regress y x1 x2
12. local i=`i'+1
13. drop eps
14. drop eps2
15. drop x2
16. drop y
17. }
18. end
. conditio 5
*** sigma = 1 ***
(obs=100)
| x1 x2
--------+------------------
x1| 1.0000
x2| 0.3241 1.0000
Source | SS df MS Number of obs = 100
---------+------------------------------ F( 2, 97) = 5784.99
Model | 11960.0944 2 5980.04718 Prob > F = 0.0000
Residual | 100.270545 97 1.03371696 R-squared = 0.9917
---------+------------------------------ Adj R-squared = 0.9915
Total | 12060.3649 99 121.821868 Root MSE = 1.0167
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | 10.12255 .3723146 27.188 0.000 9.383608 10.86149
x2 | 10.01934 .1117699 89.643 0.000 9.797503 10.24117
_cons | 1.921866 .2052406 9.364 0.000 1.51452 2.329212
------------------------------------------------------------------------------
*** sigma = .1 ***
(obs=100)
| x1 x2
--------+------------------
x1| 1.0000
x2| 0.9467 1.0000
Source | SS df MS Number of obs = 100
---------+------------------------------ F( 2, 97) = 1956.23
Model | 3426.83467 2 1713.41733 Prob > F = 0.0000
Residual | 84.9599842 97 .875876126 R-squared = 0.9758
---------+------------------------------ Adj R-squared = 0.9753
Total | 3511.79465 99 35.4726732 Root MSE = .93588
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | 10.39441 1.006406 10.328 0.000 8.396975 12.39185
x2 | 9.781533 .9688272 10.096 0.000 7.858679 11.70439
_cons | 1.864677 .1889523 9.869 0.000 1.489659 2.239695
------------------------------------------------------------------------------
*** sigma = .01 ***
(obs=100)
| x1 x2
--------+------------------
x1| 1.0000
x2| 0.9993 1.0000
Source | SS df MS Number of obs = 100
---------+------------------------------ F( 2, 97) = 1504.37
Model | 3507.75671 2 1753.87836 Prob > F = 0.0000
Residual | 113.087978 97 1.16585544 R-squared = 0.9688
---------+------------------------------ Adj R-squared = 0.9681
Total | 3620.84469 99 36.5741888 Root MSE = 1.0797
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | -2.91624 10.26391 -0.284 0.777 -23.28726 17.45478
x2 | 23.46838 10.28 2.283 0.025 3.065425 43.87133
_cons | 1.669024 .2183565 7.644 0.000 1.235646 2.102401
------------------------------------------------------------------------------
*** sigma = .001 ***
(obs=100)
| x1 x2
--------+------------------
x1| 1.0000
x2| 1.0000 1.0000
Source | SS df MS Number of obs = 100
---------+------------------------------ F( 2, 97) = 2002.94
Model | 3392.66099 2 1696.33049 Prob > F = 0.0000
Residual | 82.1511384 97 .846918953 R-squared = 0.9764
---------+------------------------------ Adj R-squared = 0.9759
Total | 3474.81213 99 35.0991124 Root MSE = .92028
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | 196.9501 89.33464 2.205 0.030 19.64554 374.2546
x2 | -176.8903 89.38894 -1.979 0.051 -354.3026 .5219925
_cons | 1.907223 .1871233 10.192 0.000 1.535835 2.278611
------------------------------------------------------------------------------
*** sigma = .0001 ***
(obs=100)
| x1 x2
--------+------------------
x1| 1.0000
x2| 1.0000 1.0000
Source | SS df MS Number of obs = 100
---------+------------------------------ F( 2, 97) = 1496.37
Model | 3420.77919 2 1710.3896 Prob > F = 0.0000
Residual | 110.87328 97 1.1430235 R-squared = 0.9686
---------+------------------------------ Adj R-squared = 0.9680
Total | 3531.65247 99 35.6732573 Root MSE = 1.0691
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | -54.96045 1065.972 -0.052 0.959 -2170.619 2060.698
x2 | 75.22354 1065.992 0.071 0.944 -2040.476 2190.923
_cons | 1.839889 .2174912 8.460 0.000 1.408229 2.271548
------------------------------------------------------------------------------
. exit,clear