. do "C:\Users\hstryhn\AppData\Local\Temp\STD5a2c_000000.tmp"

. * do-file for lecture 1b of VHM 802/812, Winter 2021
. version 16 /* works also with versions 14-15 */

. set more off

. cd "r:\"
r:\

.
. use daisy2red, clear

. * multiple regression model with parity, twin, vag_disch
. regress milk120 parity twin vag_disch

Source | SS df MS Number of obs = 1,536

+
F(3, 1532) = 90.76
Model | 112904721 3 37634906.9 Prob > F = 0.0000
Residual | 635235472 1,532 414644.564 R-squared = 0.1509

+
Adj R-squared = 0.1493
Total | 748140192 1,535 487387.748 Root MSE = 643.93

+

--------

milk120 | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | 180.893 11.02613 16.41 0.000 159.2651 202.5209
twin | -197.0058 125.9608 -1.56 0.118 -444.0797 50.06806
vag_disch | 199.717 74.45821 2.68 0.007 53.66624 345.7678
_cons | 2713.174 34.68445 78.22 0.000 2645.14 2781.208

+

--------

. * predictions, based on fitted values
. predict fit, xb

. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (line fit parity)

. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (line fit parity, sort)

. * these do not work because fitted values not on a single line (due to other predictors)
. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (lfit fit parity)

. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (lowess fit parity)

. * both commands produce a line/curve that is wrong
. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (line fit parity, sort) if twin==0&vag_disch==0

. * ok but for a single group only
. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (line fit parity if twin==0&vag_disch==0, sort) (line fit parity if twin==0&vag_disch==1) (line fit parity if twin==1&vag_disch==0) (line fit parity if twin==1&vag_disch==1)

. * ok all groups
.
. * alternative approach: predictions based on fitted values for 8 constructed settings
. set obs 1582 /* adding 8 rows to the worksheet */

number of observations (_N) was 1,574,
now 1,582

. browse milk120 fit parity twin vag_disch in 1570/1582

. replace parity=1 in 1575/1578
(4 real changes made)

. replace parity=7 in 1579/1582
(4 real changes made)

. replace twin=0 in 1575/1582
(8 real changes made)

. replace twin=1 if mod(_n,2)==0 in 1575/1582
(4 real changes made)

. replace vag_disch=0 in 1575/1582
(8 real changes made)

. replace vag_disch=1 if _n==1577|_n==1578|_n==1581|_n==1582
(4 real changes made)

. drop fit

. predict fit, xb /* fit now includes extra rows */

. predict std_fit, stdp

. twoway (line fit parity if twin==0&vag_disch==0 in 1575/1582) ///
> (line fit parity if twin==0&vag_disch==1 in 1575/1582) ///
> (line fit parity if twin==1&vag_disch==0 in 1575/1582) ///
> (line fit parity if twin==1&vag_disch==1 in 1575/1582), legend(off)

.
. * third approach: using margins command (to be discussed later in course)
. margins , over(parity twin vag_disch)

Predictive margins Number of obs = 1,536
Model VCE : OLS

Expression : Linear prediction, predict()

over : parity twin vag_disch

+

--------

| Delta-method
| Margin Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity#twin#vag_disch |
1#no#no | 2894.067 25.64273 112.86 0.000 2843.768 2944.366
1#no#yes | 3093.784 74.13194 41.73 0.000 2948.373 3239.195
1#yes#no | 2697.061 128.0076 21.07 0.000 2445.973 2948.15
1#yes#yes | 2896.778 138.7061 20.88 0.000 2624.704 3168.852
2#no#no | 3074.96 18.84781 163.15 0.000 3037.99 3111.93
2#no#yes | 3274.677 72.71415 45.03 0.000 3132.047 3417.307
2#yes#no | 2877.954 126.1001 22.82 0.000 2630.607 3125.301
3#no#no | 3255.853 17.207 189.22 0.000 3222.101 3289.605
3#no#yes | 3455.57 72.95412 47.37 0.000 3312.47 3598.671
3#yes#no | 3058.847 125.1387 24.44 0.000 2813.386 3304.308
3#yes#yes | 3258.564 136.7529 23.83 0.000 2990.322 3526.807
4#no#no | 3436.746 21.91056 156.85 0.000 3393.768 3479.724
4#no#yes | 3636.463 74.83588 48.59 0.000 3489.671 3783.255
4#yes#no | 3239.74 125.1451 25.89 0.000 2994.266 3485.214
4#yes#yes | 3439.457 137.1024 25.09 0.000 3170.529 3708.385
5#no#no | 3617.639 30.12002 120.11 0.000 3558.558 3676.72
5#no#yes | 3817.356 78.24108 48.79 0.000 3663.885 3970.827
5#yes#no | 3420.633 126.1191 27.12 0.000 3173.249 3668.018
5#yes#yes | 3620.35 138.3327 26.17 0.000 3349.009 3891.692
6#no#no | 3798.532 39.71787 95.64 0.000 3720.625 3876.439
6#no#yes | 3998.249 82.98237 48.18 0.000 3835.478 4161.02
6#yes#no | 3601.526 128.0388 28.13 0.000 3350.376 3852.676
6#yes#yes | 3801.243 140.4206 27.07 0.000 3525.806 4076.68
7#no#no | 3979.425 49.90946 79.73 0.000 3881.527 4077.323

+

--------

. marginsplot, noci

Variables that uniquely identify margins: parity twin vag_disch

. marginsplot, noci addplot(scatter milk120 parity, msymbol(circle_hollow) msize(vsmall))

Variables that uniquely identify margins: parity twin vag_disch

.
. * model reduction
. regress milk120 parity /* gives SSE(R) and DFE(R) */

Source | SS df MS Number of obs = 1,536

+
F(1, 1534) = 262.27
Model | 109234227 1 109234227 Prob > F = 0.0000
Residual | 638905966 1,534 416496.718 R-squared = 0.1460

+
Adj R-squared = 0.1455
Total | 748140192 1,535 487387.748 Root MSE = 645.37

+

--------

milk120 | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | 178.347 11.01266 16.19 0.000 156.7455 199.9484
_cons | 2727.08 34.33991 79.41 0.000 2659.722 2794.438

+

--------

. regress milk120 parity twin vag_disch /* gives SSE(F) and DFE(F) */

Source | SS df MS Number of obs = 1,536

+
F(3, 1532) = 90.76
Model | 112904721 3 37634906.9 Prob > F = 0.0000
Residual | 635235472 1,532 414644.564 R-squared = 0.1509

+
Adj R-squared = 0.1493
Total | 748140192 1,535 487387.748 Root MSE = 643.93

+

--------

milk120 | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | 180.893 11.02613 16.41 0.000 159.2651 202.5209
twin | -197.0058 125.9608 -1.56 0.118 -444.0797 50.06806
vag_disch | 199.717 74.45821 2.68 0.007 53.66624 345.7678
_cons | 2713.174 34.68445 78.22 0.000 2645.14 2781.208

+

--------

. scalar F=(638905966-635235472)/(1534-1532)/414644.564

. display "F=" F " P=" Ftail(2,1532,F)
F=4.4260727 P=.01211471

. test twin vag_disch /* F-test for dropping twin and vag_disch */

( 1) twin = 0

( 2) vag_disch = 0

F( 2, 1532) = 4.43
Prob > F = 0.0121

.
. * model reduction, expanded example
. generate milk120k=milk120/1000
(46 missing values generated)

. * first rerun the models from before with rescaled outcome
. regress milk120k parity twin vag_disch

Source | SS df MS Number of obs = 1,536

+
F(3, 1532) = 90.76
Model | 112.90472 3 37.6349065 Prob > F = 0.0000
Residual | 635.235468 1,532 .414644562 R-squared = 0.1509

+
Adj R-squared = 0.1493
Total | 748.140188 1,535 .487387745 Root MSE = .64393

+

--------

milk120k | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | .180893 .0110261 16.41 0.000 .1592651 .2025209
twin | -.1970058 .1259608 -1.56 0.118 -.4440797 .050068
vag_disch | .199717 .0744582 2.68 0.007 .0536662 .3457678
_cons | 2.713174 .0346844 78.22 0.000 2.64514 2.781208

+

--------

. regress milk120k parity

Source | SS df MS Number of obs = 1,536

+
F(1, 1534) = 262.27
Model | 109.234225 1 109.234225 Prob > F = 0.0000
Residual | 638.905962 1,534 .416496716 R-squared = 0.1460

+
Adj R-squared = 0.1455
Total | 748.140188 1,535 .487387745 Root MSE = .64537

+

--------

milk120k | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | .178347 .0110127 16.19 0.000 .1567455 .1999484
_cons | 2.72708 .0343399 79.41 0.000 2.659722 2.794438

+

--------

. * new expanded model
. regress milk120k parity twin vag_disch dyst rp

Source | SS df MS Number of obs = 1,536

+
F(5, 1530) = 54.40
Model | 112.932559 5 22.5865117 Prob > F = 0.0000
Residual | 635.207629 1,530 .415168385 R-squared = 0.1510

+
Adj R-squared = 0.1482
Total | 748.140188 1,535 .487387745 Root MSE = .64434

+

--------

milk120k | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | .180591 .0111486 16.20 0.000 .1587228 .2024591
twin | -.1938315 .1268007 -1.53 0.127 -.4425531 .05489
vag_disch | .2039539 .0763997 2.67 0.008 .0540946 .3538132
dyst | -.0116861 .0705298 -0.17 0.868 -.1500315 .1266592
rp | -.0110612 .0575734 -0.19 0.848 -.1239924 .1018699
_cons | 2.715483 .0359492 75.54 0.000 2.644968 2.785998

+

--------

. test dyst rp

( 1) dyst = 0

( 2) rp = 0

F( 2, 1530) = 0.03
Prob > F = 0.9670

. test twin dyst rp vag_disch

( 1) twin = 0

( 2) dyst = 0

( 3) rp = 0

( 4) vag_disch = 0

F( 4, 1530) = 2.23
Prob > F = 0.0640

. regress milk120k /* not really needed */

Source | SS df MS Number of obs = 1,536

+
F(0, 1535) = 0.00
Model | 0 0 . Prob > F = .
Residual | 748.140188 1,535 .487387745 R-squared = 0.0000

+
Adj R-squared = 0.0000
Total | 748.140188 1,535 .487387745 Root MSE = .69813

+

--------

milk120k | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

_cons | 3.215096 .0178132 180.49 0.000 3.180155 3.250036

+

--------

.
. * polynomial regression
. generate parity2=parity^2

. regress milk120 parity parity2

Source | SS df MS Number of obs = 1,536

+
F(2, 1533) = 212.78
Model | 162559767 2 81279883.3 Prob > F = 0.0000
Residual | 585580426 1,533 381983.318 R-squared = 0.2173

+
Adj R-squared = 0.2163
Total | 748140192 1,535 487387.748 Root MSE = 618.05

+

--------

milk120 | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | 697.5025 45.18718 15.44 0.000 608.8673 786.1378
parity2 | -82.55675 6.987264 -11.82 0.000 -96.26236 -68.85115
_cons | 2109.224 61.77411 34.14 0.000 1988.054 2230.395

+

--------

. regress milk120 c.parity##c.parity

Source | SS df MS Number of obs = 1,536

+
F(2, 1533) = 212.78
Model | 162559767 2 81279883.3 Prob > F = 0.0000
Residual | 585580426 1,533 381983.318 R-squared = 0.2173

+
Adj R-squared = 0.2163
Total | 748140192 1,535 487387.748 Root MSE = 618.05

+

--------

milk120 | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | 697.5025 45.18718 15.44 0.000 608.8673 786.1378
|
c.parity#c.parity | -82.55675 6.987264 -11.82 0.000 -96.26236 -68.85115
|
_cons | 2109.224 61.77411 34.14 0.000 1988.054 2230.395

+

--------

. * same model using factor notation (see fvvarlist help), without generating parity2
. predict fit2, xb

. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (line fit2 parity, sort)

. predict stdres2, rstandard
(46 missing values generated)

. lowess stdres2 parity, xtitle("parity")

. * cubic regression
. generate parity3=parity^3

. regress milk120 parity parity2 parity3

Source | SS df MS Number of obs = 1,536

+
F(3, 1532) = 163.18
Model | 181175181 3 60391727.1 Prob > F = 0.0000
Residual | 566965011 1,532 370081.6 R-squared = 0.2422

+
Adj R-squared = 0.2407
Total | 748140192 1,535 487387.748 Root MSE = 608.34

+

--------

milk120 | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | 1635.566 139.543 11.72 0.000 1361.85 1909.281
parity2 | -409.1231 46.55594 -8.79 0.000 -500.4432 -317.803
parity3 | 32.48599 4.580454 7.09 0.000 23.50137 41.47061
_cons | 1396.606 117.4432 11.89 0.000 1166.239 1626.972

+

--------

. predict fit3, xb

. twoway (scatter milk120 parity, msymbol(circle_hollow) msize(vsmall)) (line fit3 parity, sort)

. predict stdres3, rstandard
(46 missing values generated)

. lowess stdres3 parity, xtitle("parity")

.
. * 1-way ANOVA
. oneway milk120k parity, tab

Lactation | Summary of milk120k
number | Mean Std. Dev. Freq.

+

1 | 2.6396452 .48640371 403
2 | 3.3478585 .62647033 369
3 | 3.4294886 .65510671 308
4 | 3.4881589 .65641493 219
5 | 3.4272543 .69278456 164
6 | 3.5178058 .54256333 69
7 | 3.5656 .10381738 4

+

Total | 3.2150956 .69813161 1,536

Analysis of Variance
Source SS df MS F Prob > F

Between groups 184.637128 6 30.7728546 83.50 0.0000
Within groups 563.50306 1529 .368543532

Total 748.140188 1535 .487387745

Bartlett's test for equal variances: chi2(6) = 55.9053 Prob>chi2 = 0.000

. regress milk120k i.parity /* same with categorical predictor parity; Lecture 2a */

Source | SS df MS Number of obs = 1,536

+
F(6, 1529) = 83.50
Model | 184.637128 6 30.7728546 Prob > F = 0.0000
Residual | 563.50306 1,529 .368543532 R-squared = 0.2468

+
Adj R-squared = 0.2438
Total | 748.140188 1,535 .487387745 Root MSE = .60708

+

--------

milk120k | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity |
2 | .7082134 .0437409 16.19 0.000 .6224149 .7940118
3 | .7898435 .0459464 17.19 0.000 .6997189 .8799681
4 | .8485137 .0509642 16.65 0.000 .7485466 .9484808
5 | .7876091 .0562291 14.01 0.000 .6773147 .8979035
6 | .8781606 .0790931 11.10 0.000 .7230183 1.033303
7 | .9259548 .3050416 3.04 0.002 .3276106 1.524299
|
_cons | 2.639645 .0302407 87.29 0.000 2.580328 2.698963

+

--------

. regress milk120k parity

Source | SS df MS Number of obs = 1,536

+
F(1, 1534) = 262.27
Model | 109.234225 1 109.234225 Prob > F = 0.0000
Residual | 638.905962 1,534 .416496716 R-squared = 0.1460

+
Adj R-squared = 0.1455
Total | 748.140188 1,535 .487387745 Root MSE = .64537

+

--------

milk120k | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

parity | .178347 .0110127 16.19 0.000 .1567455 .1999484
_cons | 2.72708 .0343399 79.41 0.000 2.659722 2.794438

+

--------

. scalar F_lackfit=(638.905962-563.50306)/(1534-1529)/0.368543532

. display "F=" F_lackfit " P="Ftail(5,1529,F_lackfit)
F=40.919401 P=1.320e-39

.
. * simple example of collinearity in MER data bw5k
. use bw5k.dta, clear

. describe bwt cig*

storage display value
variable name type format label variable label

bwt double %10.0g Birth weight (gms.)

cig_1 byte %8.0g Cigarettes 1st trimester

cig_2 byte %8.0g Cigarettes 2nd trimester

cig_3 byte %8.0g Cigarettes 3rd trimester

. summarize bwt cig*

Variable | Obs Mean Std. Dev. Min Max

+

bwt | 5,000 3295.076 565.8713 480 5550
cig_1 | 5,000 .964 4.054133 0 90
cig_2 | 5,000 .743 3.28979 0 45
cig_3 | 5,000 .6704 3.036908 0 45

. regress bwt cig_3

Source | SS df MS Number of obs = 5,000

+
F(1, 4998) = 22.55
Model | 7189497.98 1 7189497.98 Prob > F = 0.0000
Residual | 1.5935e+09 4,998 318835.965 R-squared = 0.0045

+
Adj R-squared = 0.0043
Total | 1.6007e+09 4,999 320210.372 Root MSE = 564.66

+

--------

bwt | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

cig_3 | -12.48752 2.629726 -4.75 0.000 -17.64293 -7.332101
_cons | 3303.448 8.177729 403.96 0.000 3287.416 3319.48

+

--------

. estimates store cig3

. * store estimates for later display
. regress bwt cig_3 cig_1

Source | SS df MS Number of obs = 5,000

+
F(2, 4997) = 12.43
Model | 7922681.75 2 3961340.87 Prob > F = 0.0000
Residual | 1.5928e+09 4,997 318753.046 R-squared = 0.0049

+
Adj R-squared = 0.0046
Total | 1.6007e+09 4,999 320210.372 Root MSE = 564.58

+

--------

bwt | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

cig_3 | -6.481119 4.753749 -1.36 0.173 -15.80055 2.838316
cig_1 | -5.400689 3.560983 -1.52 0.129 -12.38178 1.580401
_cons | 3304.627 8.213572 402.34 0.000 3288.525 3320.729

+

--------

. estimates store cig13

. regress bwt cig_3 cig_2

Source | SS df MS Number of obs = 5,000

+
F(2, 4997) = 12.61
Model | 8037757.94 2 4018878.97 Prob > F = 0.0000
Residual | 1.5927e+09 4,997 318730.017 R-squared = 0.0050

+
Adj R-squared = 0.0046
Total | 1.6007e+09 4,999 320210.372 Root MSE = 564.56

+

--------

bwt | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

cig_3 | -.0859205 8.043799 -0.01 0.991 -15.8553 15.68346
cig_2 | -12.11372 7.425483 -1.63 0.103 -26.67093 2.44348
_cons | 3304.134 8.187191 403.57 0.000 3288.084 3320.185

+

--------

. estimates store cig23

. regress bwt cig_1 cig_2 cig_3

Source | SS df MS Number of obs = 5,000

+
F(3, 4996) = 8.58
Model | 8207559.77 3 2735853.26 Prob > F = 0.0000
Residual | 1.5925e+09 4,996 318759.826 R-squared = 0.0051

+
Adj R-squared = 0.0045
Total | 1.6007e+09 4,999 320210.372 Root MSE = 564.59

+

--------

bwt | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

cig_1 | -3.133501 4.293292 -0.73 0.466 -11.55024 5.283235
cig_2 | -8.463666 8.95284 -0.95 0.345 -26.01516 9.087831
cig_3 | -.337783 8.051574 -0.04 0.967 -16.1224 15.44684
_cons | 3304.612 8.213676 402.33 0.000 3288.509 3320.714

+

--------

. estimates store cig123

. estimates table cig3 cig13 cig23 cig123, se

-+-
---
---
---
--
Variable | cig3 cig13 cig23 cig123

-+-
---
---
---
--
cig_3 | -12.487518 -6.4811186 -.08592047 -.33778302
| 2.6297259 4.7537493 8.043799 8.0515736
cig_1 | -5.4006889 -3.1335006
| 3.5609831 4.2932916
cig_2 | -12.113724 -8.4636663
| 7.4254826 8.9528405
_cons | 3303.4476 3304.6272 3304.1341 3304.6116
| 8.1777289 8.2135723 8.1871908 8.2136761

-+-
---
---
---
--
legend: b/se

. estat vif

Variable | VIF 1/VIF

+

cig_2 | 13.60 0.073506
cig_3 | 9.38 0.106649
cig_1 | 4.75 0.210477

+

Mean VIF | 9.24

. pwcorr cig*

| cig_1 cig_2 cig_3

+

cig_1 | 1.0000
cig_2 | 0.8883 1.0000
cig_3 | 0.8331 0.9451 1.0000

. estat vce, corr

Correlation matrix of coefficients of regress model

e(V) | cig_1 cig_2 cig_3 _cons

+

cig_1 | 1.0000
cig_2 | -0.5586 1.0000
cig_3 | 0.0429 -0.8071 1.0000
_cons | -0.0797 0.0020 -0.0251 1.0000

.
. * more complex collinearity example in RC dataset Coleman
. use coleman.dta, clear

. summarize y x1-x5, sep(0)

Variable | Obs Mean Std. Dev. Min Max

+

y | 20 35.0825 5.817054 22.7 43.1
x1 | 20 2.7315 .4540957 2.07 3.83
x2 | 20 40.906 25.89855 9.99 86.27
x3 | 20 3.1405 9.625382 -16.04 15.03
x4 | 20 25.069 1.313805 21.6 28.01
x5 | 20 6.255 .6543176 5.17 7.51

. pwcorr y x1-x5

| y x1 x2 x3 x4 x5

+

y | 1.0000
x1 | 0.1923 1.0000
x2 | 0.7534 0.1811 1.0000
x3 | 0.9272 0.2296 0.8272 1.0000
x4 | 0.3336 0.5027 0.0511 0.1833 1.0000
x5 | 0.7330 0.1968 0.9271 0.8191 0.1238 1.0000

. regress y x1-x5

Source | SS df MS Number of obs = 20

+
F(5, 14) = 27.08
Model | 582.686401 5 116.53728 Prob > F = 0.0000
Residual | 60.2378924 14 4.3027066 R-squared = 0.9063

+
Adj R-squared = 0.8728
Total | 642.924294 19 33.8381207 Root MSE = 2.0743

+

--------

y | Coef. Std. Err. t P>|t| [95% Con f. Interval]

+

--------

x1 | -1.793333 1.233397 -1.45 0.168 -4.438706 .8520392
x2 | .0436015 .0532589 0.82 0.427 -.0706275 .1578304
x3 | .5557601 .0929564 5.98 0.000 .3563884 .7551318
x4 | 1.110168 .4337681 2.56 0.023 .1798279 2.040508
x5 | -1.810919 2.02739 -0.89 0.387 -6.159239 2.5374
_cons | 19.94857 13.62755 1.46 0.165 -9.279627 49.17676

+

--------

. estat vif

Variable | VIF 1/VIF

+

x2 | 8.40 0.119029
x5 | 7.77 0.128687
x3 | 3.54 0.282874
x4 | 1.43 0.697286
x1 | 1.39 0.721918

+

Mean VIF | 4.51

. estat vce, corr

Correlation matrix of coefficients of regress model

e(V) | x1 x2 x3 x4 x5 _cons

+

x1 | 1.0000
x2 | -0.0785 1.0000
x3 | -0.0282 -0.3454 1.0000
x4 | -0.4860 0.2392 -0.1713 1.0000
x5 | 0.0340 -0.7794 -0.2080 -0.1488 1.0000
_cons | 0.1221 0.4013 0.3710 -0.5739 -0.6912 1.0000

. * note: code for reduced models left for the interested student
.
end of do-file

. exit, clear