Table 10.1, page 265.
use https://stats.idre.ucla.edu/stat/stata/examples/chp/p233, clear drop if year >= 60 regress import doprod stock consum, beta Source | SS df MS Number of obs = 11 ---------+------------------------------ F( 3, 7) = 285.61 Model | 204.776154 3 68.2587179 Prob > F = 0.0000 Residual | 1.67295319 7 .238993312 R-squared = 0.9919 ---------+------------------------------ Adj R-squared = 0.9884 Total | 206.449107 10 20.6449107 Root MSE = .48887 ------------------------------------------------------------------------------ import | Coef. Std. Err. t P>|t| Beta ---------+-------------------------------------------------------------------- doprod | -.0513959 .0702801 -0.731 0.488 -.3393412 stock | .5869492 .0946185 6.203 0.000 .2130485 consum | .2868483 .1022083 2.807 0.026 1.30268 _cons | -10.12798 1.212161 -8.355 0.000 . ------------------------------------------------------------------------------
Equations 10.6 and 10.7, page 265.
Note: The signs of the coefficients for the third eigenvector are different from those given in 10.7. This difference is merely a reflection of the signs and does not change the meaning of the analysis.
factor doprod stock consum, pc factors(3)
(obs=11)
(principal components; 3 components retained)
Component Eigenvalue Difference Proportion Cumulative
------------------------------------------------------------------
1 1.99915 1.00100 0.6664 0.6664
2 0.99815 0.99546 0.3327 0.9991
3 0.00269 . 0.0009 1.0000
Eigenvectors
Variable | 1 2 3
----------+--------------------------------
doprod | 0.70633 -0.03569 0.70698
stock | 0.04350 0.99903 0.00697
consum | 0.70654 -0.02583 -0.70720
score c1 c2 c3
(based on unrotated principal components)
Scoring Coefficients
Variable | 1 2 3
----------+--------------------------------
doprod | 0.70633 -0.03569 0.70698
stock | 0.04350 0.99903 0.00697
consum | 0.70654 -0.02583 -0.70720
matrix ld = get(Ld) /* save loading matrix for later analyses */
Table 10.2, page 265.
Note: The variable import has been transformed into a standard score zimport.
egen zimport = std(import)
regress z c1 c2 c3, noconst
Source | SS df MS Number of obs = 11
---------+------------------------------ F( 3, 8) = 326.41
Model | 9.91896497 3 3.30632166 Prob > F = 0.0000
Residual | .081034631 8 .010129329 R-squared = 0.9919
---------+------------------------------ Adj R-squared = 0.9889
Total | 9.9999996 11 .909090872 Root MSE = .10064
------------------------------------------------------------------------------
zimport | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
c1 | .6899821 .0225096 30.653 0.000 .6380749 .7418892
c2 | .1913035 .031856 6.005 0.000 .1178434 .2647636
c3 | -1.159675 .6135396 -1.890 0.095 -2.5745 .2551501
------------------------------------------------------------------------------
Standardized coefficients for Table 10.3, page 268.
Note 1: We will use Stata’s matrix commands for these computations.
matrix b = get(_b)
matrix v = b'
matrix v[2,1] = 0
matrix v[3,1] = 0
matrix list v
v[3,1]
y1
c1 .68998207
c2 0
c3 0
matrix pc1 = ld*v
matrix list pc1 /* standardized coefficients for first pc */
pc1[3,1]
y1
r1 .48735532
r2 .03001462
r3 .487503
matrix v = b'
matrix v[3,1] = 0
matrix list v
v[3,1]
y1
c1 .68998207
c2 .19130349
c3 0
matrix pc2 = ld*v
matrix list pc2 /* standardized coefficients for first and second pc */
pc2[3,1]
y1
r1 .48052795
r2 .22113237
r3 .48256155
matrix v = b'
matrix list v
v[3,1]
y1
c1 .68998207
c2 .19130349
c3 -1.1596748
matrix pc3 = ld*v
matrix list pc3 /* standardized coefficients for all pcs */
pc3[3,1]
y1
r1 -.33934136
r2 .21304848
r3 1.3026802
use https://stats.idre.ucla.edu/stat/stata/examples/chp/p270, clear
list
u c1 c2 c3 c4
1. .955 1.467 1.903 -.53 .0389
2. -.746 2.136 .238 -.29 -.03
3. -2.323 -1.13 .184 -.01 -.094
4. -.82 .66 1.577 .179 -.033
5. .471 -.359 .484 -.74 .019
6. -.299 -.967 .17 .086 -.012
7. .21 -.931 -2.135 -.173 .008
8. .558 2.232 -.692 .46 .023
9. -1.119 .352 -1.432 -.032 -.045
10. .496 -1.663 1.828 .851 .02
11. .781 1.641 -1.295 .494 .031
12. .918 -1.693 -.392 -.02 .037
13. .918 -1.746 -.438 -.275 .037
Table 10.5, page 270.
regress u c1 c2 c3 c4
Source | SS df MS Number of obs = 13
-------------+------------------------------ F( 4, 8) =63662.46
Model | 11.9971847 4 2.99929618 Prob > F = 0.0000
Residual | .0003769 8 .000047112 R-squared = 1.0000
-------------+------------------------------ Adj R-squared = 1.0000
Total | 11.9975616 12 .999796801 Root MSE = .00686
------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
c1 | -.0017999 .001325 -1.36 0.211 -.0048552 .0012555
c2 | -.0025529 .0015783 -1.62 0.144 -.0061924 .0010866
c3 | .0016481 .0045872 0.36 0.729 -.0089299 .0122262
c4 | 24.7659 .0490776 504.63 0.000 24.65273 24.87908
_cons | .0001904 .0019037 0.10 0.923 -.0041995 .0045803
------------------------------------------------------------------------------
Table 10.6, page 270.
regress u c1 c2 c3
Source | SS df MS Number of obs = 13
-------------+------------------------------ F( 3, 9) = 0.00
Model | .000054633 3 .000018211 Prob > F = 1.0000
Residual | 11.997507 9 1.33305633 R-squared = 0.0000
-------------+------------------------------ Adj R-squared = -0.3333
Total | 11.9975616 12 .999796801 Root MSE = 1.1546
------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
c1 | -.0012226 .2228739 -0.00 0.996 -.5053984 .5029532
c2 | -.0001243 .2654817 -0.00 1.000 -.6006856 .6004371
c3 | .0025214 .7716171 0.00 0.997 -1.742998 1.748041
_cons | -8.83e-08 .320223 -0.00 1.000 -.7243949 .7243948
------------------------------------------------------------------------------
Figure 10.1, page 271.
graph twoway scatter u c1, nodraw ylabel(-2(1)1) xlabel(-1(1)2) saving(f101) graph twoway scatter u c2, nodraw ylabel(-2(1)1) xlabel(-2(1)2) saving(f102) graph twoway scatter u c3, nodraw ylabel(-2(1)1) xlabel(-.4(.4).8) saving(f103) graph twoway scatter u c4, nodraw ylabel(-2(1)1) xlabel(-.08(.04).04) saving(f104) graph combine f101.gph f102.gph f103.gph f104.gph
