UNIVERSITY OF CALIFORNIA, LOS ANGELES
Department of Economics
Economics 143 (Cameron) - Applied Regression
Analysis
Final Exam Exhibits
EXHIBIT A
|_sample 1 100
|_read(xhet1.dat) y x z
UNIT 88 IS NOW ASSIGNED TO: xhet1.dat
3 VARIABLES AND 100 OBSERVATIONS STARTING AT OBS 1
|_*----------------------------------------------------------------
|_* y = individual annual consumption of frozen waffles
|_* x = individual income (in thousands of dollars)
|_* z = marginal cost of electricity to heat waffles (cents per dozen)
|_*----------------------------------------------------------------
Descriptive Statistics A
|_stat y x z / pcor
NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM
Y 100 79.132 39.431 1554.8 8.1358 253.46
X 100 24.710 4.6205 21.349 12.457 35.897
Z 100 11.883 2.0110 4.0442 8.4486 17.728
CORRELATION MATRIX OF VARIABLES - 100 OBSERVATIONS
Y 1.0000
X 0.42847 1.0000
Z -0.19321 -0.83585E-01 1.0000
Y X Z
Regression A1
|_genr x2=x*x
|_ols y x x2 z
R-SQUARE = 0.2122 R-SQUARE ADJUSTED = 0.1876
VARIANCE OF THE ESTIMATE-SIGMA**2 = 1263.2
STANDARD ERROR OF THE ESTIMATE-SIGMA = 35.541
SUM OF SQUARED ERRORS-SSE= 0.12126E+06
MEAN OF DEPENDENT VARIABLE = 79.132
LOG OF THE LIKELIHOOD FUNCTION = -496.921
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 32659. 3. 10886. 8.618
ERROR 0.12126E+06 96. 1263.2 P-VALUE
TOTAL 0.15392E+06 99. 1554.8 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 96 DF P-VALUE CORR. COEFFICIENT AT MEANS
X -0.25402 5.751 -0.4417E-01 0.965-0.005 -0.0298 -0.0793
X2 0.77962E-01 0.1170 0.6664 0.507 0.068 0.4493 0.6224
Z -3.0558 1.784 -1.713 0.090-0.172 -0.1559 -0.4589
CONSTANT 72.473 72.46 1.000 0.320 0.102 0.0000 0.9158
Regression A2
|_ols y x z / resid=e
R-SQUARE = 0.2085 R-SQUARE ADJUSTED = 0.1922
VARIANCE OF THE ESTIMATE-SIGMA**2 = 1255.9
STANDARD ERROR OF THE ESTIMATE-SIGMA = 35.439
SUM OF SQUARED ERRORS-SSE= 0.12182E+06
MEAN OF DEPENDENT VARIABLE = 79.132
LOG OF THE LIKELIHOOD FUNCTION = -497.152
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 32098. 2. 16049. 12.779
ERROR 0.12182E+06 97. 1255.9 P-VALUE
TOTAL 0.15392E+06 99. 1554.8 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
X 3.5434 0.7736 4.581 0.000 0.422 0.4152 1.1065
Z -3.1077 1.777 -1.749 0.084-0.175 -0.1585 -0.4667
CONSTANT 28.505 29.86 0.9547 0.342 0.096 0.0000 0.3602
|_diagnos / het
DEPENDENT VARIABLE = Y 100 OBSERVATIONS
REGRESSION COEFFICIENTS
3.54340543975 -3.10774071452 28.5051935002
HETEROSKEDASTICITY TESTS
CHI-SQUARE D.F. P-VALUE
TEST STATISTIC
E**2 ON YHAT: 12.581 1 0.00039
E**2 ON YHAT**2: 14.833 1 0.00012
E**2 ON LOG(YHAT**2): 9.988 1 0.00158
E**2 ON X (B-P-G) TEST:
BASED ON R2: 13.987 2 0.00092
BASED ON SSR: 29.960 2 0.00000
E**2 ON LAG(E**2) ARCH TEST: 0.265 1 0.60647
LOG(E**2) ON X (HARVEY) TEST: 19.252 2 0.00007
ABS(E) ON X (GLEJSER) TEST: 23.924 2 0.00001
Regression A3
|_genr e2=e*e
|_ols e2 x z
R-SQUARE = 0.1399 R-SQUARE ADJUSTED = 0.1221
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.56376E+07
STANDARD ERROR OF THE ESTIMATE-SIGMA = 2374.4
SUM OF SQUARED ERRORS-SSE= 0.54685E+09
MEAN OF DEPENDENT VARIABLE = 1218.2
LOG OF THE LIKELIHOOD FUNCTION = -917.619
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.88929E+08 2. 0.44465E+08 7.887
ERROR 0.54685E+09 97. 0.56376E+07 P-VALUE
TOTAL 0.63578E+09 99. 0.64220E+07 0.001
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
X 204.50 51.83 3.946 0.000 0.372 0.3729 4.1480
Z -14.433 119.1 -0.1212 0.904-0.012 -0.0115 -0.1408
CONSTANT -3663.5 2000. -1.831 0.070-0.183 0.0000 -3.0072
Regression A4
|_ols e2 x x2 z / auxrsqr
R-SQUARE OF X ON OTHER INDEPENDENT VARIABLES = 0.9819
R-SQUARE OF X2 ON OTHER INDEPENDENT VARIABLES = 0.9819
R-SQUARE OF Z ON OTHER INDEPENDENT VARIABLES = 0.0089
R-SQUARE OF CONSTANT ON OTHER INDEPENDENT VARIABLES = 0.0000
R-SQUARE = 0.1913 R-SQUARE ADJUSTED = 0.1660
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.53558E+07
STANDARD ERROR OF THE ESTIMATE-SIGMA = 2314.3
SUM OF SQUARED ERRORS-SSE= 0.51416E+09
MEAN OF DEPENDENT VARIABLE = 1218.2
LOG OF THE LIKELIHOOD FUNCTION = -914.537
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.12162E+09 3. 0.40540E+08 7.569
ERROR 0.51416E+09 96. 0.53558E+07 P-VALUE
TOTAL 0.63578E+09 99. 0.64220E+07 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 96 DF P-VALUE CORR. COEFFICIENT AT MEANS
X -712.24 374.5 -1.902 0.060-0.191 -1.2986 -14.4466
X2 18.821 7.618 2.471 0.015 0.245 1.6877 9.7596
Z -1.9005 116.2 -0.1636E-01 0.987-0.002 -0.0015 -0.0185
CONSTANT 6950.8 4718. 1.473 0.144 0.149 0.0000 5.7056
Regression A5
|_ols e2 x2 z
R-SQUARE = 0.1608 R-SQUARE ADJUSTED = 0.1435
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.55003E+07
STANDARD ERROR OF THE ESTIMATE-SIGMA = 2345.3
SUM OF SQUARED ERRORS-SSE= 0.53353E+09
MEAN OF DEPENDENT VARIABLE = 1218.2
LOG OF THE LIKELIHOOD FUNCTION = -916.387
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.10225E+09 2. 0.51123E+08 9.295
ERROR 0.53353E+09 97. 0.55003E+07 P-VALUE
TOTAL 0.63578E+09 99. 0.64220E+07 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
X2 4.4645 1.041 4.287 0.000 0.399 0.4003 2.3151
Z -8.9710 117.7 -0.7624E-01 0.939-0.008 -0.0071 -0.0875
CONSTANT -1495.5 1614. -0.9263 0.357-0.094 0.0000 -1.2276
|_genr wt1=x*x
|_genr wt2=1/(x*x)
|_genr wt3=1/x
Regression A6
|_ols y x z / weight=wt1
SUM OF LOG(SQRT(ABS(WEIGHT))) = -3.5776
R-SQUARE = 0.1830 R-SQUARE ADJUSTED = 0.1661
VARIANCE OF THE ESTIMATE-SIGMA**2 = 1625.5
STANDARD ERROR OF THE ESTIMATE-SIGMA = 40.317
SUM OF SQUARED ERRORS-SSE= 0.15767E+06
MEAN OF DEPENDENT VARIABLE = 85.221
LOG OF THE LIKELIHOOD FUNCTION = -513.626
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 35305. 2. 17653. 10.860
ERROR 0.15767E+06 97. 1625.5 P-VALUE
TOTAL 0.19298E+06 99. 1949.2 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
X 3.7917 0.9336 4.061 0.000 0.381 0.3745 1.1720
Z -3.7993 2.012 -1.888 0.062-0.188 -0.1741 -0.5269
CONSTANT 30.253 36.03 0.8396 0.403 0.085 0.0000 0.3550
Regression A7
|_ols y x z / weight=wt2
SUM OF LOG(SQRT(ABS(WEIGHT))) = -4.4627
R-SQUARE = 0.2498 R-SQUARE ADJUSTED = 0.2344
VARIANCE OF THE ESTIMATE-SIGMA**2 = 919.85
STANDARD ERROR OF THE ESTIMATE-SIGMA = 30.329
SUM OF SQUARED ERRORS-SSE= 89226.
MEAN OF DEPENDENT VARIABLE = 72.146
LOG OF THE LIKELIHOOD FUNCTION = -486.044
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 29716. 2. 14858. 16.153
ERROR 89226. 97. 919.85 P-VALUE
TOTAL 0.11894E+06 99. 1201.4 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
X 3.2589 0.6091 5.351 0.000 0.477 0.4712 1.0231
Z -2.5378 1.557 -1.630 0.106-0.163 -0.1435 -0.4198
CONSTANT 28.618 23.92 1.197 0.234 0.121 0.0000 0.3967
Regression A8
|_ols y x z / weight=wt3
SUM OF LOG(SQRT(ABS(WEIGHT))) = -1.0480
R-SQUARE = 0.2265 R-SQUARE ADJUSTED = 0.2105
VARIANCE OF THE ESTIMATE-SIGMA**2 = 1084.4
STANDARD ERROR OF THE ESTIMATE-SIGMA = 32.931
SUM OF SQUARED ERRORS-SSE= 0.10519E+06
MEAN OF DEPENDENT VARIABLE = 75.782
LOG OF THE LIKELIHOOD FUNCTION = -490.860
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 30800. 2. 15400. 14.201
ERROR 0.10519E+06 97. 1084.4 P-VALUE
TOTAL 0.13599E+06 99. 1373.6 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
X 3.4005 0.6906 4.924 0.000 0.447 0.4408 1.0656
Z -2.8126 1.665 -1.690 0.094-0.169 -0.1512 -0.4421
CONSTANT 28.530 26.80 1.064 0.290 0.107 0.0000 0.3765
|_genr ly=log(y)
|_genr lx=log(x)
|_genr lz=log(z)
Regression A9
|_ols ly lx lz / loglog resid=e
R-SQUARE = 0.1332 R-SQUARE ADJUSTED = 0.1153
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.24211
STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.49205
SUM OF SQUARED ERRORS-SSE= 23.485
MEAN OF DEPENDENT VARIABLE = 4.2471
LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -494.162
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 3.6093 2. 1.8046 7.454
ERROR 23.485 97. 0.24211 P-VALUE
TOTAL 27.094 99. 0.27367 0.001
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
LX 0.80413 0.2482 3.239 0.002 0.312 0.3073 0.8041
LZ -0.53706 0.2938 -1.828 0.071-0.182 -0.1734 -0.5371
CONSTANT 3.0049 1.116 2.692 0.008 0.264 0.0000 3.0049
|_genr e2=e*e
Regression A10
|_ols e2 lx lz
R-SQUARE = 0.0513 R-SQUARE ADJUSTED = 0.0317
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.29693
STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.54492
SUM OF SQUARED ERRORS-SSE= 28.802
MEAN OF DEPENDENT VARIABLE = 0.23485
LOG OF THE LIKELIHOOD FUNCTION = -79.6584
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 1.5570 2. 0.77849 2.622
ERROR 28.802 97. 0.29693 P-VALUE
TOTAL 30.359 99. 0.30666 0.078
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 97 DF P-VALUE CORR. COEFFICIENT AT MEANS
LX 0.61237 0.2749 2.227 0.028 0.221 0.2210 8.3140
LZ 0.23166 0.3254 0.7120 0.478 0.072 0.0706 2.4276
CONSTANT -2.2878 1.236 -1.851 0.067-0.185 0.0000 -9.7416
|_stop
EXHIBIT B
|_sample 1 384
|_read(czoned.prn) yrmo private / skiplines=1
|_read(czonqe.prn) yrmo public / skiplines=1
|_read(kidpop2.dat) yrob p1 p2 p3 p4
|_*------------------------------------------------------------------
|_* yrmo = CITIBASE year and month variable (e.g. 9509 = Sept. 1995)
|_* private = CZONED; private educ. construction (mill$, NSA, monthly)
|_* public = CZONQE; public educ. construction (mill$, NSA, monthly)
|_* p1 = CITIBASE PAN1 est. pop. aged < 5 in that year (thousands, annual)
|_* p2 = CITIBASE PAN2 est. pop. aged 5-9 in that year (thousands, annual)
|_* p3 = CITIBASE PAN3 est. pop. aged 10-14 in that year (thous., annual)
|_* p4 = CITIBASE PAN4 est. pop. aged 15-19 in that year (thous., annual)
|_*------------------------------------------------------------------
|_genr t=time(0)
|_genr yr=(yrmo-mod(yrmo,100))/100
|_genr mo=mod(yrmo,100)
Descriptive Statistics B
|_stat / pcor
NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM
YRMO 384 7956.5 924.52 0.85474E+06 6401.0 9512.0
PRIVATE 384 180.17 130.79 17106. 47.000 624.00
PUBLIC 384 808.11 453.73 0.20587E+06 244.00 2337.0
YROB 384 7951.0 924.51 0.85473E+06 6401.0 9501.0
P1 384 17811. 1329.4 0.17674E+07 15564. 20165.
P2 384 18213. 1413.8 0.19987E+07 15958. 20573.
P3 384 18842. 1475.5 0.21772E+07 16377. 21099.
P4 384 19158. 1546.6 0.23919E+07 16250. 21540.
T 384 192.50 111.00 12320. 1.0000 384.00
YR 384 79.500 9.2451 85.473 64.000 95.000
MO 384 6.5000 3.4566 11.948 1.0000 12.000
CORRELATION MATRIX OF VARIABLES - 384 OBSERVATIONS
YRMO 1.0000
PRIVATE 0.84705 1.0000
PUBLIC 0.83472 0.92888 1.0000
YROB 0.99999 0.84673 0.83425 1.0000
P1 0.25721 0.59398 0.48679 0.25721 1.0000
P2 -0.51549 -0.80261E-01 -0.98371E-01 -0.51549 0.48180
1.0000
P3 -0.67197 -0.57467 -0.42998 -0.67197 -0.34128
0.50246 1.0000
P4 -0.18861 -0.53893 -0.41395 -0.18861 -0.96696
-0.52144 0.35241 1.0000
T 0.99962 0.84898 0.83787 0.99951 0.25708
-0.51524 -0.67165 -0.18852 1.0000
YR 0.99999 0.84673 0.83425 1.0000 0.25721
-0.51549 -0.67197 -0.18861 0.99951 1.0000
MO 0.37388E-02 0.85281E-01 0.12936 0.00000 0.00000
0.00000 0.00000 0.00000 0.31141E-01 0.00000
1.0000
YRMO PRIVATE PUBLIC YROB P1
P2 P3 P4 T YR
MO
|_if(mo.eq.1) jan=1
|_if(mo.eq.2) feb=1
|_if(mo.eq.3) mar=1
|_if(mo.eq.4) apr=1
|_if(mo.eq.5) may=1
|_if(mo.eq.6) jun=1
|_if(mo.eq.7) jul=1
|_if(mo.eq.8) aug=1
|_if(mo.eq.9) sep=1
|_if(mo.eq.10) oct=1
|_if(mo.eq.11) nov=1
|_if(mo.eq.12) dec=1
|_months:feb mar apr may jun jul aug sep oct nov dec
Regression B1
|_* look at what seems to affect private school construction
|_ols private public t p1 p2 p3 p4 &
| feb mar apr may jun jul aug sep oct nov dec / resid=e rstat auxrsqr
R-SQUARE OF PUBLIC ON OTHER INDEPENDENT VARIABLES = 0.9176
R-SQUARE OF T ON OTHER INDEPENDENT VARIABLES = 0.9406
R-SQUARE OF P1 ON OTHER INDEPENDENT VARIABLES = 0.9466
R-SQUARE OF P2 ON OTHER INDEPENDENT VARIABLES = 0.8723
R-SQUARE OF P3 ON OTHER INDEPENDENT VARIABLES = 0.7967
R-SQUARE OF P4 ON OTHER INDEPENDENT VARIABLES = 0.9567
R-SQUARE OF FEB ON OTHER INDEPENDENT VARIABLES = 0.4548
R-SQUARE OF MAR ON OTHER INDEPENDENT VARIABLES = 0.4550
R-SQUARE OF APR ON OTHER INDEPENDENT VARIABLES = 0.4615
R-SQUARE OF MAY ON OTHER INDEPENDENT VARIABLES = 0.4740
R-SQUARE OF JUN ON OTHER INDEPENDENT VARIABLES = 0.5015
R-SQUARE OF JUL ON OTHER INDEPENDENT VARIABLES = 0.5337
R-SQUARE OF AUG ON OTHER INDEPENDENT VARIABLES = 0.5631
R-SQUARE OF SEP ON OTHER INDEPENDENT VARIABLES = 0.5149
R-SQUARE OF OCT ON OTHER INDEPENDENT VARIABLES = 0.4819
R-SQUARE OF NOV ON OTHER INDEPENDENT VARIABLES = 0.4674
R-SQUARE OF DEC ON OTHER INDEPENDENT VARIABLES = 0.4560
R-SQUARE OF CONSTANT ON OTHER INDEPENDENT VARIABLES = 0.0000
R-SQUARE = 0.9459 R-SQUARE ADJUSTED = 0.9434
VARIANCE OF THE ESTIMATE-SIGMA**2 = 968.89
STANDARD ERROR OF THE ESTIMATE-SIGMA = 31.127
SUM OF SQUARED ERRORS-SSE= 0.35461E+06
MEAN OF DEPENDENT VARIABLE = 180.17
LOG OF THE LIKELIHOOD FUNCTION = -1855.88
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.61968E+07 17. 0.36452E+06 376.224
ERROR 0.35461E+06 366. 968.89 P-VALUE
TOTAL 0.65515E+07 383. 17106. 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 366 DF P-VALUE CORR. COEFFICIENT AT MEANS
PUBLIC 0.81598E-01 0.1221E-01 6.683 0.000 0.330 0.2831 0.3660
T 0.77073 0.5880E-01 13.11 0.000 0.565 0.6541 0.8235
P1 0.96351E-02 0.5180E-02 1.860 0.064 0.097 0.0979 0.9525
P2 0.28864E-01 0.3149E-02 9.167 0.000 0.432 0.3120 2.9179
P3 -0.12400E-01 0.2391E-02 -5.186 0.000-0.262 -0.1399 -1.2968
P4 0.69796E-03 0.4944E-02 0.1412 0.888 0.007 0.0083 0.0742
FEB -3.9790 7.784 -0.5112 0.610-0.027 -0.0084 -0.0018
MAR 5.7854 7.785 0.7431 0.458 0.039 0.0122 0.0027
APR 11.146 7.832 1.423 0.156 0.074 0.0236 0.0052
MAY 21.835 7.924 2.755 0.006 0.143 0.0462 0.0101
JUN 35.355 8.140 4.343 0.000 0.221 0.0748 0.0164
JUL 33.770 8.416 4.013 0.000 0.205 0.0715 0.0156
AUG 37.790 8.695 4.346 0.000 0.222 0.0800 0.0175
SEP 22.194 8.252 2.690 0.007 0.139 0.0470 0.0103
OCT 16.156 7.985 2.023 0.044 0.105 0.0342 0.0075
NOV 9.2077 7.875 1.169 0.243 0.061 0.0195 0.0043
DEC 1.2159 7.792 0.1560 0.876 0.008 0.0026 0.0006
CONSTANT -527.06 189.1 -2.788 0.006-0.144 0.0000 -2.9254
DURBIN-WATSON = 0.3792 VON NEUMANN RATIO = 0.3802 RHO = 0.81307
RESIDUAL SUM = -0.20520E-10 RESIDUAL VARIANCE = 968.89
SUM OF ABSOLUTE ERRORS= 8543.7
R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9459
RUNS TEST: 60 RUNS, 177 POS, 0 ZERO, 207 NEG NORMAL STATISTIC =-13.5552
COEFFICIENT OF SKEWNESS = 0.6908 WITH STANDARD DEVIATION OF 0.1245
COEFFICIENT OF EXCESS KURTOSIS = 2.6296 WITH STANDARD DEVIATION OF 0.2484
GOODNESS OF FIT TEST FOR NORMALITY OF RESIDUALS - 30 GROUPS
OBSERVED 3.0 1.0 0.0 1.0 1.0 2.0 3.0 4.0 12.0 15.0 21.0 28.0
41.0 42.0 33.0 32.0 28.0 35.0 24.0 22.0
9.0 3.0 1.0 4.0 3.0 3.0 3.0 3.0 0.0 7.0
EXPECTED 1.0 0.8 1.3 2.2 3.4 5.0 7.3 10.0 13.2 16.7 20.4 24.0
27.0 29.2 30.5 30.5 29.2 27.0 24.0 20.4
16.7 13.2 10.0 7.3 5.0 3.4 2.2 1.3 0.8 1.0
CHI-SQUARE = 93.4176 WITH 10 DEGREES OF FREEDOM
|_genr elag1=lag(e,1)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag2=lag(e,2)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag3=lag(e,3)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag4=lag(e,4)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag5=lag(e,5)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag6=lag(e,6)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag7=lag(e,7)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag8=lag(e,8)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag9=lag(e,9)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag10=lag(e,10)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag11=lag(e,11)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
|_genr elag12=lag(e,12)
..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
Regression B2
|_sample 13 384
|_ols e elag1 elag2 elag3 elag4 elag5 elag6 elag7 elag8 elag9 &
| elag10 elag11 elag12
R-SQUARE = 0.7007 R-SQUARE ADJUSTED = 0.6907
VARIANCE OF THE ESTIMATE-SIGMA**2 = 293.46
STANDARD ERROR OF THE ESTIMATE-SIGMA = 17.131
SUM OF SQUARED ERRORS-SSE= 0.10535E+06
MEAN OF DEPENDENT VARIABLE = 0.34160
LOG OF THE LIKELIHOOD FUNCTION = -1578.03
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.24661E+06 12. 20551. 70.030
ERROR 0.10535E+06 359. 293.46 P-VALUE
TOTAL 0.35196E+06 371. 948.68 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 359 DF P-VALUE CORR. COEFFICIENT AT MEANS
ELAG1 0.79088 0.5287E-01 14.96 0.000 0.620 0.7874 1.1168
ELAG2 0.23033 0.6740E-01 3.417 0.001 0.178 0.2294 0.3053
ELAG3 -0.21471 0.6869E-01 -3.126 0.002-0.163 -0.2137 -0.3092
ELAG4 -0.10620 0.7059E-01 -1.505 0.133-0.079 -0.1057 -0.1309
ELAG5 0.27500 0.7241E-01 3.798 0.000 0.197 0.2694 0.0430
ELAG6 -0.26041 0.7397E-01 -3.521 0.000-0.183 -0.2524 0.1861
ELAG7 -0.44085E-01 0.7420E-01 -0.5941 0.553-0.031 -0.0424 0.0651
ELAG8 0.62192E-01 0.7308E-01 0.8510 0.395 0.045 0.0598 -0.1009
ELAG9 0.90080E-01 0.7308E-01 1.233 0.219 0.065 0.0866 -0.1553
ELAG10 -0.85920E-01 0.7245E-01 -1.186 0.236-0.062 -0.0825 0.1370
ELAG11 0.19439 0.7123E-01 2.729 0.007 0.143 0.1865 -0.2530
ELAG12 -0.10590 0.5665E-01 -1.869 0.062-0.098 -0.1012 0.0911
CONSTANT 0.17193E-02 0.8887 0.1935E-02 0.998 0.000 0.0000 0.0050
Regression B3
|_sample 1 384
|_* try auto commands (private school constructions):
|_auto private public t p1 p2 p3 p4 &
| feb mar apr may jun jul aug sep oct nov dec / order=12
DEPENDENT VARIABLE = PRIVATE
..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS
AUTOREGRESSIVE ERROR MODEL, ORDER= 12
ITERATION 0 ESTIMATES AND ERROR SUM OF SQUARES
...(output omitted)...
ITERATION 8 ESTIMATES AND ERROR SUM OF SQUARES
0.90236E-01 0.69591 0.11902E-01 0.22573E-01 -0.10111E-01
0.18509E-02 -5.0347 4.6465 9.8204 20.477
33.802 32.123 35.964 21.478 16.536
10.006 2.8673 -509.43 -0.79038 -0.23539
0.20884 0.10378 -0.27848 0.25667 0.48324E-01
-0.63936E-01 -0.84454E-01 0.89588E-01 -0.19514 0.98484E-01
0.10546E+06
...(output omitted)...
ASYMPTOTIC
ESTIMATE VARIANCE ST.ERROR T-RATIO
RHO 1 0.79038 0.00268 0.05174 15.27690
RHO 2 0.23539 0.00427 0.06538 3.60037
RHO 3 -0.20884 0.00452 0.06723 -3.10618
RHO 4 -0.10378 0.00474 0.06887 -1.50694
RHO 5 0.27848 0.00498 0.07054 3.94768
RHO 6 -0.25667 0.00530 0.07280 -3.52548
RHO 7 -0.04832 0.00522 0.07228 -0.66859
RHO 8 0.06394 0.00507 0.07121 0.89779
RHO 9 0.08445 0.00514 0.07171 1.17763
RHO 10 -0.08959 0.00498 0.07059 -1.26921
RHO 11 0.19514 0.00479 0.06921 2.81958
RHO 12 -0.09848 0.00306 0.05528 -1.78158
R-SQUARE = 0.9839 R-SQUARE ADJUSTED = 0.9832
VARIANCE OF THE ESTIMATE-SIGMA**2 = 288.14
STANDARD ERROR OF THE ESTIMATE-SIGMA = 16.975
SUM OF SQUARED ERRORS-SSE= 0.10546E+06
MEAN OF DEPENDENT VARIABLE = 180.17
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 366 DF P-VALUE CORR. COEFFICIENT AT MEANS
PUBLIC 0.90236E-01 0.1457E-01 6.195 0.000 0.308 0.3130 0.4047
T 0.69591 0.8287E-01 8.398 0.000 0.402 0.5906 0.7435
P1 0.11902E-01 0.1036E-01 1.148 0.252 0.060 0.1210 1.1766
P2 0.22573E-01 0.6418E-02 3.517 0.000 0.181 0.2440 2.2820
P3 -0.10111E-01 0.5383E-02 -1.878 0.061-0.098 -0.1141 -1.0574
P4 0.18509E-02 0.9538E-02 0.1941 0.846 0.010 0.0219 0.1968
FEB -5.0347 3.344 -1.505 0.133-0.078 -0.0107 -0.0023
MAR 4.6465 4.834 0.9611 0.337 0.050 0.0098 0.0021
APR 9.8204 6.261 1.569 0.118 0.082 0.0208 0.0045
MAY 20.477 7.325 2.795 0.005 0.145 0.0433 0.0095
JUN 33.802 8.070 4.189 0.000 0.214 0.0715 0.0156
JUL 32.123 8.761 3.666 0.000 0.188 0.0680 0.0149
AUG 35.964 8.945 4.021 0.000 0.206 0.0761 0.0166
SEP 21.478 7.935 2.707 0.007 0.140 0.0454 0.0099
OCT 16.536 6.658 2.484 0.013 0.129 0.0350 0.0076
NOV 10.006 5.163 1.938 0.053 0.101 0.0212 0.0046
DEC 2.8673 3.449 0.8315 0.406 0.043 0.0061 0.0013
CONSTANT -509.43 358.9 -1.420 0.157-0.074 0.0000 -2.8275
Regression B4
|_genr tpublic=t*public
|_genr public2=public*public
|_auto private public t tpublic p1 p2 p3 p4 &
| feb mar apr may jun jul aug sep oct nov dec / order=12
DEPENDENT VARIABLE = PRIVATE
..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS
AUTOREGRESSIVE ERROR MODEL, ORDER= 12
ITERATION 0
...(output omitted)...
ITERATION 12 ESTIMATES AND ERROR SUM OF SQUARES
-0.13460 0.14305 0.79829E-03 0.46587E-02 0.14383E-01
-0.10560E-01 0.10686E-01 -5.9906 5.4123 13.545
25.616 37.572 35.422 38.325 25.083
18.920 12.782 4.4060 -267.31 -0.73957
-0.27717 0.14352 0.41919E-01 -0.29037 0.23525
0.76478E-01 -0.66111E-01 -0.36522E-01 0.15552 -0.19057
0.10629E-01 96032.
...(output omitted)...
ASYMPTOTIC
ESTIMATE VARIANCE ST.ERROR T-RATIO
RHO 1 0.73957 0.00273 0.05222 14.16369
RHO 2 0.27717 0.00407 0.06376 4.34672
RHO 3 -0.14352 0.00433 0.06577 -2.18204
RHO 4 -0.04192 0.00449 0.06699 -0.62576
RHO 5 0.29037 0.00462 0.06799 4.27055
RHO 6 -0.23525 0.00492 0.07012 -3.35481
RHO 7 -0.07648 0.00494 0.07028 -1.08818
RHO 8 0.06611 0.00462 0.06798 0.97252
RHO 9 0.03652 0.00479 0.06920 0.52777
RHO 10 -0.15552 0.00463 0.06807 -2.28454
RHO 11 0.19057 0.00443 0.06659 2.86183
RHO 12 -0.01063 0.00296 0.05437 -0.19551
R-SQUARE = 0.9853 R-SQUARE ADJUSTED = 0.9846
VARIANCE OF THE ESTIMATE-SIGMA**2 = 263.10
STANDARD ERROR OF THE ESTIMATE-SIGMA = 16.220
SUM OF SQUARED ERRORS-SSE= 96032.
MEAN OF DEPENDENT VARIABLE = 180.17
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 365 DF P-VALUE CORR. COEFFICIENT AT MEANS
PUBLIC -0.13460 0.3988E-01 -3.375 0.001-0.174 -0.4669 -0.6037
T 0.14305 0.1156 1.238 0.217 0.065 0.1214 0.1528
TPUBLIC 0.79829E-03 0.1163E-03 6.865 0.000 0.338 1.2416 0.8757
P1 0.46587E-02 0.1145E-01 0.4069 0.684 0.021 0.0474 0.4605
P2 0.14383E-01 0.7922E-02 1.816 0.070 0.095 0.1555 1.4540
P3 -0.10560E-01 0.6926E-02 -1.525 0.128-0.080 -0.1191 -1.1044
P4 0.10686E-01 0.1036E-01 1.032 0.303 0.054 0.1264 1.1363
FEB -5.9906 2.960 -2.024 0.044-0.105 -0.0127 -0.0028
MAR 5.4123 3.736 1.449 0.148 0.076 0.0115 0.0025
APR 13.545 4.519 2.997 0.003 0.155 0.0287 0.0063
MAY 25.616 5.042 5.081 0.000 0.257 0.0542 0.0118
JUN 37.572 5.400 6.957 0.000 0.342 0.0795 0.0174
JUL 35.422 6.086 5.820 0.000 0.291 0.0750 0.0164
AUG 38.325 6.393 5.995 0.000 0.299 0.0811 0.0177
SEP 25.083 5.699 4.401 0.000 0.224 0.0531 0.0116
OCT 18.920 4.903 3.858 0.000 0.198 0.0400 0.0088
NOV 12.782 4.119 3.103 0.002 0.160 0.0270 0.0059
DEC 4.4060 3.071 1.435 0.152 0.075 0.0093 0.0020
CONSTANT -267.31 402.6 -0.6640 0.507-0.035 0.0000 -1.4837
|_test
|_test p1=0
|_test p2=0
|_test p3=0
|_test p4=0
|_end
F STATISTIC = 1.1834878 WITH 4 AND 365 D.F. P-VALUE= 0.31766
WALD CHI-SQUARE STATISTIC = 4.7339514 WITH 4 D.F. P-VALUE= 0.31570
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 0.84496
|_stop
EXHIBIT C
|_sample 1 50
|_read(recr.dat) exp age inc fem
|_stat / pcor
NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM
EXP 50 175.70 66.647 4441.9 58.336 290.47
AGE 50 47.144 16.882 284.99 17.355 72.648
INC 50 39.511 21.061 443.57 2.3366 85.351
FEM 50 0.52000 0.50467 0.25469 0.00000 1.0000
|_genr age2=age*age
|_genr inc2=inc*inc
|_genr femage=fem*age
|_genr femage2=fem*age2
|_genr ageinc=age*inc
|_ols exp age fem inc age2 femage femage2 ageinc
R-SQUARE = 0.9463 R-SQUARE ADJUSTED = 0.9373
VARIANCE OF THE ESTIMATE-SIGMA**2 = 278.36
STANDARD ERROR OF THE ESTIMATE-SIGMA = 16.684
SUM OF SQUARED ERRORS-SSE= 11691.
MEAN OF DEPENDENT VARIABLE = 175.70
LOG OF THE LIKELIHOOD FUNCTION = -207.311
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 42 DF P-VALUE CORR. COEFFICIENT AT MEANS
AGE 4.9635 1.458 3.404 0.001 0.465 1.2573 1.3318
FEM -39.113 45.82 -0.8536 0.398-0.131 -0.2962 -0.1158
INC -0.57530 0.5049 -1.140 0.261-0.173 -0.1818 -0.1294
AGE2 -0.63225E-01 0.1844E-01 -3.429 0.001-0.468 -1.4807 -0.9003
FEMAGE -6.0847 2.109 -2.885 0.006-0.407 -2.6707 -0.9700
FEMAGE2 0.78749E-01 0.2295E-01 3.432 0.001 0.468 2.2651 0.7275
AGEINC 0.26949E-01 0.9574E-02 2.815 0.007 0.398 0.5965 0.3174
CONSTANT 129.80 26.40 4.916 0.000 0.604 0.0000 0.7387
Updated: March 17, 1998
Prepared by: Trudy Ann Cameron