UNIVERSITY OF CALIFORNIA, LOS ANGELES
Department of Economics
Economics 143 (Cameron) - Applied Regression
Analysis
Classroom Handout #17: Heteroscedasticity
Diagnostics
|_sample 1 50
|_* note the use of the format command:
|_format(3x,f4.1,f6.1,f5.0,f6.0,f6.1)
|_read(transp87.dat) taxrate price gas regist roads / format
UNIT 88 IS NOW ASSIGNED TO: transp87.dat
READ USES FORMAT:(3x,f4.1,f6.1,f5.0,f6.0,f6.1)
|_* variables are defined as follows:
|_* 50 state-level cross-sectional observations for the year 1987 on the
|_* variables GAS (transportation energy use in trillion BTUs), PRICE (cents
|_* per gallon average for all grades of fuel, excluding taxes), TAXRATE (the
|_* state gas tax, in cents per gallon), REGIST (the number of motor vehicle
|_* registrations), and ROADS (thousands of miles of public roads and
|_* streets). Note presence of character data in the first three columns.
|_ols gas price taxrate regist / resid=e
REQUIRED MEMORY IS PAR= 6 CURRENT PAR= 500
OLS ESTIMATION
50 OBSERVATIONS DEPENDENT VARIABLE = GAS
...NOTE..SAMPLE RANGE SET TO: 1, 50
R-SQUARE = 0.9257 R-SQUARE ADJUSTED = 0.9209
VARIANCE OF THE ESTIMATE-SIGMA**2 = 17532.
STANDARD ERROR OF THE ESTIMATE-SIGMA = 132.41
SUM OF SQUARED ERRORS-SSE= 0.80646E+06
MEAN OF DEPENDENT VARIABLE = 427.00
LOG OF THE LIKELIHOOD FUNCTION = -313.157
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.10055E+08 3. 0.33515E+07 191.167
ERROR 0.80646E+06 46. 17532. P-VALUE
TOTAL 0.10861E+08 49. 0.22165E+06 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 46 DF P-VALUE CORR. COEFFICIENT AT MEANS
PRICE 1.4736 4.128 0.3569 0.723 0.053 0.0158 0.2258
TAXRATE 0.92519 6.431 0.1439 0.886 0.021 0.0066 0.0307
REGIST 0.12291 0.5577E-02 22.04 0.000 0.956 0.9665 1.0292
CONSTANT -122.01 325.5 -0.3748 0.710-0.055 0.0000 -0.2857
|_genr e2=e*e
|_ols e2 price taxrate regist
REQUIRED MEMORY IS PAR= 6 CURRENT PAR= 500
OLS ESTIMATION
50 OBSERVATIONS DEPENDENT VARIABLE = E2
...NOTE..SAMPLE RANGE SET TO: 1, 50
R-SQUARE = 0.2682 R-SQUARE ADJUSTED = 0.2205
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.16523E+10
STANDARD ERROR OF THE ESTIMATE-SIGMA = 40648.
SUM OF SQUARED ERRORS-SSE= 0.76005E+11
MEAN OF DEPENDENT VARIABLE = 16129.
LOG OF THE LIKELIHOOD FUNCTION = -599.498
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.27859E+11 3. 0.92863E+10 5.620
ERROR 0.76005E+11 46. 0.16523E+10 P-VALUE
TOTAL 0.10386E+12 49. 0.21197E+10 0.002
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 46 DF P-VALUE CORR. COEFFICIENT AT MEANS
PRICE -269.10 1267. -0.2123 0.833-0.031 -0.0296 -1.0918
TAXRATE 1209.3 1974. 0.6125 0.543 0.090 0.0881 1.0613
REGIST 6.5838 1.712 3.845 0.000 0.493 0.5294 1.4595
CONSTANT -6920.7 0.9993E+05 -0.6926E-01 0.945-0.010 0.0000 -0.4291
|_sort regist gas price taxrate
DATA HAS BEEN SORTED BY VARIABLE REGIST
|_ols gas price taxrate regist
REQUIRED MEMORY IS PAR= 6 CURRENT PAR= 500
OLS ESTIMATION
50 OBSERVATIONS DEPENDENT VARIABLE = GAS
...NOTE..SAMPLE RANGE SET TO: 1, 50
R-SQUARE = 0.9257 R-SQUARE ADJUSTED = 0.9209
VARIANCE OF THE ESTIMATE-SIGMA**2 = 17532.
STANDARD ERROR OF THE ESTIMATE-SIGMA = 132.41
SUM OF SQUARED ERRORS-SSE= 0.80646E+06
MEAN OF DEPENDENT VARIABLE = 427.00
LOG OF THE LIKELIHOOD FUNCTION = -313.157
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.10055E+08 3. 0.33515E+07 191.167
ERROR 0.80646E+06 46. 17532. P-VALUE
TOTAL 0.10861E+08 49. 0.22165E+06 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 46 DF P-VALUE CORR. COEFFICIENT AT MEANS
PRICE 1.4736 4.128 0.3569 0.723 0.053 0.0158 0.2258
TAXRATE 0.92519 6.431 0.1439 0.886 0.021 0.0066 0.0307
REGIST 0.12291 0.5577E-02 22.04 0.000 0.956 0.9665 1.0292
CONSTANT -122.01 325.5 -0.3748 0.710-0.055 0.0000 -0.2857
|_diagnos / het chowtest
REQUIRED MEMORY IS PAR= 9 CURRENT PAR= 500
DEPENDENT VARIABLE = GAS 50 OBSERVATIONS
REGRESSION COEFFICIENTS
1.47359007578 0.925194440215 0.122914149650 -122.005381949
HETEROSKEDASTICITY TESTS
CHI-SQUARE D.F. P-VALUE
TEST STATISTIC
E**2 ON YHAT: 12.894 1 0.00033
E**2 ON YHAT**2: 7.356 1 0.00669
E**2 ON LOG(YHAT**2): 9.210 1 0.00241
E**2 ON X (B-P-G) TEST:
BASED ON R2: 13.411 3 0.00383
BASED ON SSR: 53.543 3 0.00000
E**2 ON LAG(E**2) ARCH TEST: 2.641 1 0.10416
LOG(E**2) ON X (HARVEY) TEST: 23.207 3 0.00004
ABS(E) ON X (GLEJSER) TEST: 35.655 3 0.00000
HARVEY-COLLIER [1977] RECURSIVE T-TEST = 0.4098 WITH 45 D.F.
HARVEY-PHILLIPS [1974] HETEROSKEDASTICITY TEST = 42.8976 WITH M = 15
BACKWARDS
HARVEY-COLLIER [1977] RECURSIVE T-TEST = 2.4063 WITH 45 D.F.
HARVEY-PHILLIPS [1974] HETEROSKEDASTICITY TEST = 0.0550 WITH M = 15
SEQUENTIAL CHOW AND GOLDFELD-QUANDT TESTS
N1 N2 SSE1 SSE2 CHOW PVALUE G-Q DF1 DF2 PVALUE
5 45 1843.9 0.79359E+06 0.14564 0.964 0.9527E-01 1 41 0.241
6 44 2765.0 0.79354E+06 0.13397 0.969 0.6969E-01 2 40 0.067
7 43 3219.2 0.79354E+06 0.12792 0.971 0.5274E-01 3 39 0.016
8 42 3237.1 0.79354E+06 0.12771 0.972 0.3875E-01 4 38 0.003
9 41 3271.0 0.78252E+06 0.27629 0.892 0.3093E-01 5 37 0.001
10 40 5446.4 0.78132E+06 0.26290 0.900 0.4183E-01 6 36 0.000
11 39 6692.9 0.78108E+06 0.24918 0.909 0.4284E-01 7 35 0.000
12 38 6692.9 0.77818E+06 0.28892 0.884 0.3655E-01 8 34 0.000
13 37 6753.4 0.77794E+06 0.29136 0.882 0.3183E-01 9 33 0.000
14 36 8609.9 0.77785E+06 0.26714 0.897 0.3542E-01 10 32 0.000
15 35 8632.2 0.77375E+06 0.32325 0.861 0.3144E-01 11 31 0.000
16 34 9614.7 0.77054E+06 0.35404 0.840 0.3119E-01 12 30 0.000
17 33 9669.8 0.76953E+06 0.36742 0.830 0.2803E-01 13 29 0.000
18 32 11805. 0.76666E+06 0.37770 0.823 0.3080E-01 14 28 0.000
19 31 14947. 0.74456E+06 0.64917 0.631 0.3614E-01 15 27 0.000
20 30 15970. 0.74085E+06 0.68881 0.604 0.3503E-01 16 26 0.000
21 29 16825. 0.74046E+06 0.68188 0.608 0.3341E-01 17 25 0.000
22 28 17906. 0.74012E+06 0.67096 0.616 0.3226E-01 18 24 0.000
23 27 18010. 0.71293E+06 1.0849 0.376 0.3058E-01 19 23 0.000
24 26 28258. 0.71283E+06 0.92635 0.458 0.4361E-01 20 22 0.000
25 25 34193. 0.70918E+06 0.89123 0.478 0.4821E-01 21 21 0.000
26 24 36385. 0.70543E+06 0.91503 0.464 0.4689E-01 22 20 0.000
27 23 36479. 0.70491E+06 0.92158 0.460 0.4275E-01 23 19 0.000
28 22 0.13281E+06 0.60211E+06 1.0221 0.407 0.1654 24 18 0.000
29 21 0.14109E+06 0.59854E+06 0.94890 0.445 0.1603 25 17 0.000
30 20 0.14260E+06 0.59584E+06 0.96731 0.435 0.1473 26 16 0.000
31 19 0.14478E+06 0.59516E+06 0.94400 0.448 0.1351 27 15 0.000
32 18 0.14675E+06 0.59418E+06 0.92866 0.457 0.1235 28 14 0.000
33 17 0.15048E+06 0.59328E+06 0.88528 0.481 0.1137 29 13 0.000
34 16 0.16462E+06 0.56524E+06 1.1020 0.368 0.1165 30 12 0.000
35 15 0.16526E+06 0.55549E+06 1.2487 0.305 0.1056 31 11 0.000
36 14 0.16820E+06 0.55160E+06 1.2643 0.299 0.9529E-01 32 10 0.000
37 13 0.17702E+06 0.54809E+06 1.1780 0.334 0.8809E-01 33 9 0.000
38 12 0.17708E+06 0.54640E+06 1.2044 0.323 0.7625E-01 34 8 0.000
39 11 0.17733E+06 0.53839E+06 1.3313 0.274 0.6588E-01 35 7 0.000
40 10 0.17873E+06 0.53173E+06 1.4188 0.244 0.5602E-01 36 6 0.000
41 9 0.17919E+06 0.47763E+06 2.3922 0.066 0.5070E-01 37 5 0.000
42 8 0.18817E+06 0.18037E+06 12.477 0.000 0.1098 38 4 0.000
43 7 0.21605E+06 0.11493E+06 15.084 0.000 0.1446 39 3 0.001
44 6 0.22221E+06 0.11464E+06 14.638 0.000 0.9692E-01 40 2 0.000
45 5 0.24167E+06 0.10933E+06 13.625 0.000 0.5391E-01 41 1 0.000
CHOW TEST - F DISTRIBUTION WITH DF1= 4 AND DF2= 42
|_stop
Updated: 4:20 PM 11/23/98; Prepared by: Trudy Ann Cameron; Site Index