UNIVERSITY OF CALIFORNIA, LOS ANGELES
Department of Economics
Economics 143 (Cameron) - Applied Regression
Analysis
Midterm Exhibits
|_* Hypothetical data on monthly demand for cigarettes, for a random sample
|_* of young adult smokers (18-30 years of age). Data include:
|_* age = age of individual
|_* inc = annual before-tax income of individual
|_* price = typical price paid per pack for this individual
|_* packs = average number of packs per month consumed by the individual
|_sample 1 30
|_read(smokes.dat) age inc price packs
|_* Descriptive Statistics
|_stat / pcor
NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM
AGE 30 24.300 4.3243 18.700 18.000 30.000
INC 30 39.967 21.227 450.59 0.00000 82.000
PRICE 30 2.1500 0.58663E-01 0.34414E-02 2.0400 2.2500
PACKS 30 14.433 6.1691 38.058 4.9180 26.127
CORRELATION MATRIX OF VARIABLES - 30 OBSERVATIONS
AGE 1.0000
INC 0.88253 1.0000
PRICE -0.22972 -0.92490E-01 1.0000
PACKS 0.94684 0.89881 -0.19051 1.0000
AGE INC PRICE PACKS
|_* Regression 1
|_ols inc packs / anova
R-SQUARE = 0.8079 R-SQUARE ADJUSTED = 0.8010
VARIANCE OF THE ESTIMATE-SIGMA**2 = 89.671
STANDARD ERROR OF THE ESTIMATE-SIGMA = 9.4695
SUM OF SQUARED ERRORS-SSE= 2510.8
MEAN OF DEPENDENT VARIABLE = 39.967
LOG OF THE LIKELIHOOD FUNCTION = -108.975
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 10556. 1. 10556. 117.722
ERROR 2510.8 28. 89.671 P-VALUE
TOTAL 13067. 29. 450.59 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 28 DF P-VALUE CORR. COEFFICIENT AT MEANS
PACKS 3.0927 0.2850 10.85 0.000 0.899 0.8988 1.1169
CONSTANT -4.6708 4.463 -1.047 0.304-0.194 0.0000 -0.1169
|_* Regression 2
|_ols packs inc / anova
R-SQUARE = 0.8079 R-SQUARE ADJUSTED = 0.8010
VARIANCE OF THE ESTIMATE-SIGMA**2 = 7.5739
STANDARD ERROR OF THE ESTIMATE-SIGMA = 2.7521
SUM OF SQUARED ERRORS-SSE= 212.07
MEAN OF DEPENDENT VARIABLE = 14.433
LOG OF THE LIKELIHOOD FUNCTION = -71.9038
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 891.61 1. 891.61 117.722
ERROR 212.07 28. 7.5739 P-VALUE
TOTAL 1103.7 29. 38.058 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 28 DF P-VALUE CORR. COEFFICIENT AT MEANS
INC 0.26122 0.2408E-01 10.85 0.000 0.899 0.8988 0.7233
CONSTANT 3.9934 1.085 3.679 0.001 0.571 0.0000 0.2767
|_* Regression 3
|_ols packs inc price / anova
R-SQUARE = 0.8195 R-SQUARE ADJUSTED = 0.8061
VARIANCE OF THE ESTIMATE-SIGMA**2 = 7.3790
STANDARD ERROR OF THE ESTIMATE-SIGMA = 2.7164
SUM OF SQUARED ERRORS-SSE= 199.23
MEAN OF DEPENDENT VARIABLE = 14.433
LOG OF THE LIKELIHOOD FUNCTION = -70.9672
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 904.45 2. 452.22 61.286
ERROR 199.23 27. 7.3790 P-VALUE
TOTAL 1103.7 29. 38.058 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 27 DF P-VALUE CORR. COEFFICIENT AT MEANS
INC 0.25830 0.2387E-01 10.82 0.000 0.901 0.8888 0.7153
PRICE -11.390 8.636 -1.319 0.198-0.246 -0.1083 -1.6967
CONSTANT 28.598 18.69 1.530 0.138 0.283 0.0000 1.9814
|_* Plot A1
|_plot inc age / gnu
|_* Plot A2
|_plot price age / gnu
|_* Regression 4
|_ols packs age inc price / anova auxrsqr
R-SQUARE OF AGE ON OTHER INDEPENDENT VARIABLES = 0.8010
R-SQUARE OF INC ON OTHER INDEPENDENT VARIABLES = 0.7917
R-SQUARE OF PRICE ON OTHER INDEPENDENT VARIABLES = 0.1077
R-SQUARE OF CONSTANT ON OTHER INDEPENDENT VARIABLES =*********
R-SQUARE = 0.9146 R-SQUARE ADJUSTED = 0.9047
VARIANCE OF THE ESTIMATE-SIGMA**2 = 3.6259
STANDARD ERROR OF THE ESTIMATE-SIGMA = 1.9042
SUM OF SQUARED ERRORS-SSE= 94.274
MEAN OF DEPENDENT VARIABLE = 14.433
LOG OF THE LIKELIHOOD FUNCTION = -59.7432
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 1009.4 3. 336.47 92.795
ERROR 94.274 26. 3.6259 P-VALUE
TOTAL 1103.7 29. 38.058 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 26 DF P-VALUE CORR. COEFFICIENT AT MEANS
AGE 0.98616 0.1833 5.380 0.000 0.726 0.6913 1.6603
INC 0.83779E-01 0.3650E-01 2.295 0.030 0.410 0.2883 0.2320
PRICE -0.53142 6.381 -0.8328E-01 0.934-0.016 -0.0051 -0.0792
CONSTANT -11.736 15.09 -0.7776 0.444-0.151 0.0000 -0.8131
|_* Confidence Ellipse
|_confid age inc / gnu lineonly
USING 95% AND 90% CONFIDENCE INTERVALS
CONFIDENCE INTERVALS BASED ON T-DISTRIBUTION WITH 26 D.F.
- T CRITICAL VALUES = 2.056 AND 1.706
NAME LOWER 2.5% LOWER 5% COEFFICIENT UPPER 5% UPPER 2.5% STD. ERROR
AGE 0.6093 0.6735 0.98616 1.299 1.363 0.183
INC 0.8739E-02 0.2151E-01 0.83779E-01 0.1460 0.1588 0.036
CONFIDENCE REGION PLOT FOR age AND inc
USING F DISTRIBUTION WITH 2 AND 26 D.F. F-VALUE = 3.370
|_test
|_test inc=0
|_test price=0
|_end
F STATISTIC = 2.7515678 WITH 2 AND 26 D.F. P-VALUE= 0.08242
WALD CHI-SQUARE STATISTIC = 5.5031356 WITH 2 D.F. P-VALUE= 0.06383
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 0.36343
|_test
|_test age=0
|_test inc=0
|_end
F STATISTIC = 133.66920 WITH 2 AND 26 D.F. P-VALUE= 0.00000
WALD CHI-SQUARE STATISTIC = 267.33840 WITH 2 D.F. P-VALUE= 0.00000
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 0.00748
|_test age=1
TEST VALUE = -0.13839E-01 STD. ERROR OF TEST VALUE 0.18329
T STATISTIC = -0.75503962E-01 WITH 26 D.F. P-VALUE= 0.94039
F STATISTIC = 0.57008483E-02 WITH 1 AND 26 D.F. P-VALUE= 0.94039
WALD CHI-SQUARE STATISTIC = 0.57008483E-02 WITH 1 D.F. P-VALUE= 0.93981
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 1.00000
|_test inc-10*age=0
TEST VALUE = -9.7778 STD. ERROR OF TEST VALUE 1.8655
T STATISTIC = -5.2415235 WITH 26 D.F. P-VALUE= 0.00002
F STATISTIC = 27.473568 WITH 1 AND 26 D.F. P-VALUE= 0.00002
WALD CHI-SQUARE STATISTIC = 27.473568 WITH 1 D.F. P-VALUE= 0.00000
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 0.03640
|_test 10*inc=age
TEST VALUE = -0.14837 STD. ERROR OF TEST VALUE 0.53453
T STATISTIC = -0.27756468 WITH 26 D.F. P-VALUE= 0.78354
F STATISTIC = 0.77042150E-01 WITH 1 AND 26 D.F. P-VALUE= 0.78354
WALD CHI-SQUARE STATISTIC = 0.77042150E-01 WITH 1 D.F. P-VALUE= 0.78135
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 1.00000
Updated: 11/2/98; Prepared by: Trudy Ann Cameron; Site Index