PROC IMPORT DATAFILE="/home/smithpc0/sasuser.v94/heterosk.xlsx"

OUT=smithpc0

DBMS=XLSX

REPLACE;

RUN;

data work.smithpc0;

SET work.smithpc0;

ODS graphics off;

PROC REG;

TITLE “White correction of Engle Curve -- the easy way, but search Leamer Tantalus to see reservations”;

MODEL EXPTRAV = INCOME /WHITE;

RUN;

COMMENT 'Do not run all these tests in doing your assessment';

COMMENT 'Use discretion and run only the ones that are called for';

PROC sort;

BY pop;

RUN;

PROC reg;

TITLE 'Engle Curve for Travel Expenditure';

MODEL exptrav = income;

RUN;

OUTPUT OUT=RESFILE RESIDUAL=E;

DATA TWO;

MERGE smithpc0 RESFILE;

BY POP;

LNSQRES = LOG(E**2);

LNPOP = LOG(POP);

RECIPOP= 1/POP;

RECIPIN = 1/INCOME;

TRAVDINC = EXPTRAV/INCOME;

DEXPTRAV = EXPTRAV/POP;

DINCOME = INCOME/POP;

RUN;

PROC REG;

TITLE 'Residual regression for Park test';

MODEL LNSQRES = LNPOP;

RUN;

PROC REG;

TITLE 'Estimation dividing by income';

MODEL TRAVDINC = RECIPIN;

RUN;

PROC REG;

TITLE 'Estimation of transformed model dividing by population';

MODEL DEXPTRAV = RECIPOP DINCOME /NOINT;

RUN;

PROC REG;

TITLE 'Inherently per-capita model';

MODEL DEXPTRAV = DINCOME;

RUN;

OUTPUT OUT=RESFILE2 RESIDUAL=DE;

DATA THREE;

MERGE THREE RESFILE2;

BY POP;

LNSQDE = LOG(DE**2);

RUN;

PROC REG;

TITLE 'Residual regression for Park test on inherently per-capita equation';

MODEL LNSQDE = LNPOP;

RUN;

“White correction of Engle Curve -- the easy way, but search Leamer Tantalus to see reservations”

The REG Procedure

Model: MODEL1

Dependent Variable: EXPTRAV EXPTRAV

Analysis of Variance
Source / DF / Sum of
Squares / Mean
Square / F Value / PrF
Model / 1 / 8313049205 / 8313049205 / 543.43 / <.0001
Error / 49 / 749572261 / 15297393
Corrected Total / 50 / 9062621467
Root MSE / 3911.18819 / R-Square / 0.9173
Dependent Mean / 11862 / Adj R-Sq / 0.9156
Coeff Var / 32.97331
Parameter Estimates
Variable / Label / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t| / Heteroscedasticity Consistent
Standard
Error / tValue / Pr|t|
Intercept / Intercept / 1 / 1027.20093 / 718.30255 / 1.43 / 0.1591 / 609.28901 / 1.69 / 0.0982
INCOME / INCOME / 1 / 0.04541 / 0.00195 / 23.31 / <.0001 / 0.00248 / 18.31 / <.0001

Engle Curve for Travel Expenditure

The REG Procedure

Model: MODEL1

Dependent Variable: EXPTRAV EXPTRAV

Analysis of Variance
Source / DF / Sum of
Squares / Mean
Square / F Value / PrF
Model / 1 / 8313049205 / 8313049205 / 543.43 / <.0001
Error / 49 / 749572261 / 15297393
Corrected Total / 50 / 9062621467
Root MSE / 3911.18819 / R-Square / 0.9173
Dependent Mean / 11862 / Adj R-Sq / 0.9156
Coeff Var / 32.97331
Parameter Estimates
Variable / Label / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t|
Intercept / Intercept / 1 / 1027.20093 / 718.30255 / 1.43 / 0.1591
INCOME / INCOME / 1 / 0.04541 / 0.00195 / 23.31 / <.0001

Residual regression for Park test

The REG Procedure

Model: MODEL1

Dependent Variable: LNSQRES

Analysis of Variance
Source / DF / Sum of
Squares / Mean
Square / F Value / PrF
Model / 1 / 51.51720 / 51.51720 / 6.71 / 0.0126
Error / 49 / 376.06639 / 7.67482
Corrected Total / 50 / 427.58359
Root MSE / 2.77035 / R-Square / 0.1205
Dependent Mean / 13.59789 / Adj R-Sq / 0.1025
Coeff Var / 20.37336
Parameter Estimates
Variable / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t|
Intercept / 1 / -1.12446 / 5.69567 / -0.20 / 0.8443
LNPOP / 1 / 0.97397 / 0.37593 / 2.59 / 0.0126

Estimation dividing by income

The REG Procedure

Model: MODEL1

Dependent Variable: TRAVDINC

Analysis of Variance
Source / DF / Sum of
Squares / Mean
Square / F Value / PrF
Model / 1 / 0.00468 / 0.00468 / 4.58 / 0.0374
Error / 49 / 0.05016 / 0.00102
Corrected Total / 50 / 0.05484
Root MSE / 0.03199 / R-Square / 0.0854
Dependent Mean / 0.05894 / Adj R-Sq / 0.0667
Coeff Var / 54.27910
Parameter Estimates
Variable / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t|
Intercept / 1 / 0.04894 / 0.00647 / 7.56 / <.0001
RECIPIN / 1 / 871.62080 / 407.49491 / 2.14 / 0.0374

Estimation of transformed model dividing by population

The REG Procedure

Model: MODEL1

Dependent Variable: DEXPTRAV

Note:No intercept in model. R-Square is redefined.

Analysis of Variance
Source / DF / Sum of
Squares / Mean
Square / F Value / PrF
Model / 2 / 0.00031264 / 0.00015632 / 89.78 / <.0001
Error / 49 / 0.00008532 / 0.00000174
Uncorrected Total / 51 / 0.00039796
Root MSE / 0.00132 / R-Square / 0.7856
Dependent Mean / 0.00233 / Adj R-Sq / 0.7769
Coeff Var / 56.69934
Parameter Estimates
Variable / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t|
RECIPOP / 1 / 1161.79589 / 406.37632 / 2.86 / 0.0062
DINCOME / 1 / 0.04738 / 0.00671 / 7.06 / <.0001

Inherently per-capita model

The REG Procedure

Model: MODEL1

Dependent Variable: DEXPTRAV

Analysis of Variance
Source / DF / Sum of
Squares / Mean
Square / F Value / PrF
Model / 1 / 0.00002767 / 0.00002767 / 14.41 / 0.0004
Error / 49 / 0.00009407 / 0.00000192
Corrected Total / 50 / 0.00012174
Root MSE / 0.00139 / R-Square / 0.2273
Dependent Mean / 0.00233 / Adj R-Sq / 0.2115
Coeff Var / 59.53729
Parameter Estimates
Variable / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t|
Intercept / 1 / -0.00192 / 0.00113 / -1.69 / 0.0976
DINCOME / 1 / 0.10889 / 0.02869 / 3.80 / 0.0004

Residual regression for Park test on inherently per-capita equation

The REG Procedure

Model: MODEL1

Dependent Variable: LNSQDE

Analysis of Variance
Source / DF / Sum of
Squares / Mean
Square / F Value / PrF
Model / 1 / 3.56714 / 3.56714 / 0.77 / 0.3830
Error / 49 / 225.56850 / 4.60344
Corrected Total / 50 / 229.13564
Root MSE / 2.14556 / R-Square / 0.0156
Dependent Mean / -15.36014 / Adj R-Sq / -0.0045
Coeff Var / -13.96838
Parameter Estimates
Variable / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t|
Intercept / 1 / -11.48613 / 4.41115 / -2.60 / 0.0122
LNPOP / 1 / -0.25629 / 0.29115 / -0.88 / 0.3830