Springer Texts in Business and Economics

Dependent Variable: LNRGDP

Analysis of Variance

Sumof

Mean

Source

DF

Squares

Square

F Value Prob > F

Model

1

53.88294

53.88294

535.903

0.0001

Error

18

1.80983

0.10055

C Total

19

55.69277

RootMSE 0.31709 R-square 0.9675 DepMean 10.60225 Adj R-sq 0.9657

C. V.

2.99078

Parameter Estimates

Parameter

Standard

T for HO:

Variable

DF

Estimate

Error

Parameter=0

Prob > |T|

INTERCEP

1

1.070317

0.41781436

2.562

0.0196

LNEN

1

0.932534

0.04028297

23.150

0.0001

e. Log-log specification

Dependent Variable: LNEN1

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob > F

Model

1

59.94798

59.94798

535.903

0.0001

Error

18

2.01354

0.11186

C Total

19

61.96153

Root MSE

0.33446

R-square

0.9675

DepMean 14.31589

Adj R-sq

0.9657

C. V.

2.33628

Variable

DF

Parameter

Estimate

Standard

Error

T for HO: Parameter=0

Prob > |T|

INTERCEP

1

3.316057

0.48101294

6.894

0.0001

LNRGDP

1

1.037499

0.04481721

23.150

0.0001

Linear Specificiation Dependent Variable: EN1

Analysis of Variance

Source

DF

Sum of Squares

Mean

Square

F Value

Prob > F

Model

1

6.7345506E14

6.7345506E14

386.28

0.0001

Error

18

3.1381407E13

1.7434115E12

6

C Total

19

7.0483646E14

Root MSE 1320383.09457 R-square 0.9555

Dep Mean 4607256.0000 Adj R-sq 0.9530

C. V. 28.65877

Parameter Estimates

Variable

DF

Parameter

Estimate

Standard

Error

T for HO: Parameter=0

Prob > |T|

INTERCEP

1

-190151

383081.08995

-0.496

0.6256

RGDP

1

46.759427

2.37911166

19.654

0.0001

Linear Specification before the multiplication by 60 Dependent Variable: EN

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob > F

Model

1

187070848717

187070848717

386.286

0.0001

Error

18

8717057582.2

484280976.79

C Total

19

195787906299

Root MSE 22006.38491 R-square 0.9555

Dep Mean 76787.60000 Adj R-sq 0.9530

C. V. 28.6587

Parameter Standard T for HO:

Variable DF Estimate Error Parameter=0 Prob > |T|

INTERCEP 1 -3169.188324 6384.6848326 -0.496 0.6256

RGDP 1 0.779324 0.03965186 19.654 0.0001

What happens when we multiply our energy variable by 60? For the linear model specification, both a * and " * are multiplied by 60, their standard errors are also multiplied by 60 and their t-statistics are the same.

For the log-log model specification, " is the same, but a is equal to the old a + log 60. The intercept therefore is affected but not the slope. Its standard error is the same, but its t-statistic is changed.

Подпись: 8 10 12 LNRGDPПодпись: 6image154Подпись: 0 100000 200000 300000 400000 500000 RGDP Подпись: 2000000Подпись: 0Подпись: -2000000Подпись: -4000000image1604000000

Подпись: Residuals

14

g. Plot of residuals for both linear and log-log models SAS PROGRAM

Data Rawdata;

Input Country $ RGDP EN;

Cards;

Data Energy; Set Rawdata;

LNRGDP=log (RGDP); LNEN=log(EN);

EN1=EN*60; LNEN1=log(EN1);

Proc reg data=energy; Model LNRGDP=LNEN;

Proc reg data=energy; Model LNEN1=LNRGDP/CLM, CLI;

Output out=OUT1 R=LN_RESID;

Proc reg data=energy; Model EN1=RGDP;

Output out=OUT2 R=RESID;

Proc reg data=energy; Model EN=RGDP; data Resid; set outl (keep=lnrgdp ln_resid);

set out2(keep=rgdp resid);

Proc plot data=resid vpercent=60 hpercent=85;

Plot ln_resid*lnrgdp=‘*’;

Plot resid*rgdp=‘*’; run;

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Springer Texts in Business and Economics

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