Springer Texts in Business and Economics

Dependent Variable: LNRGDP

Analysis of Variance

e. Log-log specification

Dependent Variable: LNEN1

Analysis of Variance

Linear Specificiation Dependent Variable: EN1

Analysis of Variance

Root MSE 1320383.09457 R-square 0.9555

Dep Mean 4607256.0000 Adj R-sq 0.9530

C. V. 28.65877

Linear Specification before the multiplication by 60 Dependent Variable: EN

Analysis of Variance

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.

4000000

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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;