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ESTIMATING THE KUZNETS CURVE WITH A POLYNOMIAL FUNCTION OF LOG GDP PER CAPITA
>USE 'C:\SYSTAT\ASA9105.SYS'
>select v3$<>'GBON' and v3$<>'PKST' and v3$<>'OMAN' and u20smp <> .
>stat l10rgdp1
 
                      L10RGDP1
  N of cases               60
  Minimum            2.451786
  Maximum            3.975845
  Mean               3.376584
  Standard Dev       0.418529
 

>mglh
>model u20smp = constant + l10rgdp1 + l10rgdp1*l10rgdp1
>estimate
 
Dep Var: U20SMP   N: 60   Multiple R: 0.575803   Squared multiple R: 0.331549
 
Adjusted squared multiple R: 0.308094   Standard error of estimate: 7.324550
 
Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)
 
CONSTANT        -63.085168    62.024609     0.0        .       -1.01710  0.31340
L10RGDP1         81.408835    37.982385     3.869360  0.003598  2.14333  0.03637
L10RGDP1
*L10RGDP1       -13.966332     5.744243    -4.389341  0.003598 -2.43136  0.01821
 
                             Analysis of Variance
 
Source             Sum-of-Squares   df  Mean-Square     F-ratio       P
 
Regression           1516.750692     2   758.375346   14.135861    0.000010
Residual             3057.995141    57    53.649038
-------------------------------------------------------------------------------
 
*** WARNING ***
Case           86 has large leverage   (Leverage =     0.279880)
Case           95 has large leverage   (Leverage =     0.246588)
 
Durbin-Watson D Statistic     1.386
First Order Autocorrelation   0.302

>let x = l10rgdp1-3.377
>model u20smp = constant + x + x*x
>estimate
 
Dep Var: U20SMP   N: 60   Multiple R: 0.575803   Squared multiple R: 0.331549
 
Adjusted squared multiple R: 0.308094   Standard error of estimate: 7.324550
 
Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)
 
CONSTANT         52.558622     1.368354     0.0        .       38.41009  0.00000
X               -12.919768     2.443388    -0.614076  0.869511 -5.28765  0.00000
X*X             -13.966332     5.744243    -0.282364  0.869511 -2.43136  0.01821
 
                             Analysis of Variance
 
Source             Sum-of-Squares   df  Mean-Square     F-ratio       P
 
Regression           1516.750692     2   758.375346   14.135861    0.000010
Residual             3057.995141    57    53.649038
-------------------------------------------------------------------------------
 
*** WARNING ***
Case           86 has large leverage   (Leverage =     0.279880)
Case           95 has large leverage   (Leverage =     0.246588)
 
Durbin-Watson D Statistic     1.386
First Order Autocorrelation   0.302

>plot u20smp*x/stick smooth=quad short