/* x = average index of central bank independence (1 = little independence
         4 = very independent)   
   y = average Inflation 1955 - 1988 
   Source: Alesina and Summers (1993) Jo. of Money,
   Credit, and Banking  */

data in;
  input x y;
cards;
1.5 8.5
1 7.6
2 6.4
1.75 7.3
2 6.7
2 6.1
2.5 6.5
2 4.1
2 6.1
2 6.1
2.5 4.5
2.5 4.2
2.5 4.9
3.5 4.1
4 3
4 3.2
;

proc means data=in;
   var x y;

run;

proc reg data = in;
   model y = x / r clm cli;
  
run;

/*  Here we use the transformed model to obtain the point
    prediction when x = 1.50 (it is the estimate of the intercept
    in the transformed model) and the ingredients for the construction
    of the standard error of the prediction error.  We use the
    Standard Error of the Transformed Regression (RMSE in SAS) or the Mean
    Square of the Error in the ANOVA table) to construct the standard error of the
    prediction error.  se(prediction error) = sqrt(RMSE^2 + se(intercept)^2)=
    sqrt(mean square error + se(intercept)^2).  */

data in;
  set in;
  xstar = x - 1.50;

proc reg data=in;
  model y = xstar;

run;