MODEL:
! Linear Regression with one independent variable;
! Linear regression is a forecasting method that
models the relationship between a dependent
variable to one or more independent variable. For
this model we wish to predict Y with the equation:
Y(i) = CONS + SLOPE * X(i);
SETS:
! The OBS set contains the data points for
X and Y;
OBS/1..11/:
Y, ! The dependent variable (annual road
casualties);
X; ! The independent or explanatory variable
(annual licensed vehicles;
! The OUT set contains the output of the model.;
OUT/ CONS, SLOPE, RSQRU, RSQRA/: R;
ENDSETS
! Our data on yearly road casualties vs. licensed
vehicles, was taken from Johnston, Econometric
Methods;
DATA:
Y = 166 153 177 201 216 208 227 238 268 268 274;
X = 352 373 411 441 462 490 529 577 641 692 743;
ENDDATA
SETS:
! The derived set OBS contains the mean shifted
values of the independent and dependent
variables;
OBSN( OBS): XS, YS;
ENDSETS
! Number of observations;
NK = @SIZE( OBS);
! Compute means;
XBAR = @SUM( OBS: X)/ NK;
YBAR = @SUM( OBS: Y)/ NK;
! Shift the observations by their means;
@FOR( OBS( I):
XS( I) = X( I)  XBAR;
YS( I) = Y( I)  YBAR);
! Compute various sums of squares;
XYBAR = @SUM( OBSN: XS * YS);
XXBAR = @SUM( OBSN: XS * XS);
YYBAR = @SUM( OBSN: YS * YS);
! Finally, the regression equation;
R( @INDEX( SLOPE)) = XYBAR/ XXBAR;
R( @INDEX( CONS)) = YBAR  R( @INDEX( SLOPE))
* XBAR;
RESID = @SUM( OBSN: ( YS  R( @INDEX( SLOPE))
* XS)^2);
! A measure of how well X can be used to predict Y 
the unadjusted (RSQRU) and adjusted (RSQRA)
fractions of variance explained;
R( @INDEX( RSQRU)) = 1  RESID/ YYBAR;
R( @INDEX( RSQRA)) = 1  ( RESID/ YYBAR) *
( NK  1)/( NK  2);
! XS and YS may take on negative values;
@FOR( OBSN: @FREE( XS); @FREE( YS));
END
