ÐÏࡱá>þÿ  þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿiable (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 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 varþÿÿÿýÿÿÿþÿÿÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRoot Entryÿÿÿÿÿÿÿÿ¹CONTENTSÿÿÿÿÿÿÿÿÿÿÿÿ¹ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRoot Entryÿÿÿÿÿÿÿÿ*0_šîÏ»òÀð^ Ž$ŠeþÄ € Contentsÿÿÿÿÿÿÿÿÿÿÿÿn ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿþÿÿÿýÿÿÿþÿÿÿ þÿÿÿ  ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ  !"#$%&'()*+,-þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ; \par XXBAR = \cf1 @SUM\cf2 ( OBSN: XS * XS); \par YYBAR = \cf1 @SUM\cf2 ( OBSN: YS * YS); \par \par \cf3 ! Finally, the regression equation;\cf2 \par R( \cf1 @INDEX\cf2 ( SLOPE)) = XYBAR/ XXBAR; \par R( \cf1 @INDEX\cf2 ( CONS)) = YBAR - R( \cf1 @INDEX\cf2 ( SLOPE)) \par * XBAR; \par RESID = \cf1 @SUM\cf2 ( OBSN: ( YS - R( \cf1 @INDEX\cf2 ( SLOPE)) \par * XS)^2); \par \cf3 ! A measure of how well X can be used to predict Y - \par the unadjusted (RSQRU) and adjusted (RSQRA) \par fractions of variance explained;\cf2 \par R( \cf1 @INDEX\cf2 ( RSQRU)) = 1 - RESID/ YYBAR; \par R( \cf1 @INDEX\cf2 ( RSQRA)) = 1 - ( RESID/ YYBAR) * \par ( NK - 1)/( NK - 2); \par \par \cf3 ! XS and YS may take on negative values;\cf2 \par \cf1 @FOR\cf2 ( OBSN: \cf1 @FREE\cf2 ( XS); \cf1 @FREE\cf2 ( YS)); \par \par \cf1 END\cf2 \par \par } ì‹{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fnil\fcharset0 Courier New;}} {\colortbl ;\red0\green0\blue255;\red0\green0\blue0;\red0\green175\blue0;} \viewkind4\uc1\pard\cf1\f0\fs20 MODEL\cf2 : \par \cf3 ! Linear Regression with one independent variable;\cf2 \par \cf3 ! Linear regression is a forecasting method that \par models the relationship between a dependent \par variable to one or more independent variable. For \par this model we wish to predict Y with the equation: \par Y(i) = CONS + SLOPE * X(i);\cf2 \par \par \cf1 SETS\cf2 : \par \cf3 ! The OBS set contains the data points for \par X and Y;\cf2 \par OBS/1..11/: \par Y, \cf3 ! The dependent variable (annual road \par casualties);\cf2 \par X; \cf3 ! The independent or explanatory variable \par (annual licensed vehicles;\cf2 \par \cf3 ! The OUT set contains the output of the model.;\cf2 \par OUT/ CONS, SLOPE, RSQRU, RSQRA/: R; \par \cf1 ENDSETS\cf2 \par \par \cf3 ! Our data on yearly road casualties vs. licensed \par vehicles, was taken from Johnston, Econometric \par Methods;\cf2 \par \cf1 DATA\cf2 : \par Y = 166 153 177 201 216 208 227 238 268 268 274; \par X = 352 373 411 441 462 490 529 577 641 692 743; \par \cf1 ENDDATA\cf2 \par \par \cf1 SETS\cf2 : \par \cf3 ! The derived set OBS contains the mean shifted \par values of the independent and dependent \par variables;\cf2 \par OBSN( OBS): XS, YS; \par \cf1 ENDSETS\cf2 \par \par \cf3 ! Number of observations;\cf2 \par NK = \cf1 @SIZE\cf2 ( OBS); \par \par \cf3 ! Compute means;\cf2 \par XBAR = \cf1 @SUM\cf2 ( OBS: X)/ NK; \par YBAR = \cf1 @SUM\cf2 ( OBS: Y)/ NK; \par \par \cf3 ! Shift the observations by their means;\cf2 \par \cf1 @FOR\cf2 ( OBS( I): \par XS( I) = X( I) - XBAR; \par YS( I) = Y( I) - YBAR); \par \par \cf3 ! Compute various sums of squares;\cf2 \par XYBAR = \cf1 @SUM\cf2 ( OBSN: XS * YS)