ÐÏࡱá>þÿ  þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿTE, RSQRU, RSQRA/: R; ENDSETS ! Data on hours per ton, cumulative tons for a papermill based on Balof, J. Ind. Eng., Jan. 1966; DATA: COST = .1666, .1428, .1250, .1111; VOLUME = 8, 60, 100 190; ENDDATA ! The model; SETS: ! The derived set OBSN contains the set of logarithms of our dependent and independent variables as well the mean shifted values; OBSN( OBS): LX, LY, XS, YS; ENDSETS NK = @SIZE( OBS); ! Take the logs; @FOR( OBSN( I): LX( I) = @LOG( VOLUME( I)); LY( I) = @LOG( COST( I)); ); ! Compute means; XBAR = @SUM( OBSN: LX)/ NK; YBAR = @SUM( OBSN: LY)/ NK; ! Shift the observations by their means; @FOR( OBSN: XS = LX - XBAR; YS = LY - 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; SLOPE = XYBAR/ XXBAR; CONS = YBAR - SLOPE * XBAR; RESID = @SUM( OBSN: ( YS - SLOPE * XS)^2); ! The unadjusted/adjusted fraction of variance explained; [X1]R( @INDEX( RSQRU)) = 1 - RESID/ YYBAR; [X2]R( @INDEX( RSQRA)) = 1 - ( RESID/ YYBAR) * ( NK - 1)/( NK - 2); [X3]R( @INDEX( A)) = @EXP( CONS); [X4]R( @INDEX( B)) = - SLOPE; [X5]R( @INDEX( RATE)) = 2 ^ SLOPE; ! Some variables must be unconstrained in sign; @FOR( OBSN: @FREE( LY); @FREE( XS); @FREE( YS)); @FREE( YBAR); @FREE( XBAR); @FREE( SLOPE); @FREE( XYBAR); @FREE( CONS); END MODEL: ! Learning curve model; ! Assuming that each time the number produced doubles, the cost per unit decreases by a constant rate, predict COST per unit with the equation: COST(i) = A * VOLUME(i) ^ B; SETS: ! The OBS set contains the data for COST and VOLUME; OBS/1..4/: COST, ! The dependent variable; VOLUME; ! The independent variable; ! The OUT set contains the outputs of the model. Note: R will contain the output results.; OUT/ A, B, RAþÿÿÿýÿÿÿþÿÿÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRoot EntryÿÿÿÿÿÿÿÿçCONTENTSÿÿÿÿÿÿÿÿÿÿÿÿçÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRoot Entryÿÿÿÿÿÿÿÿ*0_šîÏ»òÀð^°fõ´eþÄ Contentsÿÿÿÿÿÿÿÿÿÿÿÿö ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿþÿÿÿýÿÿÿþÿÿÿ þÿÿÿ  ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ  !"#$%&'()*+,-./þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿXBAR = \cf1 @SUM\cf2 ( OBSN: XS * XS); \par YYBAR = \cf1 @SUM\cf2 ( OBSN: YS * YS); \par \cf3 ! Finally, the regression equation;\cf2 \par SLOPE = XYBAR/ XXBAR; \par CONS = YBAR - SLOPE * XBAR; \par RESID = \cf1 @SUM\cf2 ( OBSN: ( YS - SLOPE * XS)^2); \par \cf3 ! The unadjusted/adjusted fraction of variance \par explained;\cf2 \par [X1]R( \cf1 @INDEX\cf2 ( RSQRU)) = 1 - RESID/ YYBAR; \par [X2]R( \cf1 @INDEX\cf2 ( RSQRA)) = 1 - ( RESID/ YYBAR) * \par ( NK - 1)/( NK - 2); \par [X3]R( \cf1 @INDEX\cf2 ( A)) = \cf1 @EXP\cf2 ( CONS); \par [X4]R( \cf1 @INDEX\cf2 ( B)) = - SLOPE; \par [X5]R( \cf1 @INDEX\cf2 ( RATE)) = 2 ^ SLOPE; \par \par \cf3 ! Some variables must be unconstrained in sign;\cf2 \par \cf1 @FOR\cf2 ( OBSN: \cf1 @FREE\cf2 ( LY); \cf1 @FREE\cf2 ( XS); \cf1 @FREE\cf2 ( YS)); \par \cf1 @FREE\cf2 ( YBAR); \cf1 @FREE\cf2 ( XBAR); \cf1 @FREE\cf2 ( SLOPE); \par \cf1 @FREE\cf2 ( XYBAR); \cf1 @FREE\cf2 ( CONS); \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 ! Learning curve model;\cf2 \par \cf3 ! Assuming that each time the number produced \par doubles, the cost per unit decreases by a \par constant rate, predict COST per unit with \par the equation: \par COST(i) = A * VOLUME(i) ^ B;\cf2 \par \cf1 SETS\cf2 : \par \cf3 ! The OBS set contains the data for COST \par and VOLUME;\cf2 \par OBS/1..4/: \par COST, \cf3 ! The dependent variable;\cf2 \par VOLUME; \cf3 ! The independent variable;\cf2 \par \cf3 ! The OUT set contains the outputs of the model. \par Note: R will contain the output results.;\cf2 \par OUT/ A, B, RATE, RSQRU, RSQRA/: R; \par \cf1 ENDSETS\cf2 \par \cf3 ! Data on hours per ton, cumulative tons for a \par papermill based on Balof, J. Ind. Eng., \par Jan. 1966;\cf2 \par \cf1 DATA\cf2 : \par COST = .1666, .1428, .1250, .1111; \par VOLUME = 8, 60, 100 190; \par \cf1 ENDDATA\cf2 \par \par \cf3 ! The model;\cf2 \par \cf1 SETS\cf2 : \par \cf3 ! The derived set OBSN contains the set of \par logarithms of our dependent and independent \par variables as well the mean shifted values;\cf2 \par OBSN( OBS): LX, LY, XS, YS; \par \cf1 ENDSETS\cf2 \par NK = \cf1 @SIZE\cf2 ( OBS); \par \cf3 ! Take the logs;\cf2 \par \cf1 @FOR\cf2 ( OBSN( I): \par LX( I) = \cf1 @LOG\cf2 ( VOLUME( I)); \par LY( I) = \cf1 @LOG\cf2 ( COST( I)); ); \par \cf3 ! Compute means;\cf2 \par XBAR = \cf1 @SUM\cf2 ( OBSN: LX)/ NK; \par YBAR = \cf1 @SUM\cf2 ( OBSN: LY)/ NK; \par \cf3 ! Shift the observations by their means;\cf2 \par \cf1 @FOR\cf2 ( OBSN: \par XS = LX - XBAR; \par YS = LY - YBAR); \par \cf3 ! Compute various sums of squares;\cf2 \par XYBAR = \cf1 @SUM\cf2 ( OBSN: XS * YS); \par X