╨╧рб▒с>■  ■                                                                                                                                                                                                                                                                                                                                                                                                                                                   ¤   ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Root Entry            ■                                       Root Entry        *0_Ъю╧╗Є└Ё^Алt$ц№─А Contents            ^                                 ■   ¤   ■    ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         !"#$%&'()■                                                                                                                                                                                                                                                                                                                                                           ьЛ{\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 \cf1 TITLE\cf2 Linear Regression with one independent variable - LING20c; \par \cf3 ! Linear regression is a forecasting method that models \par the relationship between a dependent variable to one or \par more independent variable. For this model we wish to \par predict Y with the equation: Y(i) = CONS + SLOPE * X(i);\cf2 \par \cf1 SETS\cf2 : \par \cf3 ! The OBS set contains the data points for X and Y;\cf2 \par OBS/1..15/: \par Y, \cf3 ! The dependent variable (Bookstore sales);\cf2 \par X; \cf3 ! The independent or explanatory variable \par (Mail order sales);\cf2 \par \cf1 ENDSETS\cf2 \par \cf3 ! Data on Bookstore vs. Mail order sales;\cf2 \par \cf1 DATA\cf2 : \par Y = \par 4360 4590 4520 4770 4760 5070 5230 5080 5550 5390 5670 5490 5810 6060 5940; \par X = \par 1310 1313 1320 1322 1338 1340 1347 1355 1360 1364 1373 1376 1384 1395 1400; \par \cf1 ENDDATA\cf2 \par \par \cf3 ! The model;\cf2 \par \cf1 SETS\cf2 : \par \cf3 ! The derived set OBS contains the mean shifted values of \par the independent and dependent variables;\cf2 \par OBSN( OBS): XS, YS; \par \cf1 ENDSETS\cf2 \par NK = \cf1 @SIZE\cf2 ( OBS); \par \cf3 ! Assume NK > 2;\cf2 \par \cf3 ! Compute means;\cf2 \par XBAR = \cf1 @SUM\cf2 ( OBS: X)/ NK; \par YBAR = \cf1 @SUM\cf2 ( OBS: Y)/ NK; \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 \cf1 @FREE\cf2 ( XS(I)); \cf1 @FREE\cf2 ( YS( I)); \par ); \par \cf3 ! Compute various sums of squares;\cf2 \par XYBAR = \cf1 @SUM\cf2 ( OBSN: XS * YS); \par XXBAR = \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 ! A measure of how well X can be used to predict Y - \par the unadjusted (RSQRU) and adjusted (RSQRA) fractions \par of variance explained;\cf2 \par RSQRU = 1 - RESID/ YYBAR; \par RSQRA = 1 - ( RESID/ YYBAR) * ( NK - 1)/( NK - 2); \par \cf1 @FREE\cf2 ( CONS); \cf1 @FREE\cf2 ( SLOPE); \par \par \cf3 ! A copy of LINGO can be downloaded from: \par http://www.lindo.com;\cf2 \par \cf1 END\cf2 \par \par }