$TITLE: M5-1.GMS, ordinary least squares using NLP $ONTEXT there - - PowerPoint PPT Presentation

▶

Sep 14, 2023 412 likes •461 views

C:\jim\COURSES\8858\code-bk 2012\M5-1.gms Monday, January 09, 2012 6:05:32 AM Page 1 $TITLE: M5-1.GMS, ordinary least squares using NLP $ONTEXT there are I observations on two variables (set J), a dependent variables Y and an independent

SLIDE 1

C:\jim\COURSES\8858\code-bk 2012\M5-1.gms Monday, January 09, 2012 6:05:32 AM Page 1

$TITLE: M5-1.GMS, ordinary least squares using NLP $ONTEXT there are I observations on two variables (set J), a dependent variables Y and an independent variable X. the objective is to estimate a linear relationship vias OLS minimizing the sum of squared deviations $OFFTEXT SETS I o b s e r v a t i

s /I1I4/ J dep and ind var /J1J2/; PARAMETERS Y0(I) X0(I); TABLE BENCH(I,J) J1 J2 I1 4 2 I2 3 4 I3 10 6 I4 14 11; DISPLAY BENCH;

SLIDE 2

C:\jim\COURSES\8858\code-bk 2012\M5-1.gms Monday, January 09, 2012 6:05:32 AM Page 2

Y0(I) = BENCH(I, "J1"); X0(I) = BENCH(I, "J2"); DISPLAY Y0, X0; VARIABLES ALPHA BETA DEV YHAT(I); EQUATIONS EYHAT(I) OBJECTIVE; OBJECTIVE.. DEV =E= SUM(I, (YHAT(I) - Y0(I))(YHAT(I) - Y0(I))); EYHAT(I).. YHAT(I) =E= ALPHA + BETAX0(I); MODEL OLS /ALL/; ALPHA.L = 1; BETA.L = 1; SOLVE OLS USING NLP MINIMIZING DEV;

SLIDE 3

C:\jim\COURSES\8858\code-bk 2012\M5-1.gms Monday, January 09, 2012 6:05:32 AM Page 3

* process output to get observed and fitted values of Y PARAMETER RESULTS(I,*); RESULTS(I, "X0") = X0(I); RESULTS(I, "YHAT") = YHAT.L(I); RESULTS(I, "Y0") = Y0(I); DISPLAY RESULTS; $LIBINCLUDE XLDUMP RESULTS M5-1.XLS SHEET1!C3