OLS Single Nonlinear Equation
/*--------------------------------------------------------------
SAS Sample Library
Name: modex01.sas
Description: Example program from SAS/ETS User's Guide,
The MODEL Procedure
Title: OLS Single Nonlinear Equation
Product: SAS/ETS Software
Keys: nonlinear simultaneous equation models
PROC: MODEL
Notes:
--------------------------------------------------------------*/
title 'Logistic Growth Curve Model of U.S. Population';
data uspop;
input pop :6.3 @@;
retain year 1780;
year=year+10;
label pop='U.S. Population in Millions';
datalines;
3929 5308 7239 9638 12866 17069 23191 31443 39818 50155
62947 75994 91972 105710 122775 131669 151325 179323 203211
226542 248710
;
proc model data=uspop;
label a = 'Maximum Population'
b = 'Location Parameter'
c = 'Initial Growth Rate';
pop = a / ( 1 + exp( b - c * (year-1790) ) );
fit pop start=(a 1000 b 5.5 c .02) / out=resid outresid;
run;
title2 "Residuals Plot";
proc sgplot data=resid;
refline 0;
scatter x=year y=pop / markerattrs=(symbol=circlefilled);
xaxis values=(1780 to 2000 by 20);
run;