*
* Example 14.1, page 570
* Non-linear least squares
*
data(org=columns,unit=input) 1 12 fee asset
 0.5200      0.5
 0.5080      5.0
 0.4840     10.0
 0.4600     15.0
 0.4398     20.0
 0.4238     25.0
 0.4115     30.0
 0.4020     35.0
 0.3944     40.0
 0.3880     45.0
 0.3825     55.0
 0.3738     60.0
nonlin b1 b2
frml exgrowth = b1*exp(b2*asset)
nlls(frml=exgrowth) fee
*
*  Try again with different guess values
*
compute b1=.45,b2=.01
nlls(frml=exgrowth) fee
*
* Compute dy/dx at asset=20. The number in the book seems to be incorrect.
*
disp b2*b1*exp(b2*20)
*
* From Appendix 14A.3. Linearized regression. ystar and x1 in table 14.4 are
* incorrect. (x1 clearly so, since it's supposed to be exp(positive number) for
* all t, and thus has to be >1.0). The regression below is correct.
*
compute b1=.45,b2=.01
set ystar = fee-exgrowth
set x1 = exp(b2*asset)
set x2 = b1*asset*exp(b2*asset)
linreg ystar
# x1 x2
disp b1+%beta(1) b2+%beta(2)