29a11305-e1ca-4bf0-a175-7f13fd2d4655 13 4 3 decimal

&[DATE] &[TIME] - &[FILENAME]

T P char size color plotG n T length : plot T 1 el P 1 el char size color augment : i 2 n range plot plot T i el P i el char size color augment stack : for plot 41 line :

These data are the result of a NIST study involving semiconductor electron mobility. The response variable is a measure of electron mobility, and the predictor variable is the natural log of the density. http://www.itl.nist.gov/div898/strd/nls/data/LINKS/i-thurber.shtml

data 2.981 - 84.248 2.921 - 87.264 2.912 - 87.185 2.84 - 89.076 2.797 - 89.608 2.702 - 89.868 2.699 - 90.101 2.633 - 92.405 2.481 - 95.854 2.363 - 100.696 2.322 - 101.06 1.501 - 401.672 1.46 - 390.724 1.274 - 567.534 1.212 - 635.316 1.1 - 7330.54 1.046 - 759.087 0.915 - 894.206 0.714 - 990.785 0.566 - 1090 0.545 - 1080 0.4 - 1120 0.309 - 1180 0.109 - 1260 0.103 - 1270 0.01 1290 0.119 1330 0.377 1350 0.79 1420 0.963 1430 1.006 1420 1.115 1440 1.572 1460 1.841 1470 2.047 1450 2.2 1460362 mat :

Here again, we give the fit from Mathcad 11 LGC fails, Levenberg-Marquardt is robust. NIST persits with a rational fraction, that must be rejected compared to SGompertz. Observe the two flat datum.

x β f β 1 el β 2 el β 3 el x β 4 el - (* - exp - exp * + :

x β φ x β f x β f β 1 el diff x β f β 2 el diff x β f β 3 el diff x β f β 4 el diff 51 mat :

X data 1 col :

Y data 2 col :

n X length :

n 36

k x β φ length :

k 5

L H N xd dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 21 line 21 line :

901375 1.6 1.25 - 41 mat

L X 1 el 5 - :

H 3 :

β 901375 1.6 1.25 - 41 mat :

N 1000 :

U L H N xd :

j 1 k range i 1 n range M i j el X i el β φ j 1 + el : for for

i 1 Y length range vx i el X i el β f : for

Φ M transpose M * :

d M transpose Y 1 vx * - (* :

Δβ Φ 1 -^eval d * :

β β Δβ + :

<= ... the active β

x fit x β f eval :

FIT i 1 U rows range FIT i el U i el fit eval : for FIT 21 line :

β 901375 1.6 1.25 - 41 mat

MyFit U FIT augment :

data X Y o 8 blue plotG :

Title 1 - 500 SGompertz fit Thurber 12 black 15 mat :

data MyFit Y 1 el Y 36 el Title 5 1 sys