<p> plotG, mesh discrete,Scale(M,Low,High) </p>

01135cb0-a13f-48f1-ae07-2fba495b8fbe 27 6 9 decimal

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

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

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct : for U f augment 31 line :

A robust construct of the Scale function M Low High Scale min M Min : max M Max : 12 mat maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 M rows range j 1 M cols range N i j el M i j el min - maxmin / : for for HighLow N * Low + 51 line :

High order polyfit

High order polynomials are numerically unstable @ high range of the variate 'x'. In this example order 7 and range 0..19 fail to fit. We scale the samples 'x' in the range x => 0..1

XY 0 2113.3 0.05 2111.7 0.11 2109.2 0.16 2105.2 0.21 2099.4 0.26 2092.1 0.32 2084.7 0.37 2078.6 0.42 2075.1 0.47 2073.9 0.53 2074.1 0.58 2074.4 0.63 2074 0.68 2072.5 0.74 2070.1 0.79 2067.2 0.84 2064.4 0.89 2062 0.95 2060.5 1 2059.6 202 mat :

samples 0 2113.3 1 2111.7 2 2109.2 3 2105.2 4 2099.4 5 2092.1 6 2084.7 7 2078.6 8 2075.1 9 2073.9 10 2074.1 11 2074.4 12207413 2072.5 14 2070.1 15 2067.2 16 2064.4 17206218 2060.5 19 2059.6 202 mat :

X XY 1 col : Y XY 2 col : Data X Y . 12 black plotG : 31 line

x φ 1 x x 2^x 3^x 4^x 5^x 6^x 7^81 mat :

Cholesky companion solver degree x φ rows : j 1 degree range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 51 line

x β f β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + β 5 el x 4^* + 1 β 6 el x * + β 7 el x 2^* + β 8 el x 3^* + β 9 el x 4^* + / :

2113.244 637.7119 - 84.21096 5.026034 - 0.1213578 0.3012873 - 0.03988496 0.002389478 - 0.00005800783 91 mat

Mathcad 11 GenfitMatrix delivers a sensibly better rational fit on the native 0..19 range... better @ the extrapolated ends.

x fit b x φ * :

<= recast the scalar model

Δr i 1 Y rows range resd i el Y i el X i el fit - : for X resd augment 21 line :

poly 01 0.005 x fit inc :

Discrete polyfit on reduced 'x'

Data poly 2 1 sys

Absolute residuals

Δr

b 2113.361894 72.032419 - 1145.939392 10733.874944 - 35277.612557 53413.139864 - 38299.927203 10558.278353 - 81 mat

χ X Mean : μ Y Mean : n XY rows : 31 line

χ μ n 31 mat 0.5 2081.1 2031 mat

Pearson’s correlation coefficient corr X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el fit eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el fit eval μ - (2^(i 1 n sum * sqrt / / : 0.99984

correlation between [X,Y]

correlation of the model

correlation between [X,fitted model]

sx samples 1 col : sy samples 2 col : 21 line

vx poly 1 col : vy poly 2 col : data sx sy . 12 black plotG : 31 line

Origin vx 019 Scale vy augment :

data Origin 2 1 sys