data

d736e929-f6c5-4881-9bfb-7eae29dbaf81 9 15 12 decimal

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

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

data

data 31 6.94 - 30 7.39 - 29 6.9 - 28 7.23 - 27 6.94 - 26 6.91 - 25 7.14 - 24 7.12 - 23 6.95 - 22 6.65 - 21 6.82 - 20 7.01 - 19 6.68 - 18 6.53 - 17 6.85 - 16 6.58 - 15 6.74 - 14 6.59 - 13 6.48 - 12 6.46 - 11 6.31 - 10 6.38 - 9 6.36 - 8 5.84 - 7 5.65 - 6 5.74 - 5 5.45 - 4 5.37 - 3 5.3 - 2 4.67 - 1 4.18 - 312 mat :

ε 1012 -^:

linfit MCD style . . .

1. The vector style is intuitive of inventing components.

2. Very robust wrt model Φ(x) ... auto-minimize LS.

3. Is of same style as polynomial fits.

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model combination x Φ 1 x sqrt x ε + ln 13 mat transpose :

Cholesky solver ... NUMERIC X data 1 col : Y data 2 col : 12 mat j 1 x Φ length range i 1 X length range M i j el X i el Φ j el : for for Q M transpose M * : d M transpose Y * : b Q 1 -^eval d * : 61 line

x fit b x Φ * :

b 4.183439 - 0.080548 0.998177 - 31 mat

FIT x 0.0125 50 0.05 range : i 1 x rows range fit i el x i el fit eval : for x fit augment 31 line :

pts data . 12 black plot :

ε b Clear 1

pts FIT 2 1 sys

b x f b k el x Φ k el * k 1 x Φ rows sum :

clean ... 
export [b, ε] b x f b 1 el 1 * b 2 el x 12 /^* + b 3 el x ε + ln * +

b 4.183439 - 0.080548 0.998177 - 31 mat :

ε 1012 -^:

pts b x f 2 1 sys

Pearson independent of f(b,x) ... [X,Y] from Cholesky X Y corr n X length : xy X Y * vectorize : x2 X X * vectorize : y2 Y Y * vectorize : n xy sum (* X sum (Y sum (* - n x2 sum (* X sum (2^- (n y2 sum (* Y sum (2^- (* (sqrt / 51 line :

X Y corr 0.89 -

Cholesky algo style as a general utility  ...
Observe much different construction style ! data # Φ linfit X data 1 col : Y data 2 col : 12 mat j 1 x Φ length range i 1 X length range M i j el X i el Φ j el : for for M transpose M * (1 -^M transpose Y * (* eval 31 line :

3 appVersion 0.98.6179 ≡

data

data 31 6.94 - 30 7.39 - 29 6.9 - 28 7.23 - 27 6.94 - 26 6.91 - 25 7.14 - 24 7.12 - 23 6.95 - 22 6.65 - 21 6.82 - 20 7.01 - 19 6.68 - 18 6.53 - 17 6.85 - 16 6.58 - 15 6.74 - 14 6.59 - 13 6.48 - 12 6.46 - 11 6.31 - 10 6.38 - 9 6.36 - 8 5.84 - 7 5.65 - 6 5.74 - 5 5.45 - 4 5.37 - 3 5.3 - 2 4.67 - 1 4.18 - 312 mat :

ε 1012 -^:

model combination x Φ 1 x sqrt x ε + ln 13 mat transpose :

coeffs data x Φ linfit :

coeffs 4.1834393719342 - 0.080547779580317 0.998177171695454 - 31 mat