PolyFit

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PolyFit

x y n PolyFit m x length : r 1 m range : c 1 n 1 + (range : A m n 1 + matrix 1 + : 14 mat A r c el x r el x r el 0 ≡ (c 1 ≡ (& (+ (c 1 -^: A transpose A * (1 -^A transpose y * (* eval 31 line :

You can try to substitute the last line with someone of the following, from dislin plugin, which are more robust and general

A y dn_LinAlgLLS_COF

In matlab: (A\y).'

A y dn_LinAlgLLS_SVD

A y dn_LinAlgLLS_QRorLQ

A is the Vandermonde matrix. The code

x r el 0 ≡ (c 1 ≡ (&

is for avoid the SMath error 0^0, Uncertainty.

p x PolyVal P 0 : k 0 : 12 mat c p P P c x k^vectorize * + eval : k k 1 + : 12 mat for P 31 line :

Horner Method

p k el x k 1 -^vectorize * k 1 n sum

X Y R.Pearson Ξ Ψ 12 mat X Y 12 mat 1 X length / X sum Y sum 12 mat * - : Ξ Ψ * vectorize sum Ξ 2^vectorize sum (Ψ 2^vectorize sum (* sqrt / 21 line :

Shorthands:

M n plot C X Y n PolyFit : C x PolyVal M X Y o augment X C X PolyVal x augment 41 sys 21 line :

X Y n R2 Y X Y n PolyFit X PolyVal R.Pearson 2^11 line :

MCols(M) returns the columns of M as a row vector. M MCols n M cols : R 1 n matrix : c 1 n range : 13 mat R c el M c col : eval 21 line :

PolyFit

Lineal Polyfit

n 1 :

Data 0.5 32 1.1 33 1.5 34.2 2.1 35.1 2.3 35.7 52 mat :

X Y 12 mat Data MCols :

X Y n R2 0.9895656

C X Y n PolyFit : 30.9306 2.0463 21 mat

C X PolyVal 31.9537 33.1815 34 35.2278 35.637 51 mat

Data n plot

Amarasekera Excel screenshot

Horinzontal Line Polyfit

n 0 :

The polynom is the mean of tye Y-data. In this case, R2 is not defined

Data 0.5 9 1.1 7.2 1.5 8.3 2.1 6 2.3 7.8 52 mat :

X Y 12 mat Data MCols :

C X Y n PolyFit : 7.66

C X PolyVal 7.66 7.66 7.66 7.66 7.66 51 mat

Y sum Y length / 7.66

Some data are better interpreted as if they had a constant performance.

n 1 ≡

n 0 ≡

Data 1 plot Data n plot

Quadratic Polyfit

n 2 :

Data 1 0.9 2 2.4 374 17.4 5 30.5 6 48.3 62 mat :

X Y 12 mat Data MCols :

X Y n R2 0.9997121

C X Y n PolyFit : 3.83 4.9604 - 2.0625 31 mat

C X PolyVal 0.9321 2.1593 7.5114 16.9886 30.5907 48.3179 61 mat

Data n plot

Amarasekera Excel screenshot

Matlab example

n 7 :

https://la.mathworks.com/help/matlab/ref/polyfit.html?lang=en

x f x sin :

X 04 π * 0.1 + (49 / π * range :

Y X f vectorize :

X Y n R2 0.9995795

Matlab screenshot

x f n plot

X Y 7 PolyFit 0.0002 0.1141 - 1.9084 1.3808 - 0.3702 0.0464 - 0.0028 6.2606 105 -^* - 81 mat

Matlab screenshoot

Matlab example in Excel

Notice that Excel accept only 6 as maximum n

n 6 :

X Y n R2 0.9057328

Excel screenshot

x f n plot

The coefficients are the same in SMath, Matlab and Excel

X Y 6 PolyFit 0.034 - 2.8327 1.9611 - 0.4452 0.0407 - 0.0013 2.2 1014 -^* - 71 mat

Matlab screenshoot

Alvaro