<content> PolyFit </content>

f8651a64-c3ed-4660-b007-5d86a62898c3 17 Alvaro Diaz Falconi 4 5 false false 0 0 decimal

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

Polynomial Fitting

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 :

X Y n R2 n 0 ≡ Not defined Y X Y n PolyFit X PolyVal R.Pearson (2^if 11 line :

<content> PolyFit </content>

Empirical Data

Data 1891771791831801851781861761851841801801881831951941881821959080737385837575777376746881798875898580220 mat transpose :

X Y 12 mat Data 1 col Data 2 col 12 mat :

Target: interpolate at

xo 189.3 :

Lineal Fit

n 1 :

Same results in excel.

C.1 X Y 1 PolyFit : 2.8331 0.4129 21 mat

X Y n R2 0.1512

Quadratic Polyfit

n 2 :

C.2 X Y 2 PolyFit : 284.2923 - 3.5061 0.0083 - 31 mat

X Y 2 R2 0.1533

Cubic Polyfit

n 3 :

C.3 X Y 3 PolyFit : 75332.7348 1219.9398 - 6.5857 0.0118 - 41 mat

X Y 3 R2 0.2334

Yo C.1 xo PolyVal C.2 xo PolyVal C.3 xo PolyVal 31 mat : 80.9938 81.1741 84.1616 31 mat

Plot C.1 x PolyVal C.2 x PolyVal C.3 x PolyVal X Y o augment xo Yo x augment 51 sys :

Plot

Alvaro

4 appVersion 1.0.8348.30405