4601ee8e-d341-4b89-bcb3-60fa7462aed7 3 4 5 decimal

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Example of Quadratic Fit

The data to be fitted

y b 1 el b 2 el x * + b 3 el x 2^* + ≡

x 12345661 mat :

y 0.9 2.4 7.0 17.4 30.5 48.3 61 mat :

Just to show what equation we are fitting

List of functions to make X matrix

x φ 1 x x 2^31 mat :

n x length :

n 6

k x φ length :

k 3

x y augment 1 0.9 2 2.4 374 17.4 5 30.5 6 48.3 62 mat

j 1 k range i 1 n range X i j el x i el φ j el : for for

X 11112413914161525163663 mat

Compute the two matrices that will be multiplied to give matrix B

M1 X transpose X * :

M2 X transpose y * :

B M1 1 -^eval M2 * :

B 3.83 4.9604 - 2.0625 31 mat

Compute the fitted values and plot

i 1 n range yfit i el B x i el φ * : for

yfit 0.9321 2.1593 7.5114 16.9886 30.5907 48.3179 61 mat

Expt x y augment :

Fit x yfit augment :

Expt Fit 2 1 sys

chr char ≡

sz size ≡

clr color ≡

vx vy chr sz clr plotG n vx length : plot vx 1 el vy 1 el chr sz clr augment : i 2 n range plot plot vx i el vy i el chr sz clr 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 :

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

X Data 1 col :

Y Data 2 col :

x φ 1 x x 2^31 mat :

n X length :

n 6

PolyOrder 2 :

degree PolyOrder 1 + :

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 * :

b 3.83 4.9604 - 2.0625 31 mat

'b' coeffs are sanity checked

x fit b x φ * :

<= recast the scalar model

Poly 18 1.01_x fit inc :

data X Y . 14 red plotG :

Smath QuickPlot discrete fit

Poly data 2 1 sys x fit