true 4 decimal true

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

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