Bestfit: Lines of Best Fit

8.16.0.1

Bestfit: Lines of Best Fit🔗ℹ

Bestfit is a library for calculating lines of best fit using Least Squares Fitting.

procedure
(graph/linear xs ys [errors])
→ (Values renderer2d? renderer2d? renderer2d?)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)
  errors : (U #f (Listof Flonum)) = #f
procedure
(graph/exponential xs ys [errors])
→ (Values renderer2d? renderer2d? renderer2d?)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)
  errors : (U #f (Listof Flonum)) = #f
procedure
(graph/log xs ys [errors])
→ (Values renderer2d? renderer2d? renderer2d?)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)
  errors : (U #f (Listof Flonum)) = #f
procedure
(graph/power xs ys [errors])
→ (Values renderer2d? renderer2d? renderer2d?)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)
  errors : (U #f (Listof Flonum)) = #f

Uses linear-fit, exp-fit, log-fit, power-fit, to generate three renderer2d?s: A plot of the points given by xs and ys, a plot of the function of best fit, and error bars generated. The error bars are generated from error, which is the percentage error on each y coordinate.

> (define (3x^2 x) (* 3.0 (expt x 2.0)))
> (define (add-error y) (+ y (* y (/ (- (random 4) 2) 10.0))))
> (define exact (function 3x^2 #:label "exact" #:color "blue"))
> (define-values (pts fit _)
    (graph/power (build-list 10 (compose fl add1))
                 (build-list 10 (compose 3x^2 fl add1))))
> (plot (list exact fit pts))
> (define-values (pts fit err)
    (graph/power (build-list 10 (compose fl add1))
                 (build-list 10 (compose add-error 3x^2 fl add1))
                 (build-list 10 (const 0.2))))
> (plot (list exact fit pts err))

procedure
(linear-fit xs ys) → (-> Nonnegative-Flonum Real)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)
procedure
(exp-fit xs ys) → (-> Nonnegative-Flonum Real)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)
procedure
(log-fit xs ys) → (-> Nonnegative-Flonum Real)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)
procedure
(power-fit xs ys) → (-> Nonnegative-Flonum Real)
  xs : (Listof Nonnegative-Flonum)
  ys : (Listof Nonnegative-Flonum)

Uses Least Squares Fitting to generate a best fit function of the given type.

> (define line (linear-fit '(1.0 2.0 3.0) '(1.0 2.0 3.0)))
> (line 10.0)
10.0
> (line 12.0)
12.0

procedure
(linear-fit-params xs ys) → (Values Real Real)
xs : (Listof Nonnegative-Flonum)
ys : (Listof Nonnegative-Flonum)

Returns values a and b used to generate a best fit function of the form y = a + b x.

> (linear-fit-params '(1.0 2.0 3.0) '(2.0 4.0 6.0))
0.0
2.0

procedure
(exp-fit-params xs ys) → (Values Real Real)
xs : (Listof Nonnegative-Flonum)
ys : (Listof Nonnegative-Flonum)

Returns values A and B used to generate a best fit function of the form y = A e^(B x).

> (exp-fit-params '(1.0 2.0 3.0) '(2.0 4.0 8.0))
1.0000000000000044
0.6931471805599438

procedure
(log-fit-params xs ys) → (Values Real Real)
xs : (Listof Nonnegative-Flonum)
ys : (Listof Nonnegative-Flonum)

Returns values a and b used to generate a best fit function of the form y = a + b ln(x).

> (log-fit-params '(2.0 4.0 8.0) '(1.0 2.0 3.0))
1.833333333333333
0.12022458674074712

procedure
(power-fit-params xs ys) → (Values Real Real)
xs : (Listof Nonnegative-Flonum)
ys : (Listof Nonnegative-Flonum)

Returns values A and B used to generate a best fit function of the form y = A x^B.

> (power-fit-params '(1.0 2.0 3.0) '(2.0 8.0 18.0))
0.6931471805599457
1.9999999999999991