Best fit using least-squares estimation in Scheme

gistfile1.scm

(define (best-fit points)
    ;; Use least-squares estimation to find best fit line for given set of points
    (let* ((sumx (apply + (map car points)))
          (sumy (apply + (map cadr points)))
          (sumxy (apply + (map (lambda (p) (* (car p) (cadr p))) points)))
          (sumx2 (apply + (map (lambda (p) (* (car p) (car p))) points)))
          (n (length points))
          (slope (/ (- sumxy (/ (* sumx sumy) n)) (- sumx2 (/ (* sumx sumx) n))))
          (y-int (/ (- sumy (* slope sumx)) n)))
      (cons slope y-int)))


(define (best-fit_func points)
    ;; Given a set of points, use `best-fit` to a return the function for the
    ;; best fit line. (Can be called with a given x to return f(x) and used to
    ;; estimate further points)
    (let* ((fx (best-fit points))
          (slope (car fx))
          (y-int (cdr fx)))
        (lambda (x)
            (+ (* slope x) y-int))))


;; Example run (> shows output)
;; --------------------------
(define points '(
  (-4 -3)
  (-3 -1)
  (-2 -2)
  (-1.5 -0.5)
  (-0.5 1)
  (1 0)
  (2 1.5)
  (3.5 1)
  (4 2.5)
))

(display (best-fit points))
> (0.551931330472103 . -0.0248927038626609)


(map (lambda (e) (begin (display e) (newline))) (map (best-fit_func points) (iota 10)))
> -0.0248927038626609
> 0.527038626609442
> 1.07896995708154
> 1.63090128755365
> 2.18283261802575
> 2.73476394849785
> 3.28669527896996
> 3.83862660944206
> 4.39055793991416
> 4.94248927038627