least-squares.rkt
```#lang racket/base
(require ;;racket/sequence
lang/posn)

;; The Method of Least Squares.
;;
;; Given a set of points (x1, y1), (x2, y2), ... (xn, yn), we want to find
;; the slope `b` and y-intersect `a` that the line y = a + bx best approximates the
;; points.

(provide least-squares
(rename-out [new-least-squares-function least-squares-function])
least-squares-function?
least-squares-function-slope
least-squares-function-intersect)

(define (sqr x) (* x x))

(define (least-squares points)
(-least-squares 'least-squares points))

;; least-squares: symbol (sequenceof (sequence number number)) -> (values [slope number] [intersect number])
(define (-least-squares who points)
(define-values (xs ys) (split-xs-ys who points))
(define n (length xs))
(when (< n 2)
(raise-type-error who "sequence of at least two points" points))

(define xs-sum (sum xs))
(define ys-sum (sum ys))

(define slope (/ (- (* n (sum (map * xs ys)))
(* xs-sum ys-sum))
(- (* n (sum (map sqr xs)))
(sqr xs-sum))))

(define intersect (- (/ ys-sum n)
(* slope (/ xs-sum n))))

(values slope intersect))

;; Split up the sequence into (xs..., ys...) lists.
(define (split-xs-ys who points)
(unless (sequence? points)
(raise-type-error who "sequence of 2d-points" points))
(define-values (xs ys)
(for/fold ([xs '()]
[ys '()])
([p points])
(define (on-element-error seen-so-far)
(raise-type-error who "a 2d-point"
p))
(cond [(sequence? p)
(define-values (more? next) (sequence-generate p))
(unless (more?) (on-element-error '()))
(define x (next))
(unless (more?) (on-element-error (list x)))
(define y (next))
(when (more?) (on-element-error (list x y)))
(values (cons x xs) (cons y ys))]

[(posn? p)
(values (cons (posn-x p) xs)
(cons (posn-y p) ys))]

[else
(on-element-error '())])))
(values (reverse xs) (reverse ys)))

(define (sum nums)
(apply + nums))

(struct least-squares-function (slope intersect)
#:transparent
#:property prop:procedure (lambda (an-ls x)
(+ (* x (least-squares-function-slope an-ls))
(least-squares-function-intersect an-ls))))

(define (new-least-squares-function points)
(define-values (slope intersect) (-least-squares 'least-squares-function points))
(least-squares-function slope intersect))
```