#lang racket


(define (findoutlier data)
  (define found #f)
  (for ([i data])
    (cond
      [(outlier i (mean data) (std. data)) (set! found #t)]))
  found
  )


(define (outlier observation mean stdev)
  (or (> (- mean (* (iqr stdev) 1.5)) observation) (< (+ mean (* (iqr stdev) 1.5)) observation))
  )


(define (iqr stdev)
  (* (* stdev 0.674) 2)
  )


(define (zscore observed mean stdev)
   (/ (- observed mean) stdev)
   )


(define (mean numbers)
  (define sum 0)
  (for ((x numbers)) (set! sum (+ x sum)))
  (/ sum (length numbers))
  )


(define (std. numbers)
  (define center (mean numbers))
  (define sum 0)
  (for ((x numbers))
    (set! sum (+ sum (expt (- x center) 2)))
    )
  (expt (/ sum (- (length numbers) 1)) (/ 1 2))
  )


(define (correlation list1 list2)

  (define mean1 (mean list1))
  (define mean2 (mean list2))
  (define ldevs1 (for/list ((x list1)) (- x mean1)))
  (define ldevs2 (for/list ((x list2)) (- x mean2)))

  (define numerator 0)
  (for ((x (length list1))) (set! numerator (+ numerator (* (list-ref ldevs1 x) (list-ref ldevs2 x)) ) ))

  (define sqsums1 0)
  (define sqsums2 0)
  (for (( x ldevs1)) (set! sqsums1 (+ sqsums1 (expt x 2))))
  (for (( x ldevs2)) (set! sqsums2 (+ sqsums2 (expt x 2))))
  (define denominator (expt (* sqsums1 sqsums2) (/ 1 2)))

  (/ numerator denominator)

  )

(define (logorithm x y) (/ (log y) (log x)))

(define (linreg list1 list2)

  (define mean1 (mean list1))
  (define mean2 (mean list2))
  (define std1 (std. list1))
  (define std2 (std. list2))
  (define r (correlation list1 list2))

  (define slope (/ (* r std2) std1))
  (define intercept (- mean2 (* slope mean1)))

  (list intercept slope)

  )