linear-regression.rkt

#lang racket

(require 2htdp/batch-io) ; provides read-csv-file
(require srfi/1)         ; provides reduce function
(require plot)           ; provides plot function

;; helper functions 
(define (sum xs) (reduce + 0 xs))
(define (square x) (* x x))

; define our regression model
;   x : list of numbers
;   y : list of numbers
(define (linear-regression x y)
    (let* ([mean_x       (/ (sum x) (length x))]
           [mean_y       (/ (sum y) (length x))]
           
           ; Σ(x_i - mean_x)(y_i - mean_y)
           [numerator    (sum (map (λ(xi yi) (* (- xi mean_x) (- yi mean_y))) x y))]  
           
           ; Σ(x_i - mean_x)
           [denominator  (sum (map (λ(xi) (square (- xi mean_x))) x))]
           
           ; beta = [Σ(x_i - mean_x)(y_i - mean_y)] / [Σ(x_i - mean_x)]
           [beta         (/ numerator denominator)]
           
           ; alpha = mean_y - beta * mean_x
           [alpha        (- mean_y (* beta mean_x))])
      
      ; return both the slope and itercept as a tuple
      (list beta alpha)))


;; start working on the data -------------------------

; some more helpful names
(define sepal-length (compose string->number first))
(define sepal-width  (compose string->number second))

(define (get-columns row) (list (sepal-length row) 
                                (sepal-width row) ))


(define setosa-points     (map get-columns (read-csv-file "setosa.txt")))

; save the results of our linear model
(define lm (linear-regression 
            (map first setosa-points) 
            (map second setosa-points)))

; show the results
(plot (list 
        ; plot the data points
        (points setosa-points    #:color "red")
        
        ; also plot the calculated regression line
        (function 
          (λ(x) (+ (* (first lm) x) (second lm))) ; f(x) = m * x + b  where (m,b) = lm
        )))

setosa.txt

5.1,3.5,1.4,0.2,Iris-setosa
4.9,3.0,1.4,0.2,Iris-setosa
4.7,3.2,1.3,0.2,Iris-setosa
4.6,3.1,1.5,0.2,Iris-setosa
5.0,3.6,1.4,0.2,Iris-setosa
5.4,3.9,1.7,0.4,Iris-setosa
4.6,3.4,1.4,0.3,Iris-setosa
5.0,3.4,1.5,0.2,Iris-setosa
4.4,2.9,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.4,3.7,1.5,0.2,Iris-setosa
4.8,3.4,1.6,0.2,Iris-setosa
4.8,3.0,1.4,0.1,Iris-setosa
4.3,3.0,1.1,0.1,Iris-setosa
5.8,4.0,1.2,0.2,Iris-setosa
5.7,4.4,1.5,0.4,Iris-setosa
5.4,3.9,1.3,0.4,Iris-setosa
5.1,3.5,1.4,0.3,Iris-setosa
5.7,3.8,1.7,0.3,Iris-setosa
5.1,3.8,1.5,0.3,Iris-setosa
5.4,3.4,1.7,0.2,Iris-setosa
5.1,3.7,1.5,0.4,Iris-setosa
4.6,3.6,1.0,0.2,Iris-setosa
5.1,3.3,1.7,0.5,Iris-setosa
4.8,3.4,1.9,0.2,Iris-setosa
5.0,3.0,1.6,0.2,Iris-setosa
5.0,3.4,1.6,0.4,Iris-setosa
5.2,3.5,1.5,0.2,Iris-setosa
5.2,3.4,1.4,0.2,Iris-setosa
4.7,3.2,1.6,0.2,Iris-setosa
4.8,3.1,1.6,0.2,Iris-setosa
5.4,3.4,1.5,0.4,Iris-setosa
5.2,4.1,1.5,0.1,Iris-setosa
5.5,4.2,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.0,3.2,1.2,0.2,Iris-setosa
5.5,3.5,1.3,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
4.4,3.0,1.3,0.2,Iris-setosa
5.1,3.4,1.5,0.2,Iris-setosa
5.0,3.5,1.3,0.3,Iris-setosa
4.5,2.3,1.3,0.3,Iris-setosa
4.4,3.2,1.3,0.2,Iris-setosa
5.0,3.5,1.6,0.6,Iris-setosa
5.1,3.8,1.9,0.4,Iris-setosa
4.8,3.0,1.4,0.3,Iris-setosa
5.1,3.8,1.6,0.2,Iris-setosa
4.6,3.2,1.4,0.2,Iris-setosa
5.3,3.7,1.5,0.2,Iris-setosa
5.0,3.3,1.4,0.2,Iris-setosa