I had some fun time reading http://onlinestatbook.com/2/regression/intro.html today. It includes formulas for calculating linear regression of a data set.

Linear regression is used for predicting a value of a variable from a list of known values.

For example if a and b are related variables, then linear regression can predict the value of the one given the value for the other.

Here’s an implementation in Racket:

#lang racket (require plot) (define (sum l) (apply + l)) (define (average l) (/ (sum l) (length l))) (define (square x) (* x x)) (define (variance l) (let ((avg (average l))) (/ (sum (map (lambda (x) (square (- x avg))) l)) (- (length l) 1)))) (define (standard-deviation l) (sqrt (variance l))) (define (correlation l) (letrec ((X (map car l)) (Y (map cadr l)) (avgX (average X)) (avgY (average Y)) (x (map (lambda (x) (- x avgX)) X)) (y (map (lambda (y) (- y avgY)) Y)) (xy (map (lambda (x) (apply * x)) (map list x y))) (x-squared (map square x)) (y-squared (map square y))) (/ (sum xy) (sqrt (* (sum x-squared) (sum y-squared)))))) (define (linear-regression l) (letrec ((X (map car l)) (Y (map cadr l)) (avgX (average X)) (avgY (average Y)) (sX (standard-deviation X)) (sY (standard-deviation Y)) (r (correlation l)) (b (* r (/ sY sX))) (A (- avgY (* b avgX)))) (lambda (x) (+ (* x b) A)))) (define (plot-points-and-linear-regression the-points) (plot (list (points the-points #:color 'red) (function (linear-regression the-points) 0 10 #:label "y = linear-regression(x)"))))

So, for example if we call it with this data set:

(define the-points '( ( 1.00 1.00 ) ( 2.00 2.00 ) ( 3.00 1.30 ) ( 4.00 3.75 ) ( 5.00 2.25 ))) (plot-points-and-linear-regression the-points)

This is the graph that we get:

Cool, right?

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