linearRegression.go

// Statistics refresher: The R-squared formula
// Time complexity: O(3n)

package main

import "fmt"

type Point struct { 
	x, y float64 
}

func getMean(points []Point) Point {
	
	xSum := 0.0
	ySum := 0.0
	for i := 0; i < len(points); i++ {
		point := points[i]
		xSum += point.x
		ySum += point.y
	}
	pointsTotal := float64(len(points))
	xMean := xSum / pointsTotal
	yMean := ySum / pointsTotal

	return Point{xMean, yMean}
}

func getRegressionFeatures(points []Point) (float64, float64, Point) {

	// Average point
	pointMean := getMean(points)

	xyDeltaSum := 0.0
	xDeltaSquaredSum := 0.0
	for i := 0; i < len(points); i++ {
		point := points[i]
		xDelta := point.x - pointMean.x
		yDelta := point.y - pointMean.y
		xyDeltaSum += (xDelta * yDelta)
		xDeltaSquaredSum += (xDelta * xDelta)
	}

	// Slope of line
	b1 := xyDeltaSum / xDeltaSquaredSum

	// Y-intercept
	b0 := pointMean.y - (b1 * pointMean.x)

	return b0, b1, pointMean
}


func getRSquared(points []Point) (float64) {

	b0, b1, pointMean := getRegressionFeatures(points)

	yDeltaSquaredSum := 0.0
	yHatDeltaSquaredSum := 0.0
	for i := 0; i < len(points); i++ {
		point := points[i]
		yDelta := point.y - pointMean.y
		yDeltaSquaredSum += (yDelta * yDelta)
		yhat := b0 + (b1 * point.x)
		yhatdiff := yhat - pointMean.y
		yHatDeltaquared := (yhatdiff * yhatdiff)
		yHatDeltaSquaredSum += yHatDeltaquared
	}

	rSquared := yHatDeltaSquaredSum / yDeltaSquaredSum

	return rSquared
}

func main() {
	points := []Point {
		{1, 2},
		{3, 3},
		{5, 6},
		{8, 6},
		{11, 12},
	}

	rsquared := getRSquared(points)
	fmt.Printf("R squared: %6.3f\n", rsquared)
}