regression.go

package stats

import "math"

// Series is a container for a series of data
type Series []Coordinate

// Coordinate holds the data in a series
type Coordinate struct {
	X, Y float64
}

// LinearRegression finds the least squares linear regression on data series
func LinearRegression(s Series) (regressions Series, err error) {

	if len(s) == 0 {
		return nil, EmptyInputErr
	}

	// Placeholder for the math to be done
	var sum [5]float64

	// Loop over data keeping index in place
	i := 0
	for ; i < len(s); i++ {
		sum[0] += s[i].X
		sum[1] += s[i].Y
		sum[2] += s[i].X * s[i].X
		sum[3] += s[i].X * s[i].Y
		sum[4] += s[i].Y * s[i].Y
	}

	// Find gradient and intercept
	f := float64(i)
	gradient := (f*sum[3] - sum[0]*sum[1]) / (f*sum[2] - sum[0]*sum[0])
	intercept := (sum[1] / f) - (gradient * sum[0] / f)

	// Create the new regression series
	for j := 0; j < len(s); j++ {
		regressions = append(regressions, Coordinate{
			X: s[j].X,
			Y: s[j].X*gradient + intercept,
		})
	}

	return regressions, nil
}

// ExponentialRegression returns an exponential regression on data series
func ExponentialRegression(s Series) (regressions Series, err error) {

	if len(s) == 0 {
		return nil, EmptyInputErr
	}

	var sum [6]float64

	for i := 0; i < len(s); i++ {
		if s[i].Y < 0 {
			return nil, YCoordErr
		}
		sum[0] += s[i].X
		sum[1] += s[i].Y
		sum[2] += s[i].X * s[i].X * s[i].Y
		sum[3] += s[i].Y * math.Log(s[i].Y)
		sum[4] += s[i].X * s[i].Y * math.Log(s[i].Y)
		sum[5] += s[i].X * s[i].Y
	}

	denominator := (sum[1]*sum[2] - sum[5]*sum[5])
	a := math.Pow(math.E, (sum[2]*sum[3]-sum[5]*sum[4])/denominator)
	b := (sum[1]*sum[4] - sum[5]*sum[3]) / denominator

	for j := 0; j < len(s); j++ {
		regressions = append(regressions, Coordinate{
			X: s[j].X,
			Y: a * math.Exp(b*s[j].X),
		})
	}

	return regressions, nil
}

// LogarithmicRegression returns an logarithmic regression on data series
func LogarithmicRegression(s Series) (regressions Series, err error) {

	if len(s) == 0 {
		return nil, EmptyInputErr
	}

	var sum [4]float64

	i := 0
	for ; i < len(s); i++ {
		sum[0] += math.Log(s[i].X)
		sum[1] += s[i].Y * math.Log(s[i].X)
		sum[2] += s[i].Y
		sum[3] += math.Pow(math.Log(s[i].X), 2)
	}

	f := float64(i)
	a := (f*sum[1] - sum[2]*sum[0]) / (f*sum[3] - sum[0]*sum[0])
	b := (sum[2] - a*sum[0]) / f

	for j := 0; j < len(s); j++ {
		regressions = append(regressions, Coordinate{
			X: s[j].X,
			Y: b + a*math.Log(s[j].X),
		})
	}

	return regressions, nil
}