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4408afacd1
This CL adds an example showing how to compute the confidence interval of the mean for a small sample. Signed-off-by: Sebastien Binet <binet@cern.ch>
99 lines
2.3 KiB
Go
99 lines
2.3 KiB
Go
// Copyright ©2018 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package stat_test
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import (
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"fmt"
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"math"
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"math/rand/v2"
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"gonum.org/v1/gonum/stat"
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"gonum.org/v1/gonum/stat/distuv"
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)
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func ExampleLinearRegression() {
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var (
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xs = make([]float64, 100)
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ys = make([]float64, 100)
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weights []float64
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)
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line := func(x float64) float64 {
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return 1 + 3*x
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}
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rnd := rand.New(rand.NewPCG(1, 1))
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for i := range xs {
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xs[i] = float64(i)
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ys[i] = line(xs[i]) + 0.1*rnd.NormFloat64()
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}
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// Do not force the regression line to pass through the origin.
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origin := false
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alpha, beta := stat.LinearRegression(xs, ys, weights, origin)
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r2 := stat.RSquared(xs, ys, weights, alpha, beta)
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fmt.Printf("Estimated offset is: %.6f\n", alpha)
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fmt.Printf("Estimated slope is: %.6f\n", beta)
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fmt.Printf("R^2: %.6f\n", r2)
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// Output:
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// Estimated offset is: 0.999675
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// Estimated slope is: 2.999971
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// R^2: 0.999999
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}
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func Example_confidenceInterval() {
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// This example shows how one can compute a confidence interval to quantify
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// the uncertainty around an estimated parameter, when working with a small
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// sample from a normally distributed variable.
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//
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// For small samples (N ≤ 30), confidence intervals are computed with
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// the t-distribution:
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//
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// Conf.Interval = $\hat{x} ± t \frac{s}{\sqrt{n}}
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//
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// where:
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// - x is the sample mean,
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// - s is the sample standard deviation,
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// - n is the sample size, and
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// - t is the critical value from the t-distribution based on the desired
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// confidence level and degrees of freedom (df=n-1)
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//
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// For more details, see:
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//
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// https://en.wikipedia.org/wiki/Student's_t-distribution
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var (
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// First 10 sepal widths from iris data set.
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xs = []float64{3.5, 3.0, 3.2, 3.1, 3.6, 3.9, 3.4, 3.4, 2.9, 3.1}
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ws = []float64(nil) // weights
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n = float64(len(xs))
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df = n - 1
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µ, std = stat.MeanStdDev(xs, ws)
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lvl = 0.95 // 95% confidence level
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t = distuv.StudentsT{
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Mu: 0,
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Sigma: 1,
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Nu: df,
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}.Quantile(0.5 * (1 + lvl))
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err = t * std / math.Sqrt(n)
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lo = µ - err
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hi = µ + err
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)
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fmt.Printf("Mean: %2.2f\n", µ)
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fmt.Printf("CI(@%g%%): [%.2f, %.2f]\n", lvl*100, lo, hi)
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// Output:
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// Mean: 3.31
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// CI(@95%): [3.09, 3.53]
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}
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