数据集的简单线性回归

Question

我希望在c#中为一组数据创建一个趋势函数，似乎使用一个大的数学库对我的需求有点过分。

给定一个值列表，如6,13,7,9,12,4,2,2,1。我想得到简单线性回归的斜率(看看它是减少还是增加)和下一个估计值。我知道有大量的库可以做到这一点，甚至更多，但我想要一个更简单的方法。

我不太喜欢统计，所以如果有人能引导我做这件事，我会很感激。

Answer 1

我自己的未来预测代码(以第一天开始的第15天为例)

  static void Main(string[] args)
    {
        double[] xVal = new double[9]
        {
    ...

           };
        double[] yVal = new double[9]  {
     ...
        };
        double rsquared;
        double yintercept;
        double slope;
        LinearRegression(xVal, yVal,0,9, out rsquared, out yintercept, out slope);
        Console.WriteLine( yintercept + (slope*15));//15 is xvalue of future(no of day from 1)
        Console.ReadKey();
    }
    public static void LinearRegression(double[] xVals, double[] yVals,
                                        int inclusiveStart, int exclusiveEnd,
                                        out double rsquared, out double yintercept,
                                        out double slope)
    {
        Debug.Assert(xVals.Length == yVals.Length);
        double sumOfX = 0;
        double sumOfY = 0;
        double sumOfXSq = 0;
        double sumOfYSq = 0;
        double ssX = 0;
        double ssY = 0;
        double sumCodeviates = 0;
        double sCo = 0;
        double count = exclusiveEnd - inclusiveStart;
        for (int ctr = inclusiveStart; ctr < exclusiveEnd; ctr++)
        {
            double x = xVals[ctr];
            double y = yVals[ctr];
            sumCodeviates += x * y;
            sumOfX += x;
            sumOfY += y;
            sumOfXSq += x * x;
            sumOfYSq += y * y;
        }
        ssX = sumOfXSq - ((sumOfX * sumOfX) / count);
        ssY = sumOfYSq - ((sumOfY * sumOfY) / count);
        double RNumerator = (count * sumCodeviates) - (sumOfX * sumOfY);
        double RDenom = (count * sumOfXSq - (sumOfX * sumOfX))
         * (count * sumOfYSq - (sumOfY * sumOfY));
        sCo = sumCodeviates - ((sumOfX * sumOfY) / count);
        double meanX = sumOfX / count;
        double meanY = sumOfY / count;
        double dblR = RNumerator / Math.Sqrt(RDenom);
        rsquared = dblR * dblR;
        yintercept = meanY - ((sCo / ssX) * meanX);
        slope = sCo / ssX;
    }

Answer 2

您不需要大量的库。公式相对简单。

给定x和y数据的一对数组，您将计算如下的最小二乘拟合系数

公式(27)和(28)是您需要的两个。编码只涉及输入数组值的和和平方和。

下面是一个Java类和它的JUnit测试类:

import java.util.Arrays;
/**
 * Simple linear regression example using Wolfram Alpha formulas.
 * User: mduffy
 * Date: 10/22/2018
 * Time: 10:56 AM
 * @link https://stackoverflow.com/questions/15623129/simple-linear-regression-for-data-set/15623183?noredirect=1#comment92773017_15623183
 */
public class SimpleLinearRegressionExample {
    public static double slope(double [] x, double [] y) {
        double slope = 0.0;
        if ((x != null) && (y != null) && (x.length == y.length) && (x.length > 0)) {
            slope = correlation(x, y)/sumOfSquares(x);
        }
        return slope;
    }
    public static double intercept(double [] x, double [] y) {
        double intercept = 0.0;
        if ((x != null) && (y != null) && (x.length == y.length) && (x.length > 0)) {
            double xave = average(x);
            double yave = average(y);
            intercept = yave-slope(x, y)*xave;
        }
        return intercept;
    }
    public static double average(double [] values) {
        double average = 0.0;
        if ((values != null) && (values.length > 0)) {
            average = Arrays.stream(values).average().orElse(0.0);
        }
        return average;
    }
    public static double sumOfSquares(double [] values) {
        double sumOfSquares = 0.0;
        if ((values != null) && (values.length > 0)) {
            sumOfSquares = Arrays.stream(values).map(v -> v*v).sum();
            double average = average(values);
            sumOfSquares -= average*average*values.length;
        }
        return sumOfSquares;
    }
    public static double correlation(double [] x, double [] y) {
        double correlation = 0.0;
        if ((x != null) && (y != null) && (x.length == y.length) && (x.length > 0)) {
            for (int i = 0; i < x.length; ++i) {
                correlation += x[i]*y[i];
            }
            double xave = average(x);
            double yave = average(y);
            correlation -= xave*yave*x.length;
        }
        return correlation;
    }
}

JUnit测试类

import org.junit.Assert;
import org.junit.Test;
/**
 * JUnit tests for simple linear regression example.
 * User: mduffy
 * Date: 10/22/2018
 * Time: 11:53 AM
 * @link https://stackoverflow.com/questions/15623129/simple-linear-regression-for-data-set/15623183?noredirect=1#comment92773017_15623183
 */
public class SimpleLinearRegressionExampleTest {
    public static double tolerance = 1.0e-6;
    @Test
    public void testAverage_NullArray() {
        // setup
        double [] x = null;
        double expected = 0.0;
        // exercise
        double actual = SimpleLinearRegressionExample.average(x);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testAverage_EmptyArray() {
        // setup
        double [] x = {};
        double expected = 0.0;
        // exercise
        double actual = SimpleLinearRegressionExample.average(x);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testAverage_Success() {
        // setup
        double [] x = { 1.0, 2.0, 2.0, 3.0, 4.0, 7.0, 9.0 };
        double expected = 4.0;
        // exercise
        double actual = SimpleLinearRegressionExample.average(x);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }

    @Test
    public void testSumOfSquares_NullArray() {
        // setup
        double [] x = null;
        double expected = 0.0;
        // exercise
        double actual = SimpleLinearRegressionExample.sumOfSquares(x);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testSumOfSquares_EmptyArray() {
        // setup
        double [] x = {};
        double expected = 0.0;
        // exercise
        double actual = SimpleLinearRegressionExample.sumOfSquares(x);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testSumOfSquares_Success() {
        // setup
        double [] x = { 1.0, 2.0, 2.0, 3.0, 4.0, 7.0, 9.0 };
        double expected = 52.0;
        // exercise
        double actual = SimpleLinearRegressionExample.sumOfSquares(x);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testCorrelation_NullX_NullY() {
        // setup
        double [] x = null;
        double [] y = null;
        double expected = 0.0;
        // exercise
        double actual = SimpleLinearRegressionExample.correlation(x, y);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testCorrelation_DifferentLengths() {
        // setup
        double [] x = { 1.0, 2.0, 3.0, 5.0, 8.0 };
        double [] y = { 0.11, 0.12, 0.13, 0.15, 0.18, 0.20 };
        double expected = 0.0;
        // exercise
        double actual = SimpleLinearRegressionExample.correlation(x, y);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testCorrelation_Success() {
        // setup
        double [] x = { 1.0, 2.0, 3.0, 5.0, 8.0 };
        double [] y = { 0.11, 0.12, 0.13, 0.15, 0.18 };
        double expected = 0.308;
        // exercise
        double actual = SimpleLinearRegressionExample.correlation(x, y);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testSlope() {
        // setup
        double [] x = { 1.0, 2.0, 3.0, 4.0 };
        double [] y = { 6.0, 5.0, 7.0, 10.0 };
        double expected = 1.4;
        // exercise
        double actual = SimpleLinearRegressionExample.slope(x, y);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
    @Test
    public void testIntercept() {
        // setup
        double [] x = { 1.0, 2.0, 3.0, 4.0 };
        double [] y = { 6.0, 5.0, 7.0, 10.0 };
        double expected = 3.5;
        // exercise
        double actual = SimpleLinearRegressionExample.intercept(x, y);
        // assert
        Assert.assertEquals(expected, actual, tolerance);
    }
}