数据集的简单线性回归
本文关键字：回归 线性 简单 数据集 | 更新日期: 2023-09-27 18:05:40
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。
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;
}
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);
}
}