public static double AdjustedRSquared(double[] expected, double[] predicted)
{
var loss = new RSquaredLoss(expected.Length, expected);
loss.Adjust = true;
return(loss.Loss(predicted));
}
public MultipleLinearRegression Learn(double[][] inputs, double[] outputs)
{
var ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
// Use Ordinary Least Squares to estimate a regression model
MultipleLinearRegression regression = ols.Learn(inputs, outputs);
// As result, we will be given the following:
//double a = regression.Weights[0]; // a = 0
//double b = regression.Weights[1]; // b = 0
//double c = regression.Intercept; // c = 1
// This is the plane described by the equation
// ax + by + c = z => 0x + 0y + 1 = z => 1 = z.
// We can compute the predicted points using
double[] predicted = regression.Transform(inputs);
// And the squared error loss using
double error = new SquareLoss(outputs).Loss(predicted);
// We can also compute other measures, such as the coefficient of determination r²
double r2 = new RSquaredLoss(numberOfInputs: 2, expected: outputs).Loss(predicted); // should be 1
// We can also compute the adjusted or weighted versions of r² using
var r2loss = new RSquaredLoss(numberOfInputs: 2, expected: outputs)
{
Adjust = true,
// Weights = weights; // (if you have a weighted problem)
};
double ar2 = r2loss.Loss(predicted); // should be 1
// Alternatively, we can also use the less generic, but maybe more user-friendly method directly:
double ur2 = regression.CoefficientOfDetermination(inputs, outputs, adjust: true); // should be 1
Console.WriteLine("Weights:");
foreach (var w in regression.Weights)
{
Console.WriteLine($",{w}");
}
Console.WriteLine("Intercept:");
Console.WriteLine($",{regression.Intercept}");
Console.WriteLine($"error:{error}");
Console.WriteLine($"r2:{r2}");
Console.WriteLine($"r2loss:{r2loss}");
Console.WriteLine($"ar2:{ar2}");
Console.WriteLine($"ur2:{ur2}");
return(regression);
}
/// <summary>
/// Gets the coefficient of determination, as known as R² (r-squared).
/// </summary>
///
/// <remarks>
/// <para>
/// The coefficient of determination is used in the context of statistical models
/// whose main purpose is the prediction of future outcomes on the basis of other
/// related information. It is the proportion of variability in a data set that
/// is accounted for by the statistical model. It provides a measure of how well
/// future outcomes are likely to be predicted by the model.</para>
/// <para>
/// The R² coefficient of determination is a statistical measure of how well the
/// regression line approximates the real data points. An R² of 1.0 indicates
/// that the regression line perfectly fits the data.</para>
/// </remarks>
///
/// <returns>The R² (r-squared) coefficient for the given data.</returns>
///
public double CoefficientOfDetermination(double[] inputs, double[] outputs, bool adjust, double[] weights = null)
{
var rsquared = new RSquaredLoss(NumberOfInputs, outputs);
rsquared.Adjust = adjust;
if (weights != null)
{
rsquared.Weights = weights;
}
return(rsquared.Loss(Transform(inputs)));
}
public static void RegressionStatistics()
{
// Compute the predicted points using
double[] predictedMGR = Predictor.MultipleGeneralRegression.Transform(PredictorPoints);
// We can also compute other measures, such as the coefficient of determination r²
double r2 = new RSquaredLoss(numberOfInputs: PredictorPoints.Length, expected: FrequencyLabelsDouble).Loss(predictedMGR);
Console.WriteLine($"Multiple Linear Regression R^2 VALIDATION: {r2}\n");
Console.Write("Multiple Linear regression fit succesfully!");
}
private static void ValidateModelResults(string modelName, double[] regInSamplePreds, double[] regOutSamplePreds, double[][] trainX, double[] trainY, double[][] testX, double[] testY)
{
// RMSE for in-sample
double regInSampleRMSE = Math.Sqrt(new SquareLoss(trainX).Loss(regInSamplePreds));
// RMSE for out-sample
double regOutSampleRMSE = Math.Sqrt(new SquareLoss(testX).Loss(regOutSamplePreds));
Console.WriteLine("RMSE: {0:0.0000} (Train) vs. {1:0.0000} (Test)", regInSampleRMSE, regOutSampleRMSE);
// R^2 for in-sample
double regInSampleR2 = new RSquaredLoss(trainX[0].Length, trainX).Loss(regInSamplePreds);
// R^2 for out-sample
double regOutSampleR2 = new RSquaredLoss(testX[0].Length, testX).Loss(regOutSamplePreds);
Console.WriteLine("R^2: {0:0.0000} (Train) vs. {1:0.0000} (Test)", regInSampleR2, regOutSampleR2);
// Scatter Plot of expected and actual
ScatterplotBox.Show(
String.Format("Actual vs. Prediction ({0})", modelName), testY, regOutSamplePreds
);
}
private PolynomialRegression GenerateRegressionFitting(SortedDictionary <double, double> values, char result)
{
// Extract inputs and outputs
double[] inputs = values.Keys.ToArray();
double[] outputs = values.Values.ToArray();
// We can create a learning algorithm
PolynomialLeastSquares ls = new PolynomialLeastSquares()
{
Degree = 2
};
// Now, we can use the algorithm to learn a polynomial
PolynomialRegression poly = ls.Learn(inputs, outputs);
// The learned polynomial will be given by
#pragma warning disable IDE0059 // Unnecessary assignment of a value
string str = poly.ToString("N1"); // "y(x) = 1.0x^2 + 0.0x^1 + 0.0"
// Where its weights can be accessed using
double[] weights = poly.Weights; // { 1.0000000000000024, -1.2407665029287351E-13 }
double intercept = poly.Intercept; // 1.5652369518855253E-12
#pragma warning restore IDE0059 // Unnecessary assignment of a value
// Finally, we can use this polynomial
// to predict values for the input data
double[] prediction = poly.Transform(inputs);
double r2 = new RSquaredLoss(outputs.Length, outputs).Loss(prediction); // should be > 0.85 (close to 1 is ok)
//LastGamesMetric: 0.77 0.81 0.08
//GoalsScoredMetric: 0.75 0.85 0.02
if (r2 == 1.0)
{
r2 = 0.0;
}
r2Values_.Add(result, r2);
return(poly);
}
public void learn_test_2()
{
#region doc_learn_2
// Let's say we would like predict a continuous number from a set
// of discrete and continuous input variables. For this, we will
// be using the Servo dataset from UCI's Machine Learning repository
// as an example: http://archive.ics.uci.edu/ml/datasets/Servo
// Create a Servo dataset
Servo servo = new Servo();
object[][] instances = servo.Instances; // 167 x 4
double[] outputs = servo.Output; // 167 x 1
// This dataset contains 4 columns, where the first two are
// symbolic (having possible values A, B, C, D, E), and the
// last two are continuous.
// We will use a codification filter to transform the symbolic
// variables into one-hot vectors, while keeping the other two
// continuous variables intact:
var codebook = new Codification <object>()
{
{ "motor", CodificationVariable.Categorical },
{ "screw", CodificationVariable.Categorical },
{ "pgain", CodificationVariable.Continuous },
{ "vgain", CodificationVariable.Continuous },
};
// Learn the codebook
codebook.Learn(instances);
// We can gather some info about the problem:
int numberOfInputs = codebook.NumberOfInputs; // should be 4 (since there are 4 variables)
int numberOfOutputs = codebook.NumberOfOutputs; // should be 12 (due their one-hot encodings)
// Now we can use it to obtain double[] vectors:
double[][] inputs = codebook.ToDouble().Transform(instances);
// We will use Ordinary Least Squares to create a
// linear regression model with an intercept term
var ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
// Use Ordinary Least Squares to estimate a regression model:
MultipleLinearRegression regression = ols.Learn(inputs, outputs);
// We can compute the predicted points using:
double[] predicted = regression.Transform(inputs);
// And the squared error using the SquareLoss class:
double error = new SquareLoss(outputs).Loss(predicted);
// We can also compute other measures, such as the coefficient of determination r² using:
double r2 = new RSquaredLoss(numberOfOutputs, outputs).Loss(predicted); // should be 0.55086630162967354
// Or the adjusted or weighted versions of r² using:
var r2loss = new RSquaredLoss(numberOfOutputs, outputs)
{
Adjust = true,
// Weights = weights; // (uncomment if you have a weighted problem)
};
double ar2 = r2loss.Loss(predicted); // should be 0.51586887058782993
// Alternatively, we can also use the less generic, but maybe more user-friendly method directly:
double ur2 = regression.CoefficientOfDetermination(inputs, outputs, adjust: true); // should be 0.51586887058782993
#endregion
Assert.AreEqual(4, numberOfInputs);
Assert.AreEqual(12, numberOfOutputs);
Assert.AreEqual(12, regression.NumberOfInputs);
Assert.AreEqual(1, regression.NumberOfOutputs);
Assert.AreEqual(1.0859586717266123, error, 1e-6);
double[] expected = regression.Compute(inputs);
double[] actual = regression.Transform(inputs);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
Assert.AreEqual(0.55086630162967354, r2);
Assert.AreEqual(0.51586887058782993, ar2);
Assert.AreEqual(0.51586887058782993, ur2);
}
public void learn_test()
{
#region doc_learn
// We will try to model a plane as an equation in the form
// "ax + by + c = z". We have two input variables (x and y)
// and we will be trying to find two parameters a and b and
// an intercept term c.
// We will use Ordinary Least Squares to create a
// linear regression model with an intercept term
var ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
// Now suppose you have some points
double[][] inputs =
{
new double[] { 1, 1 },
new double[] { 0, 1 },
new double[] { 1, 0 },
new double[] { 0, 0 },
};
// located in the same Z (z = 1)
double[] outputs = { 1, 1, 1, 1 };
// Use Ordinary Least Squares to estimate a regression model
MultipleLinearRegression regression = ols.Learn(inputs, outputs);
// As result, we will be given the following:
double a = regression.Weights[0]; // a = 0
double b = regression.Weights[1]; // b = 0
double c = regression.Intercept; // c = 1
// This is the plane described by the equation
// ax + by + c = z => 0x + 0y + 1 = z => 1 = z.
// We can compute the predicted points using
double[] predicted = regression.Transform(inputs);
// And the squared error loss using
double error = new SquareLoss(outputs).Loss(predicted);
// We can also compute other measures, such as the coefficient of determination r²
double r2 = new RSquaredLoss(numberOfInputs: 2, expected: outputs).Loss(predicted); // should be 1
// We can also compute the adjusted or weighted versions of r² using
var r2loss = new RSquaredLoss(numberOfInputs: 2, expected: outputs)
{
Adjust = true,
// Weights = weights; // (if you have a weighted problem)
};
double ar2 = r2loss.Loss(predicted); // should be 1
// Alternatively, we can also use the less generic, but maybe more user-friendly method directly:
double ur2 = regression.CoefficientOfDetermination(inputs, outputs, adjust: true); // should be 1
#endregion
Assert.AreEqual(2, regression.NumberOfInputs);
Assert.AreEqual(1, regression.NumberOfOutputs);
Assert.AreEqual(0.0, a, 1e-6);
Assert.AreEqual(0.0, b, 1e-6);
Assert.AreEqual(1.0, c, 1e-6);
Assert.AreEqual(0.0, error, 1e-6);
double[] expected = regression.Compute(inputs);
double[] actual = regression.Transform(inputs);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
Assert.AreEqual(1.0, r2);
Assert.AreEqual(1.0, ar2);
Assert.AreEqual(1.0, ur2);
}
static void Main(string[] args)
{
//for separating the training and test samples
int traintPos = 18;
int testPos = 22;
int allData = testPos + (testPos - traintPos);
//for correct reading symbol of float point in csv
System.Globalization.CultureInfo customCulture = (System.Globalization.CultureInfo)System.Threading.Thread.CurrentThread.CurrentCulture.Clone();
customCulture.NumberFormat.NumberDecimalSeparator = ".";
System.Threading.Thread.CurrentThread.CurrentCulture = customCulture;
//read data
string CsvFilePath = @"msc_appel_data.csv";
DataTable mscTable = new CsvReader(CsvFilePath, true).ToTable();
//for encoding the string values of months into numerical values
Dictionary <string, double> monthNames = new Dictionary <string, double>
{
["January"] = 1,
["February"] = 2,
["March"] = 3,
["April"] = 4,
["May"] = 5,
["June"] = 6,
["July"] = 7,
["August"] = 8,
["September"] = 9,
["October"] = 10,
["November"] = 11,
["December"] = 12
};
string[] months = mscTable.Columns["month"].ToArray <String>();
double[] dMonths = new double[months.Length];
for (int i = 0; i < months.Length; i++)
{
dMonths[i] = monthNames[months[i]];
//Console.WriteLine(dMonths[i]);
}
//select the target column
double[] OutResPositive = mscTable.Columns["res_positive"].ToArray();
// separation of the test and train target sample
double[] OutResPositiveTrain = OutResPositive.Get(0, traintPos);
double[] OutResPositiveTest = OutResPositive.Get(traintPos, testPos);
//deleting unneeded columns
mscTable.Columns.Remove("total_appeals");
mscTable.Columns.Remove("month");
mscTable.Columns.Remove("res_positive");
mscTable.Columns.Remove("year");
//add coded in a double column month into Table
//create new column
DataColumn newCol = new DataColumn("dMonth", typeof(double));
newCol.AllowDBNull = true;
// add new column
mscTable.Columns.Add(newCol);
//fill new column
int counter = 0;
foreach (DataRow row in mscTable.Rows)
{
row["dMonth"] = dMonths[counter];
counter++;
}
//receiving input data from a table
double[][] inputs = mscTable.ToArray();
//separation of the test and train sample
double[][] inputsTrain = inputs.Get(0, traintPos);
double[][] inputsTest = inputs.Get(traintPos, testPos);
//simple linear regression model
var ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
//linear regression model for several features
MultipleLinearRegression regression = ols.Learn(inputsTrain, OutResPositiveTrain);
//make a prediction
double[] predicted = regression.Transform(inputsTest);
//console output
for (int i = 0; i < testPos - traintPos; i++)
{
Console.WriteLine("predicted: {0} real: {1}", predicted[i], OutResPositiveTest[i]);
}
// And print the squared error using the SquareLoss class:
Console.WriteLine("error = {0}", new SquareLoss(OutResPositiveTest).Loss(predicted));
// print the coefficient of determination
double r2 = new RSquaredLoss(numberOfInputs: 29, expected: OutResPositiveTest).Loss(predicted);
Console.WriteLine("R^2 = {0}", r2);
// alternative print the coefficient of determination
double ur2 = regression.CoefficientOfDetermination(inputs, OutResPositiveTest, adjust: true);
Console.WriteLine("alternative version of R2 = {0}", r2);
Console.WriteLine("Press enter and close chart to exit");
// for chart
int[] classes = new int[allData];
double[] mountX = new double[allData];
for (int i = 0; i < allData; i++)
{
if (i < testPos)
{
// for csv data
mountX[i] = i + 1;
classes[i] = 0; //csv data is class 0
}
else
{
//for predicted
mountX[i] = i - (testPos - traintPos) + 1;
classes[i] = 1; //predicted is class 1
}
}
// make points of chart
List <double> OutChart = new List <double>();
OutChart.AddRange(OutResPositive);
OutChart.AddRange(predicted);
// plot chart
ScatterplotBox.Show("res_positive from months", mountX, OutChart.ToArray(), classes).Hold();
// for pause
Console.ReadLine();
}
private List <AccordResult> CalculateLinearRegression(List <BalancePointPair> allBalancePointPairs, WthNormalParams normalParamsKey)
{
var allBalancePointGroups = allBalancePointPairs.GroupBy(s => new { s.CoolingBalancePoint, s.HeatingBalancePoint });
List <AccordResult> accordResults = new List <AccordResult>();
List <AccordResult> rejectedAccords = new List <AccordResult>();
foreach (var group in allBalancePointGroups)
{
try
{
List <BalancePointPair> IdenticalBalancePointPairsForAllReadings = group.ToList();
BalancePointPair _pointPair = IdenticalBalancePointPairsForAllReadings.First();
int readingsCount = IdenticalBalancePointPairsForAllReadings.Count;
double[] fullYData = new double[readingsCount];
double[] fullYDataDailyAvg = new double[readingsCount];
double[][] hcddMatrix = new double[readingsCount][];
double[][] hcddMatrixNonDaily = new double[readingsCount][];
foreach (BalancePointPair balancePointPair in IdenticalBalancePointPairsForAllReadings)
{
fullYData[IdenticalBalancePointPairsForAllReadings.IndexOf(balancePointPair)] = (balancePointPair.ActualUsage);
fullYDataDailyAvg[IdenticalBalancePointPairsForAllReadings.IndexOf(balancePointPair)]
= (balancePointPair.ActualUsage / balancePointPair.DaysInReading);
hcddMatrix[IdenticalBalancePointPairsForAllReadings.IndexOf(balancePointPair)] = new double[]
{
(balancePointPair.HeatingDegreeDays / balancePointPair.DaysInReading),
(balancePointPair.CoolingDegreeDays / balancePointPair.DaysInReading)
};
}
double[] avgHddsForEachReadingInYear = new double[readingsCount];
double[] avgCddsForEachReadingInYear = new double[readingsCount];
for (int i = 0; i < readingsCount; i++)
{
avgHddsForEachReadingInYear[i] = hcddMatrix[i][0];
avgCddsForEachReadingInYear[i] = hcddMatrix[i][1];
}
double[] modelParams = new double[3];
modelParams[0] = 0;
modelParams[1] = 0;
modelParams[2] = 0;
if (fullYData.Sum() == 0)
{
AccordResult empty = new AccordResult
{
bpPair = _pointPair
};
accordResults.Add(empty);
}
else if (_pointPair.HeatingBalancePoint == 0 && _pointPair.CoolingBalancePoint == 0)
{
double[] onesVector = new double[readingsCount];
for (int i = 0; i < readingsCount; i++)
{
onesVector[i] = 1;
}
modelParams[0] = Fit.LineThroughOrigin(onesVector, fullYDataDailyAvg);
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = false
};
SimpleLinearRegression regressionAccord = ols.Learn(onesVector, fullYDataDailyAvg);
//double[] predictedAccord = regressionAccord.Transform(onesVector);
double r2 = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(onesVector.Select(x => x * modelParams[0]), fullYDataDailyAvg);
//double mean = fullYDataDailyAvg.Mean();
//if (mean != modelParams[0] || mean != regressionAccord.Slope)
//{
// Console.WriteLine("Hey!");
//}
//double r2Accord = regressionAccord.CoefficientOfDetermination(onesVector, fullYDataDailyAvg);
//double sxx = onesVector.Subtract(onesVector.Mean()).Pow(2).Sum();
//double hypothesizedValue = 0;
//try
//{
// TTest test = new TTest(
// estimatedValue: regressionAccord.Slope, standardError: sxx, degreesOfFreedom: _pointPair.ReadingsInNormalYear - 2,
// hypothesizedValue: hypothesizedValue, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis
// );
// if (test.Significant)
// {
AccordResult accordResult = new AccordResult()
{
SimpleLinearRegression = regressionAccord,
R2Accord = r2,
IsSimpleSingleRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
Intercept = regressionAccord.Slope,
bpPair = _pointPair
};
accordResults.Add(accordResult);
// }
//}
//catch (Exception e)
//{
// Console.WriteLine(e.Message + e.StackTrace);
//}
}
else if (_pointPair.CoolingBalancePoint != 0 && _pointPair.HeatingBalancePoint != 0)
{
//modelParams = MultipleRegression.QR(hcddMatrix, fullYDataDailyAvg, intercept: true);
//Accord
//var ols = new OrdinaryLeastSquares()
//{
// UseIntercept = true
//};
try
{
MultipleLinearRegressionAnalysis mlra = new MultipleLinearRegressionAnalysis(intercept: true);
mlra.Learn(hcddMatrix, fullYDataDailyAvg);
//
//MultipleLinearRegression regressionAccord = ols.Learn(hcddMatrix, fullYDataDailyAvg);
var regressionAccord = mlra.Regression;
double[] predicted = regressionAccord.Transform(hcddMatrix);
double r2Accord = new RSquaredLoss(numberOfInputs: 2, expected: fullYDataDailyAvg)
{
Adjust = false
}.Loss(predicted);
double r2Coeff = regressionAccord.CoefficientOfDetermination(hcddMatrix, fullYDataDailyAvg, adjust: false);
//double r2Math = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(hcddMatrix.Select(
// x => (x[0] * regressionAccord.Weights[0]) + (x[1] * regressionAccord.Weights[1]) + regressionAccord.Intercept
//), fullYDataDailyAvg);
//double r2MathPred = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(predicted, fullYDataDailyAvg);
AccordResult accordResult = new AccordResult()
{
//MultipleRegression = regressionAccord,
R2Accord = r2Accord,
R2Coeff = r2Coeff,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
IsSimpleSingleRegression = false,
MLRA = mlra,
Intercept = regressionAccord.Intercept,
bpPair = _pointPair,
IsMultipleLinearRegression = true
};
if (mlra.Coefficients.All(x => x.TTest.Significant))
{
accordResults.Add(accordResult);
}
else
{
rejectedAccords.Add(accordResult);
}
}
catch (Exception e)
{
Console.WriteLine(e.Message + " " + e.StackTrace);
}
}
else if (_pointPair.HeatingBalancePoint > 0)
{
// Tuple<double, double> heatingTuple = Fit.Line(avgHddsForEachReadingInYear, fullYDataDailyAvg);
// modelParams[0] = heatingTuple.Item1;
// modelParams[1] = heatingTuple.Item2;
// double r = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(
// avgHddsForEachReadingInYear.Select(x => heatingTuple.Item1 + heatingTuple.Item2 * x), fullYDataDailyAvg);
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
SimpleLinearRegression regressionAccord = ols.Learn(avgHddsForEachReadingInYear, fullYDataDailyAvg);
double[] predictedAccord = regressionAccord.Transform(avgHddsForEachReadingInYear);
double rAccord = new RSquaredLoss(1, fullYDataDailyAvg).Loss(predictedAccord);
//double rAccord2 = regressionAccord.CoefficientOfDetermination(avgHddsForEachReadingInYear, fullYDataDailyAvg, adjust: false);
//double r2Math = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(avgHddsForEachReadingInYear.Select(
// x => (x * regressionAccord.Slope) + regressionAccord.Intercept
// ), fullYDataDailyAvg);
//double r2 = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(predictedAccord, fullYDataDailyAvg);
int degreesOfFreedom = _pointPair.ReadingsInNormalYear - 2;
double ssx = Math.Sqrt((avgHddsForEachReadingInYear.Subtract(avgHddsForEachReadingInYear.Mean())).Pow(2).Sum());
double s = Math.Sqrt(((fullYDataDailyAvg.Subtract(predictedAccord).Pow(2)).Sum()) / degreesOfFreedom);
double error = regressionAccord.GetStandardError(avgHddsForEachReadingInYear, fullYDataDailyAvg);
double seSubB = s / ssx;
double hypothesizedValue = 0;
TTest tTest = new TTest(
estimatedValue: regressionAccord.Slope, standardError: seSubB, degreesOfFreedom: degreesOfFreedom,
hypothesizedValue: hypothesizedValue, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis
);
AccordResult accordResult = new AccordResult()
{
SimpleLinearRegression = regressionAccord,
R2Accord = rAccord,
IsSimpleSingleRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
TTest = tTest,
Intercept = regressionAccord.Intercept,
bpPair = _pointPair
};
if (tTest.Significant)
{
accordResults.Add(accordResult);
}
else
{
rejectedAccords.Add(accordResult);
}
}
else if (_pointPair.CoolingBalancePoint > 0)
{
//Tuple<double, double> coolingTuple = Fit.Line(avgCddsForEachReadingInYear, fullYDataDailyAvg);
//modelParams[0] = coolingTuple.Item1;
//modelParams[2] = coolingTuple.Item2;
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
SimpleLinearRegression regressionAccord = ols.Learn(avgCddsForEachReadingInYear, fullYDataDailyAvg);
double[] predictedAccord = regressionAccord.Transform(avgCddsForEachReadingInYear);
double rAccord = new RSquaredLoss(1, fullYDataDailyAvg).Loss(predictedAccord);
//double r2Math = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(avgCddsForEachReadingInYear.Select(
// x => (x * regressionAccord.Slope) + regressionAccord.Intercept
// ), fullYDataDailyAvg);
//double r2 = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(predictedAccord, fullYDataDailyAvg);
int degreesOfFreedom = _pointPair.ReadingsInNormalYear - 2;
double ssx = Math.Sqrt(avgCddsForEachReadingInYear.Subtract(avgCddsForEachReadingInYear.Mean()).Pow(2).Sum());
double s = Math.Sqrt(((fullYDataDailyAvg.Subtract(predictedAccord).Pow(2)).Sum()) / degreesOfFreedom);
double seSubB = s / ssx;
double hypothesizedValue = 0;
double myT = seSubB / regressionAccord.Slope;
TTest tTest = new TTest(
estimatedValue: regressionAccord.Slope, standardError: seSubB, degreesOfFreedom: degreesOfFreedom,
hypothesizedValue: hypothesizedValue, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis
);
AccordResult accordResult = new AccordResult()
{
SimpleLinearRegression = regressionAccord,
R2Accord = rAccord,
IsSimpleSingleRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
TTest = tTest,
Intercept = regressionAccord.Intercept,
bpPair = _pointPair
};
if (tTest.Significant)
{
accordResults.Add(accordResult);
}
else
{
rejectedAccords.Add(accordResult);
}
}
;
}
catch (Exception e)
{
Console.WriteLine(normalParamsKey.AccID + " " + normalParamsKey.UtilID + " " + normalParamsKey.UnitID + " " + e.Message + e.StackTrace);
}
}
//rejectedAccords = rejectedAccords.OrderByDescending(s => s.R2Accord).ToList();
//accordResults = accordResults.OrderByDescending(s => s.R2Accord).ToList();
return(accordResults);
}
private AccordResult CalculateLinearRegression(List <BalancePointPair> allBalancePointPairs, WthNormalParams normalParamsKey)
{
var allBalancePointGroups = allBalancePointPairs.GroupBy(s => new { s.CoolingBalancePoint, s.HeatingBalancePoint });
List <AccordResult> accordResults = new List <AccordResult>();
foreach (var group in allBalancePointGroups)
{
try
{
List <BalancePointPair> IdenticalBalancePointPairsFromAllReadings = group.ToList();
BalancePointPair _pointPair = IdenticalBalancePointPairsFromAllReadings.First();
int readingsCount = IdenticalBalancePointPairsFromAllReadings.Count;
double[] fullYData = new double[readingsCount];
double[] fullYDataDailyAvg = new double[readingsCount];
double[][] hcddMatrix = new double[readingsCount][];
double[][] hcddMatrixNonDaily = new double[readingsCount][];
foreach (BalancePointPair balancePointPair in IdenticalBalancePointPairsFromAllReadings)
{
fullYData[IdenticalBalancePointPairsFromAllReadings.IndexOf(balancePointPair)] = (balancePointPair.ActualUsage);
fullYDataDailyAvg[IdenticalBalancePointPairsFromAllReadings.IndexOf(balancePointPair)]
= (balancePointPair.ActualUsage / balancePointPair.DaysInReading);
hcddMatrix[IdenticalBalancePointPairsFromAllReadings.IndexOf(balancePointPair)] = new double[]
{
(balancePointPair.HeatingDegreeDays / balancePointPair.DaysInReading),
(balancePointPair.CoolingDegreeDays / balancePointPair.DaysInReading)
};
}
double[] avgHddsForEachReadingInYear = new double[readingsCount];
double[] avgCddsForEachReadingInYear = new double[readingsCount];
for (int i = 0; i < readingsCount; i++)
{
avgHddsForEachReadingInYear[i] = hcddMatrix[i][0];
avgCddsForEachReadingInYear[i] = hcddMatrix[i][1];
}
double[] modelParams = new double[3];
modelParams[0] = 0;
modelParams[1] = 0;
modelParams[2] = 0;
if (_pointPair.HeatingBalancePoint == 0 && _pointPair.CoolingBalancePoint == 0)
{
double[] onesVector = new double[readingsCount];
for (int i = 0; i < readingsCount; i++)
{
onesVector[i] = 1;
}
modelParams[0] = Fit.LineThroughOrigin(onesVector, fullYDataDailyAvg);
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = false
};
double r2 = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(
onesVector.Select(x => x * modelParams[0]), fullYDataDailyAvg);
AccordResult accordResult = new AccordResult()
{
IsSimpleSingleRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
Intercept = modelParams[0],
R2Accord = r2,
};
accordResults.Add(accordResult);
}
else if (_pointPair.CoolingBalancePoint != 0 && _pointPair.HeatingBalancePoint != 0)
{
try
{
MultipleLinearRegressionAnalysis mlra = new MultipleLinearRegressionAnalysis(intercept: true);
mlra.Learn(hcddMatrix, fullYDataDailyAvg);
var regressionAccord = mlra.Regression;
double[] predicted = regressionAccord.Transform(hcddMatrix);
double r2Accord = new RSquaredLoss(numberOfInputs: 2, expected: fullYDataDailyAvg)
{
Adjust = false
}.Loss(predicted);
double r2Coeff = regressionAccord.CoefficientOfDetermination(hcddMatrix, fullYDataDailyAvg, adjust: false);
bool FTestFailed = !mlra.FTest.Significant;
AccordResult accordResult = new AccordResult()
{
IsMultipleLinearRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
Intercept = regressionAccord.Intercept,
B2 = regressionAccord.Weights[0],
B4 = regressionAccord.Weights[1],
R2Accord = r2Accord,
FTestFailed = FTestFailed
};
if (mlra.Coefficients.All(x => x.TTest.Significant))
{
accordResults.Add(accordResult);
}
}
catch (Exception e)
{
Log.Debug(normalParamsKey.AccID + " " + normalParamsKey.UtilID + " " + normalParamsKey.UnitID + " " + e.Message + " " + e.StackTrace);
}
}
else if (_pointPair.HeatingBalancePoint > 0)
{
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
SimpleLinearRegression regressionAccord = ols.Learn(avgHddsForEachReadingInYear, fullYDataDailyAvg);
double[] predictedAccord = regressionAccord.Transform(avgHddsForEachReadingInYear);
double r2Accord = new RSquaredLoss(1, fullYDataDailyAvg).Loss(predictedAccord);
int degreesOfFreedom = normalParamsKey.MoCt - 2;
double ssx = Math.Sqrt((avgHddsForEachReadingInYear.Subtract(avgHddsForEachReadingInYear.Mean())).Pow(2).Sum());
double s = Math.Sqrt(((fullYDataDailyAvg.Subtract(predictedAccord).Pow(2)).Sum()) / degreesOfFreedom);
double error = regressionAccord.GetStandardError(avgHddsForEachReadingInYear, fullYDataDailyAvg);
double seSubB = s / ssx;
double hypothesizedValue = 0;
TTest tTest = new TTest(
estimatedValue: regressionAccord.Slope, standardError: seSubB, degreesOfFreedom: degreesOfFreedom,
hypothesizedValue: hypothesizedValue, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis
);
AccordResult accordResult = new AccordResult()
{
IsSimpleSingleRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
Intercept = regressionAccord.Intercept,
B2 = regressionAccord.Slope,
R2Accord = r2Accord
};
if (tTest.Significant)
{
accordResults.Add(accordResult);
}
}
else if (_pointPair.CoolingBalancePoint > 0)
{
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
SimpleLinearRegression regressionAccord = ols.Learn(avgCddsForEachReadingInYear, fullYDataDailyAvg);
double[] predictedAccord = regressionAccord.Transform(avgCddsForEachReadingInYear);
double rAccord = new RSquaredLoss(1, fullYDataDailyAvg).Loss(predictedAccord);
int degreesOfFreedom = normalParamsKey.MoCt - 2;
double ssx = Math.Sqrt(avgCddsForEachReadingInYear.Subtract(avgCddsForEachReadingInYear.Mean()).Pow(2).Sum());
double s = Math.Sqrt(((fullYDataDailyAvg.Subtract(predictedAccord).Pow(2)).Sum()) / degreesOfFreedom);
double seSubB = s / ssx;
double hypothesizedValue = 0;
double myT = seSubB / regressionAccord.Slope;
TTest tTest = new TTest(
estimatedValue: regressionAccord.Slope, standardError: seSubB, degreesOfFreedom: degreesOfFreedom,
hypothesizedValue: hypothesizedValue, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis
);
AccordResult accordResult = new AccordResult()
{
IsSimpleSingleRegression = true,
CoolingBP = _pointPair.CoolingBalancePoint,
Intercept = regressionAccord.Intercept,
B4 = regressionAccord.Slope,
R2Accord = rAccord
};
if (tTest.Significant)
{
accordResults.Add(accordResult);
}
}
;
}
catch (Exception e)
{
Log.Debug(normalParamsKey.AccID + " " + normalParamsKey.UtilID + " " + normalParamsKey.UnitID + " " + e.Message + e.StackTrace);
}
}
AccordResult accordWinner = accordResults
.Where(s => s.Intercept >= 0)
.OrderByDescending(s => s.R2Accord).ToList().FirstOrDefault();
return(accordWinner);
}
private AccordResult CalculateLinearRegression(List <BalancePointPair> allBalancePointPairs, WthNormalParams normalParamsKey)
{
var allBalancePointGroups = allBalancePointPairs.GroupBy(s => new { s.CoolingBalancePoint, s.HeatingBalancePoint });
List <AccordResult> accordResults = new List <AccordResult>();
foreach (var group in allBalancePointGroups)
{
try
{
List <BalancePointPair> IdenticalBalancePointPairsFromAllReadings = group.ToList();
BalancePointPair _pointPair = IdenticalBalancePointPairsFromAllReadings.First();
int readingsCount = IdenticalBalancePointPairsFromAllReadings.Count;
double[] fullYData = new double[readingsCount];
double[] fullYDataDailyAvg = new double[readingsCount];
double[][] hcddMatrix = new double[readingsCount][];
double[][] hcddMatrixNonDaily = new double[readingsCount][];
foreach (BalancePointPair balancePointPair in IdenticalBalancePointPairsFromAllReadings)
{
fullYData[IdenticalBalancePointPairsFromAllReadings.IndexOf(balancePointPair)] = (balancePointPair.ActualUsage);
fullYDataDailyAvg[IdenticalBalancePointPairsFromAllReadings.IndexOf(balancePointPair)]
= (balancePointPair.ActualUsage / balancePointPair.DaysInReading);
hcddMatrix[IdenticalBalancePointPairsFromAllReadings.IndexOf(balancePointPair)] = new double[]
{
(balancePointPair.HeatingDegreeDays / balancePointPair.DaysInReading),
(balancePointPair.CoolingDegreeDays / balancePointPair.DaysInReading)
};
}
if (!(fullYData.Sum() > 0))
{
return(new AccordResult());
}
double[] avgHddsForEachReadingInYear = new double[readingsCount];
double[] avgCddsForEachReadingInYear = new double[readingsCount];
for (int i = 0; i < readingsCount; i++)
{
avgHddsForEachReadingInYear[i] = hcddMatrix[i][0];
avgCddsForEachReadingInYear[i] = hcddMatrix[i][1];
}
double[] modelParams = new double[3];
modelParams[0] = 0;
modelParams[1] = 0;
modelParams[2] = 0;
if (_pointPair.HeatingBalancePoint == 0 && _pointPair.CoolingBalancePoint == 0)
{
double[] onesVector = new double[readingsCount];
for (int i = 0; i < readingsCount; i++)
{
onesVector[i] = 1;
}
modelParams[0] = Fit.LineThroughOrigin(onesVector, fullYDataDailyAvg);
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = false
};
double r2 = MathNet.Numerics.GoodnessOfFit.CoefficientOfDetermination(
onesVector.Select(x => x * modelParams[0]), fullYDataDailyAvg);
AccordResult accordResult = new AccordResult()
{
IsSimpleSingleRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
Intercept = modelParams[0],
R2Accord = r2,
//R2Accord = 0
};
accordResults.Add(accordResult);
}
else if (_pointPair.CoolingBalancePoint != 0 && _pointPair.HeatingBalancePoint != 0)
{
try
{
MultipleLinearRegressionAnalysis mlra = new MultipleLinearRegressionAnalysis(intercept: true);
mlra.Learn(hcddMatrix, fullYDataDailyAvg);
var regressionAccord = mlra.Regression;
double[] predictedAccord = regressionAccord.Transform(hcddMatrix);
double r2Accord = new RSquaredLoss(numberOfInputs: 2, expected: fullYDataDailyAvg)
{
Adjust = false
}.Loss(predictedAccord);
double r2Coeff = regressionAccord.CoefficientOfDetermination(hcddMatrix, fullYDataDailyAvg, adjust: false);
bool FTestFailed = !mlra.FTest.Significant;
AccordResult accordResult = new AccordResult()
{
IsMultipleLinearRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
CoolingBP = _pointPair.CoolingBalancePoint,
Intercept = regressionAccord.Intercept,
B2 = regressionAccord.Weights[0],
B4 = regressionAccord.Weights[1],
R2Accord = r2Accord,
FTestFailed = FTestFailed
};
//int degreesOfFreedom = normalParamsKey.MoCt - 3;
double degreesOfFreedomAsDouble = mlra.Regression.GetDegreesOfFreedom(readingsCount);
int degreesOfFreedom = Convert.ToInt32(degreesOfFreedomAsDouble);
//if (degreesOfFreedom != 9)
//{
// Log.Warning($"Multivariable regression. DOF expected to be 9. is: {degreesOfFreedom}");
//}
//if (degreesOfFreedom != dof)
//{
// Console.WriteLine($"dof different. mlra.dof = {dof} expected = {degreesOfFreedom}");
//}
double s = Math.Sqrt(fullYDataDailyAvg.Subtract(predictedAccord).Pow(2).Sum() / degreesOfFreedom);
double ssxHdd = Math.Sqrt((avgHddsForEachReadingInYear.Subtract(avgHddsForEachReadingInYear.Mean())).Pow(2).Sum());
double ssxCdd = Math.Sqrt((avgCddsForEachReadingInYear.Subtract(avgCddsForEachReadingInYear.Mean())).Pow(2).Sum());
double seSubHdd = s / ssxHdd;
double seSubCdd = s / ssxCdd;
double tStatisticHdd = regressionAccord.Weights[0] / seSubHdd;
double tStatisticCdd = regressionAccord.Weights[1] / seSubCdd;
double tCriticalFivePercent = 2.262156;
double tCriticalTenPercent = 1.833113;
bool myTestHdd = Math.Abs(tStatisticHdd) >= tCriticalTenPercent;
bool myTestCdd = Math.Abs(tStatisticCdd) >= tCriticalTenPercent;
//if (myTestHdd != mlra.Coefficients[0].TTest.Significant && degreesOfFreedom != 9)
//{
// Console.WriteLine($"nope. mystat - {tStatisticHdd} accordstat - {mlra.Coefficients[0].TTest.Statistic} " +
// $"accordCritical - {mlra.Coefficients[0].TTest.CriticalValue}");
//}
//if (myTestCdd != mlra.Coefficients[1].TTest.Significant && degreesOfFreedom != 9)
//{
// Console.WriteLine($"nope. mystat - {tStatisticCdd} accordstat - {mlra.Coefficients[1].TTest.Statistic} " +
// $"accordCritical - {mlra.Coefficients[1].TTest.CriticalValue}");
//}
//if (mlra.Coefficients.All(x => x.TTest.Significant) &&
// mlra.Coefficients.All(x => x.Value > 0) &&
// mlra.Regression.Intercept > 0 &&
// r2Accord >= 0.7500)
//{
// accordResults.Add(accordResult);
//}
if (
myTestHdd &&
myTestCdd &&
mlra.Coefficients.All(x => x.Value > 0) &&
mlra.Regression.Intercept > 0
//&& accordResult.R2Accord >= 0.75
)
{
accordResults.Add(accordResult);
}
}
catch (Exception e)
{
Log.Debug($"AccID/UtilID/UnitID: {normalParamsKey.AccID}/{normalParamsKey.UtilID}/{normalParamsKey.UnitID} >> " +
$"MultipleLinearRegressionAnalysis Exception: {e.Message}");
}
}
else if (_pointPair.HeatingBalancePoint > 0)
{
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
SimpleLinearRegression regressionAccord = ols.Learn(avgHddsForEachReadingInYear, fullYDataDailyAvg);
double[] predictedAccord = regressionAccord.Transform(avgHddsForEachReadingInYear);
double r2Accord = new RSquaredLoss(1, fullYDataDailyAvg).Loss(predictedAccord);
//int degreesOfFreedom = normalParamsKey.MoCt - 2;
double degreesOfFreedomAsDouble = regressionAccord.GetDegreesOfFreedom(readingsCount);
int degreesOfFreedom = Convert.ToInt32(degreesOfFreedomAsDouble);
//if (degreesOfFreedom != 10)
//{
// Log.Warning($"Single variable regression. DOF expected to be 10. is: {degreesOfFreedom}");
//}
double ssx = Math.Sqrt((avgHddsForEachReadingInYear.Subtract(avgHddsForEachReadingInYear.Mean())).Pow(2).Sum());
double s = Math.Sqrt(fullYDataDailyAvg.Subtract(predictedAccord).Pow(2).Sum() / degreesOfFreedom);
double error = regressionAccord.GetStandardError(avgHddsForEachReadingInYear, fullYDataDailyAvg);
double seSubB = s / ssx;
double hypothesizedValue = 0;
double tStatistic = regressionAccord.Slope / seSubB;
double tCriticalFivePercent = 2.228138;
double tCriticalTenPercent = 1.812461;
bool myTest = Math.Abs(tStatistic) >= tCriticalTenPercent;
//TTest tTest = new TTest(
// estimatedValue: regressionAccord.Slope, standardError: seSubB, degreesOfFreedom: degreesOfFreedom,
// hypothesizedValue: hypothesizedValue, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis
// );
//if (myTest != tTest.Significant)
//{
// Console.WriteLine($"nope. mystat - {tStatistic} accordstat - {tTest.Statistic} accordCritical - {tTest.CriticalValue}");
//}
AccordResult accordResult = new AccordResult()
{
IsSimpleSingleRegression = true,
HeatingBP = _pointPair.HeatingBalancePoint,
Intercept = regressionAccord.Intercept,
B2 = regressionAccord.Slope,
R2Accord = r2Accord
};
//if (tTest.Significant && accordResult.B2 > 0 && r2Accord >= 0.7500)
//{
// accordResults.Add(accordResult);
//}
if (myTest &&
accordResult.B2 > 0 &&
accordResult.Intercept > 0
//&& r2Accord >= 0.7500
)
{
accordResults.Add(accordResult);
}
}
else if (_pointPair.CoolingBalancePoint > 0)
{
OrdinaryLeastSquares ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
SimpleLinearRegression regressionAccord = ols.Learn(avgCddsForEachReadingInYear, fullYDataDailyAvg);
double[] predictedAccord = regressionAccord.Transform(avgCddsForEachReadingInYear);
double r2Accord = new RSquaredLoss(1, fullYDataDailyAvg).Loss(predictedAccord);
//int degreesOfFreedom = normalParamsKey.MoCt - 2;
double degreesOfFreedomAsDouble = regressionAccord.GetDegreesOfFreedom(readingsCount);
int degreesOfFreedom = Convert.ToInt32(degreesOfFreedomAsDouble);
//if (degreesOfFreedom != 10)
//{
// Log.Warning($"Single variable regression. DOF expected to be 10. is: {degreesOfFreedom}");
//}
double ssx = Math.Sqrt(avgCddsForEachReadingInYear.Subtract(avgCddsForEachReadingInYear.Mean()).Pow(2).Sum());
double s = Math.Sqrt(fullYDataDailyAvg.Subtract(predictedAccord).Pow(2).Sum() / degreesOfFreedom);
double seSubB = s / ssx;
double hypothesizedValue = 0;
double tStatistic = regressionAccord.Slope / seSubB;
double tCriticalFivePercent = 2.22813885198627;
double tCriticalTenPercent = 1.812461;
bool myTest = Math.Abs(tStatistic) >= tCriticalTenPercent;
//TTest tTest = new TTest(
// estimatedValue: regressionAccord.Slope, standardError: seSubB, degreesOfFreedom: degreesOfFreedom,
// hypothesizedValue: hypothesizedValue, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis
// );
//if (myTest != tTest.Significant)
//{
// Console.WriteLine($"nope. mystat - {tStatistic} accordstat - {tTest.Statistic} accordCritical - {tTest.CriticalValue}");
//}
AccordResult accordResult = new AccordResult()
{
IsSimpleSingleRegression = true,
CoolingBP = _pointPair.CoolingBalancePoint,
Intercept = regressionAccord.Intercept,
B4 = regressionAccord.Slope,
R2Accord = r2Accord
};
//if (tTest.Significant && accordResult.B4 > 0 && r2Accord >= 0.7500)
//{
// accordResults.Add(accordResult);
//}
if (
myTest &&
accordResult.B4 > 0
//&& r2Accord >= 0.7500
)
{
accordResults.Add(accordResult);
}
}
}
catch (Exception e)
{
Log.Debug($"AccID/UtilID/UnitID: {normalParamsKey.AccID}/{normalParamsKey.UtilID}/{normalParamsKey.UnitID} >> {e.Message} {e.StackTrace}");
}
}
AccordResult accordWinner = accordResults
.Where(s => s.Intercept >= 0)
.OrderByDescending(s => s.R2Accord).ToList().FirstOrDefault();
return(accordWinner);
}
