Bactrim double strength, We are sometimes asked how to reproduce the various Excel Trendline types in NMath, including printing out the form of the equation and the R2 value (coefficient of determination). Excel offers these trend types:

• Linear


• Logarithmic


• Exponential


• Power


• Polynomial


• Moving Average

These can all be easily computed using NMath. Let's see how. First, let's start with a simple data series:

DoubleVector x = new DoubleVector(11, Bactrim children, 15, 18, 23, 26, bactrim over the counter, 31, 39, Bactrim ds 800 mg, 44, 54, 64, 74);

DoubleVector y = new DoubleVector(0.00476, bactrim for lice, 0.0105, 0.0207, Bactrim wikipedia, 0.0619, 0.337, 0.74, 1.7, bactrim pseudomonas, 2.45, 3.5, Bactrim urinary tract infections, 4.5, 5.09);

These data represent the evolution of an algal bloom in the Adriatic Sea. The x-values are time expressed in days, and the y-values are the size of the surface of the bloom in mm², bactrim ds tablet.

Linear

The Linear trendline fits a line, y = a*x + b, Bactrim ds package insert, to the data. This is easily computed using the LinearRegression class in NMath Stats, as shown in the following C# code:

bool addIntercept = true;

LinearRegression lr = new LinearRegression(new DoubleMatrix(x), y, uses for bactrim, addIntercept);

LinearRegressionAnova lrAnova = new LinearRegressionAnova(lr);

double a = lr.Parameters[0];

double b = lr.Parameters[1];

double r2 = lrAnova.RSquared;

Console.WriteLine("y = {0}x + {1}", a, How much does bactrim cost, b);

Console.WriteLine("r2 = {0}", r2);

Output

y = -1.63908651994092x + 0.0913403802489977

r2 = 0.967828167696715

Note that to compute the coefficient of determination (R2), we construct a LinearRegressionAnova object from the LinearRegression instance. This class tests overall model significance for regressions computed by LinearRegression, bactrim double strength.

Logarithmic

The Logarithmic trendline fits a line to ln(x), bactrim for sinus infection, y--that is, y = a*ln(x) + b. Uses of bactrim, Again, we can use the LinearRegression class for this:

DoubleVector logX = NMathFunctions.Log(x);

lr = new LinearRegression(new DoubleMatrix(logX), y, addIntercept);

a = lr.Parameters[0];

b = lr.Parameters[1];

r2 = new LinearRegressionAnova(lr).RSquared;

Console.WriteLine("y = {0}ln(x) + {1}", bactrim coverage, a, b);

Console.WriteLine("r2 = {0}", Bactrim to treat mrsa, r2);

Output:

y = -8.17805531083818ln(x) + 2.87283105614145

r2= 0.840393353070466

Exponential

The Exponential trendline fits the function y = a * e ^(b * x). This can also be computed using LinearRegression by fitting a line to x, ln(y). Taking the log of both sides of the function gives:

ln(y) = ln(a * e ^(b * x)) = ln(a) + bx

The following C# code does this:

DoubleVector logY = NMathFunctions.Log(y);

lr = new LinearRegression(new DoubleMatrix(x), bactrim warfarin, logY, addIntercept);

a = Math.Exp(lr.Parameters[0]);

b = lr.Parameters[1];

r2 = new LinearRegressionAnova(lr).RSquared;

Console.WriteLine("y = {0}e^{1}x", Bactrim staph, a, b);

Console.WriteLine("r2 = {0}", r2);

Output:

y = 0.00552689525130073e^0.112876522212724x

r2 = 0.812366433832176

Note that because the intercept of the fitted line is the natural log of the "a" parameter in the exponential function, we need to take the exponential of the found intercept (using Math.Exp) to recover the value of "a", bactrim ds 800.

Power

The Power trendline fits the function y = a * x^b Bactrim double strength, . This can be computed using LinearRegression by fitting a line to ln(x), ln(y). Bactrim ds for sinus infection, Taking the log of both sides of the equation gives:

ln(y) = ln(a * x^b) = ln(a) + b * ln(x)

lr = new LinearRegression(new DoubleMatrix(logX), logY, addIntercept);

lrAnova = new LinearRegressionAnova(lr);

a = Math.Exp(lr.Parameters[0]);

b = lr.Parameters[1];

r2 = new LinearRegressionAnova(lr).RSquared;

Console.WriteLine("y = {0}x^{1}", a, does bactrim interact with birth control, b);

Console.WriteLine("r2 = {0}", r2);

Output:

y = 2.46993343563889E-07x^4.11443630332377

r2 = 0.947447653331871

Again, Buy bactrim canadian, we recover the value of parameter "a" by taking the exponential of the found intercept.

Polynomial

NMath provides class PolynomialLeastSquares for fitting a polynomial of the specified degree to paired vectors of x- and y-values. For example, this code fits a cubic to our data:

int degree = 3;

PolynomialLeastSquares pls = new PolynomialLeastSquares(degree, buy cheap bactrim online, x, y);

// compute R2

DoubleVector predictions = pls.FittedPolynomial.Evaluate(x);

double regressionSumOfSquares = StatsFunctions.SumOfSquares(predictions - StatsFunctions.Mean(y));

double residualSumOfSquares = pls.LeastSquaresSolution.Residuals.TwoNormSquared();

r2 = regressionSumOfSquares / (regressionSumOfSquares + residualSumOfSquares);
Console.WriteLine("y = " + pls.FittedPolynomial);

Console.WriteLine("r2 = {0}", Bactrim online, r2);

Output:

y = -4.68278158094222E-05x^3 + 0.00640408381023593x^2 -

      0.1643720340709x + 1.12703300920657

r2 = 0.998634459376868

Note that PolynomialLeastSquares does not currently provide the R2 value, so in the code above we compute it directly.

Moving Average

Unlike the trendlines we've examined so far, a moving average does not fit a functional form to data, bactrim double strength. Rather, it filters data in order to smooth out noise, bactrim toxicity. NMath provides class MovingWindowFilter for this purpose.

Class MovingWindowFilter replaces data points with a linear combination of the data points immediately to the left and right of each point, Bactrim joint pain, based on a given set of coefficients to use in the linear combination. Static class methods are provided for generating coefficients to implement a moving average filter and a Savitzky-Golay smoothing filter.

For example, the following C# code filters the data using a window of width 3 (the "period" parameter in Excel):

int numberLeft = 1;

int numberRight = 1;

DoubleVector movingAvgCoefficents = MovingWindowFilter.MovingAverageCoefficients(numberLeft, numberRight);

MovingWindowFilter filter = new MovingWindowFilter(numberLeft, numberRight, movingAvgCoefficents);

DoubleVector yfiltered = filter.Filter(y, MovingWindowFilter.BoundaryOption.DoNotFilterBoundaryPoints);

Console.WriteLine("yfiltered = " + yfiltered);

Output:

yfiltered = [ 0.00476 0.0119866666666667 0.0310333333333333

              0.139866666666667 0.379633333333333 0.925666666666667 1.63

              2.55 3.48333333333333 4.36333333333333 5.09 ]

Advanced Curve Fitting

That covers the simple trendlines produced by Excel. For advanced curve fitting, NMath provides class OneVariableFunctionFitter which fits arbitrary one variable functions to a set of points. (You must supply at least as many data points to fit as your function has parameters.) In a future post, we'll take a look at this class. In the meantime, see this page for an example demonstrating the use of OneVariableFunctionFitter, including how to define your own function.

Ken.

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Tags: .NET exponential regression, .NET linear regression, .NET logarithmic regression, .NET moving average filter, .NET polynomial regression, .NET power regression, C# exponential regression, C# linear regression, C# logarithmic regression, C# moving average filter, C# polynomial regression, C# power regression

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