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package par

The par package contains classes, traits and objects for parallel analytics including clustering and prediction.

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  1. class ANCOVA extends Predictor with Error

    The ANCOVA class supports ANalysis of COVAriance (ANCOVA).

    The ANCOVA class supports ANalysis of COVAriance (ANCOVA). It allows the addition of a categorical treatment variable 't' into a multiple linear regression. This is done by introducing dummy variables 'dj' to distinguish the treatment level. The problem is again to fit the parameter vector 'b' in the augmented regression equation

    y = b dot x + e = b0 + b_1 * x_1 + b_2 * x_2 + ... b_k * x_k + b_k+1 * d_1 + b_k+2 * d_2 + ... b_k+l * d_l + e

    where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

    b = x_pinv * y

    where 'x_pinv' is the pseudo-inverse.

    See also

    see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

  2. class PolyRegression extends Predictor with Error

    The PolyRegression class supports polynomial regression.

    The PolyRegression class supports polynomial regression. In this case, 't' is expanded to [1, t, t2 ... tk]. Fit the parameter vector 'b' in the regression equation

    y = b dot x + e = b_0 + b_1 * t + b_2 * t2 ... b_k * tk + e

    where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

    b = x_pinv * y

    where 'x_pinv' is the pseudo-inverse.

    See also

    www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx

  3. class Regression extends PredictorMat

    The Regression class supports multiple linear regression.

    The Regression class supports multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the regression equation

    y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e

    where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

    b = x_pinv * y [ alternative: b = solve (y) ]

    where 'x_pinv' is the pseudo-inverse. Three techniques are provided:

    'Fac_QR' // QR Factorization: slower, more stable (default) 'Fac_Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

    This version uses parallel processing to speed up execution.

    See also

    see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

  4. class RidgeRegression extends PredictorMat

    The RidgeRegression class supports multiple linear regression.

    The RidgeRegression class supports multiple linear regression. In this case, 'x' is multi-dimensional [x_1, ... x_k]. Both the input matrix 'x' and the response vector 'y' are centered (zero mean). Fit the parameter vector 'b' in the regression equation

    y = b dot x + e = b_1 * x_1 + ... b_k * x_k + e

    where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

    b = x_pinv * y [ alternative: b = solve (y) ]

    where 'x_pinv' is the pseudo-inverse. Three techniques are provided:

    'Fac_QR' // QR Factorization: slower, more stable (default) 'Fac_Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

    This version uses parallel processing to speed up execution.

    See also

    statweb.stanford.edu/~tibs/ElemStatLearn/

Value Members

  1. val BASE_DIR: String

    The relative path for base directory

  2. object ANCOVATest extends App

    The ANCOVATest object tests the ANCOVA class using the following regression equation.

    The ANCOVATest object tests the ANCOVA class using the following regression equation.

    y = b dot x = b_0 + b_1*x_1 + b_2*x_2 + b_3*d_1 + b_4*d_2

  3. object PolyRegressionTest extends App

    The PolyRegressionTest object tests PolyRegression class using the following regression equation.

    The PolyRegressionTest object tests PolyRegression class using the following regression equation.

    y = b dot x = b_0 + b_1*t + b_2*t^2.

  4. object RegressionTest extends App

    The RegressionTest object tests Regression class using the following regression equation.

    The RegressionTest object tests Regression class using the following regression equation.

    y = b dot x = b_0 + b_1*x_1 + b_2*x_2.

    Test regression and backward elimination.

    See also

    http://statmaster.sdu.dk/courses/st111/module03/index.html

  5. object RegressionTest2 extends App

    The RegressionTest2 object tests Regression class using the following regression equation.

    The RegressionTest2 object tests Regression class using the following regression equation.

    y = b dot x = b_0 + b_1*x1 + b_2*x_2.

    Test regression using QR Decomposition and Gaussian Elimination for computing the pseudo-inverse.

  6. object RegressionTest3 extends App

    The RegressionTest3 object tests the multi-collinearity method in the Regression class using the following regression equation.

    The RegressionTest3 object tests the multi-collinearity method in the Regression class using the following regression equation.

    y = b dot x = b_0 + b_1*x_1 + b_2*x_2 + b_3*x_3 + b_4 * x_4

    See also

    online.stat.psu.edu/online/development/stat501/data/bloodpress.txt

    online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html

  7. object RidgeRegression

    The RidgeRegression companion object is used to center the input matrix 'x'.

    The RidgeRegression companion object is used to center the input matrix 'x'. This is done by subtracting the column means from each value.

  8. object RidgeRegressionTest extends App

    The RidgeRegressionTest object tests RidgeRegression class using the following regression equation.

    The RidgeRegressionTest object tests RidgeRegression class using the following regression equation.

    y = b dot x = b_1*x_1 + b_2*x_2.

    Test regression and backward elimination.

    See also

    http://statmaster.sdu.dk/courses/st111/module03/index.html

  9. object RidgeRegressionTest2 extends App

    The RidgeRegressionTest2 object tests RidgeRegression class using the following regression equation.

    The RidgeRegressionTest2 object tests RidgeRegression class using the following regression equation.

    y = b dot x = b_1*x1 + b_2*x_2.

    Test regression using QR Decomposition and Gaussian Elimination for computing the pseudo-inverse.

  10. object RidgeRegressionTest3 extends App

    The RidgeRegressionTest3 object tests the multi-collinearity method in the RidgeRegression class using the following regression equation.

    The RidgeRegressionTest3 object tests the multi-collinearity method in the RidgeRegression class using the following regression equation.

    y = b dot x = b_1*x_1 + b_2*x_2 + b_3*x_3 + b_4 * x_4

    See also

    online.stat.psu.edu/online/development/stat501/data/bloodpress.txt

    online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html

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