package analytics
The analytics
package contains classes, traits and objects for
analytics including clustering and prediction.
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-
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 equationy = 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
-
class
ANOVA
extends Predictor with Error
The
ANOVA
class supports one-way ANalysis Of VAriance (ANOVA).The
ANOVA
class supports one-way ANalysis Of VAriance (ANOVA). It is framed using General Linear Model 'GLM' notation and supports the use of one binary/categorical treatment variable 't'. This is done by introducing dummy variables 'd_j' to distinguish the treatment level. The problem is again to fit the parameter vector 'b' in the following equationy = b dot x + e = b_0 + b_1 * d_1 + b_1 * d_2 ... b_k * d_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
where 'x_pinv' is the pseudo-inverse.
- See also
psych.colorado.edu/~carey/Courses/PSYC5741/handouts/GLM%20Theory.pdf
-
class
ARMA
extends Predictor with Error
The
ARMA
class provide basic time series analysis capabilities for Auto- Regressive 'AR' and Moving Average 'MA' models.The
ARMA
class provide basic time series analysis capabilities for Auto- Regressive 'AR' and Moving Average 'MA' models. In an 'ARMA(p, q)' model, 'p' and 'q' refer to the order of the Auto-Regressive and Moving Average components of the model.ARMA
models are often used for forecasting. -
class
CanCorrelation
extends Reducer with Error
The
CanCorrelation
class performs Canonical Correlation Analysis 'CCA' on two random vectors.The
CanCorrelation
class performs Canonical Correlation Analysis 'CCA' on two random vectors. Samples for the first one are stored in the 'x' data matrix and samples for the second are stored in the 'y' data matrix. Find vectors a and b that maximize the correlation between x * a and y * b.max {rho (x * a, y * b)}
Additional vectors orthogonal to a and b can also be found.
-
trait
Clusterer
extends AnyRef
The
Clusterer
trait provides a common framework for several clustering algorithms. -
class
ExpRegression
extends Predictor with Error
The
ExpRegression
class supports exponential regression.The
ExpRegression
class supports exponential regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the exponential regression equationlog (mu (x)) = b dot x = b_0 + b_1 * x_1 + ... b_k * x_k
- See also
www.stat.uni-muenchen.de/~leiten/Lehre/Material/GLM_0708/chapterGLM.pdf
-
trait
GLM
extends AnyRef
A General Linear Model 'GLM' can be developed using the
GLM
trait and object (see below).A General Linear Model 'GLM' can be developed using the
GLM
trait and object (see below). The implementation currently supports univariate models with multivariate models (where each response is a vector) planned for the future. It provides factory methods for the following special types of GLMs:SimpleRegression
- simple linear regression,Regression
- multiple linear regression using Ordinary Least Squares 'OLS'Regression_WLS
- multiple linear regression using Weighted Least Squares 'WLS'RidgeRegression
- robust multiple linear regression,TranRegression
- transformed (e.g., log) multiple linear regression,PolyRegression
- polynomial regression,TrigRegression
- trigonometric regressionResponseSurface
- response surface regression,ANOVA
- GLM form of ANalysis Of VAriance,ANCOVA
- GLM form of ANalysis of COVAriance. -
class
HierClustering
extends Clusterer with Error
Cluster several vectors/points using hierarchical clustering.
Cluster several vectors/points using hierarchical clustering. Start with each point forming its own cluster and merge clusters until there are only 'k'.
-
class
KMeansClustering
extends Clusterer with Error
The
KMeansClustering
class cluster several vectors/points using k-means clustering.The
KMeansClustering
class cluster several vectors/points using k-means clustering. Either (1) randomly assign points to 'k' clusters or (2) randomly pick 'k' points as initial centroids (technique (1) to work better and is the primary technique). Iteratively, reassign each point to the cluster containing the closest centroid. Stop when there are no changes to the clusters. -
class
KalmanFilter
extends AnyRef
The
KalmanFilter
class is used to fit state-space models.The
KalmanFilter
class is used to fit state-space models.- See also
en.wikipedia.org/wiki/Kalman_filter FIX: needs more thorough testing
-
class
MarkovClustering
extends Clusterer with Error
The
MarkovClustering
class implements a Markov Clustering Algorithm 'MCL' and is used to cluster nodes in a graph.The
MarkovClustering
class implements a Markov Clustering Algorithm 'MCL' and is used to cluster nodes in a graph. The graph is represented as an edge-weighted adjacency matrix (a non-zero cell indicates nodes i and j are connected).The primary constructor takes either a graph (adjacency matrix) or a Markov transition matrix as input. If a graph is passed in, the normalize method must be called to convert it into a Markov transition matrix. Before normalizing, it may be helpful to add self loops to the graph. The matrix (graph or transition) may be either dense or sparse. See the
MarkovClusteringTest
object at the bottom of the file for examples. -
class
NMFactorization
extends AnyRef
The
NMFactorization
class factors a matrix 'v' into two non negative matrices 'w' and 'h' such that 'v = wh' approximately.The
NMFactorization
class factors a matrix 'v' into two non negative matrices 'w' and 'h' such that 'v = wh' approximately.- See also
en.wikipedia.org/wiki/Non-negative_matrix_factorization
-
class
NeuralNet
extends Predictor with Error
The
NeuralNet
class supports basic 3-layer (input, hidden and output) Neural Networks.The
NeuralNet
class supports basic 3-layer (input, hidden and output) Neural Networks. Given several input and output vectors (training data), fit the weights connecting the layers, so that for a new input vector 'zi', the net can predict the output vector 'zo' ('zh' is the intermediate value at the hidden layer), i.e.,zi --> zh = f (w * zi) --> zo = g (v * zh)
Note, w_0 and v_0 are treated as biases, so zi_0 and zh_0 must be 1.0.
-
class
NonLinRegression
extends Predictor with Error
The
NonLinRegression
class supports non-linear regression.The
NonLinRegression
class supports non-linear regression. In this case, 'x' can be multi-dimensional '[1, x1, ... xk]' and the function 'f' is non-linear in the parameters 'b'. Fit the parameter vector 'b' in the regression equationy = f(x, b) + 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' by using Non-linear Programming to minimize Sum of Squares Error 'SSE'.
- See also
www.bsos.umd.edu/socy/alan/stats/socy602_handouts/kut86916_ch13.pdf
-
class
Perceptron
extends Predictor with Error
The
Perceptron
class supports single-valued 2-layer (input and output) Neural-Networks.The
Perceptron
class supports single-valued 2-layer (input and output) Neural-Networks. Given several input vectors and output values (training data), fit the weights 'w' connecting the layers, so that for a new input vector 'zi', the net can predict the output value 'zo', i.e., 'zi --> zo = f (w dot zi)'. Note, w0 is treated as the bias, so x0 must be 1.0. -
class
PoissonRegression
extends Predictor with Error
The
PoissonRegression
class supports Poisson regression.The
PoissonRegression
class supports Poisson regression. In this case, x' may be multi-dimensional '[1, x_1, ... x_k]'. Fit the parameter vector 'b' in the Poisson regression equationlog (mu(x)) = b dot x = b_0 + b_1 * x_1 + ... b_k * x_k
where 'e' represents the residuals (the part not explained by the model) and 'y' is now integer valued.
- See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
-
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 equationy = 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
-
trait
Predictor
extends AnyRef
The
Predictor
trait provides a common framework for several predictors.The
Predictor
trait provides a common framework for several predictors. A predictor is for unbounded responses (real or integer). When the number of distinct responses is bounded by some integer 'k', a classifier should be used. -
class
PrincipalComponents
extends Reducer with Error
The
PrincipalComponents
class performs the Principal Component Analysis 'PCA' on data matrix 'x'.The
PrincipalComponents
class performs the Principal Component Analysis 'PCA' on data matrix 'x'. It can be used to reduce the dimensionality of the data. First find the Principal Components 'PC's by calling 'findPCs' and then call 'reduce' to reduce the data (i.e., reduce matrix 'x' to a lower dimensionality matrix). -
class
QuadraticFit
extends AnyRef
The
QuadraticFit
class uses multiple regression to fit a quadratic surface to the function 'f'.The
QuadraticFit
class uses multiple regression to fit a quadratic surface to the function 'f'. This is useful when computing 'f' is costly, for example in simulation optimization. The fit is over a multi-dimensional grid and can be used for interpolation and limited extrapolation. -
class
RandomGraph
extends AnyRef
The
RandomGraph
class generates random undirected graphs with clusters (as adjacency matrices). -
trait
Reducer
extends AnyRef
The
Reducer
trait provides a common framework for several data reduction algorithms. -
class
Regression
[MatT <: MatriD, VecT <: VectoD] extends Predictor with Error
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 equationy = 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:
'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)
- See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
-
class
Regression_WLS
extends Predictor with Error
The
Regression_WLS
class supports weighted multiple linear regression.The
Regression_WLS
class supports weighted multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the regression equationy = 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 Weighted 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)
- See also
www.markirwin.net/stat149/Lecture/Lecture3.pdf
-
class
ResponseSurface
extends Predictor with Error
The
ResponseSurface
class uses multiple regression to fit a quadratic/cubic surface to the data.The
ResponseSurface
class uses multiple regression to fit a quadratic/cubic surface to the data. For example in 2D, the quadratic regression equation isy = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_0*x_1, x_12] + e
- See also
scalation.metamodel.QuadraticFit
-
class
RidgeRegression
extends Predictor with Error
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 equationy = 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:
'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)
- See also
statweb.stanford.edu/~tibs/ElemStatLearn/
-
class
SimpleRegression
extends Predictor with Error
The
SimpleRegression
class supports simple linear regression.The
SimpleRegression
class supports simple linear regression. In this case, the vector 'x' consists of the constant one and a single variable 'x_1', i.e., (1, x_1). Fit the parameter vector 'b' in the regression equationy = b dot x + e = (b_0, b_1) dot (1, x_1) + e = b_0 + b_1 * x_1 + e
where 'e' represents the residuals (the part not explained by the model).
- class SimpleTest [VecT <: VectoD] extends AnyRef
-
class
TranRegression
extends Predictor with Error
The
TranRegression
class supports transformed multiple linear regression.The
TranRegression
class supports transformed multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the transformed regression equationtransform (y) = b dot x + e = b_0 + b_1 * x_1 + b_2 * x_2 ... b_k * x_k + e
where 'e' represents the residuals (the part not explained by the model) and 'transform' is the function (defaults to log) used to transform the response vector 'y'. Common transforms: log (y), sqrt (y) when y > 0 More generally, a Box-Cox Transformation may be applied.
- See also
www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.469.7176&rep=rep1&type=pdf Use Least-Squares (minimizing the residuals) to fit the parameter vector b = x_pinv * y where 'x_pinv' is the pseudo-inverse. Caveat: this class does not provide transformations on columns of matrix 'x'.
-
class
TrigRegression
extends Predictor with Error
The
TrigRegression
class supports trigonometric regression.The
TrigRegression
class supports trigonometric regression. In this case, 't' is expanded to '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'. Fit the parameter vector 'b' in the regression equationy = b dot x + e = b_0 + b_1 sin (wt) + b_2 cos (wt) + b_3 sin (2wt) + b_4 cos (2wt) + ... + 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
link.springer.com/article/10.1023%2FA%3A1022436007242#page-1
Value Members
-
val
BASE_DIR: String
The relative path for base directory
-
object
ANCOVATest
extends App
The
ANCOVATest
object tests theANCOVA
class using the following regression equation.The
ANCOVATest
object tests theANCOVA
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
-
object
ANOVATest
extends App
The
ANOVATest
object tests theANOVA
class using the following regression equation.The
ANOVATest
object tests theANOVA
class using the following regression equation.y = b dot x = b_0 + b_1*d_1 + b_2*d_2
-
object
ARMATest
extends App
The
ARMATest
object is used to test theARMA
class. -
object
Centering
The
Centering
object is used to center the input matrix 'x'.The
Centering
object is used to center the input matrix 'x'. This is done by subtracting the column means from each value. -
object
ExpRegressionTest
extends App
The
ExpRegressionTest
object testsExpRegression
class using the following exponential regression problem. -
object
ExpRegressionTest2
extends App
The
ExpRegressionTest2
object has a basic test for theExpRegression
class. -
object
GLM
extends GLM
The
GLM
object makes theGLM
trait's methods directly available.The
GLM
object makes theGLM
trait's methods directly available. This approach (using traits and objects) allows the methods to also be inherited. -
object
GLMTest
extends App
The
GLMTest
object tests theGLM
object using the following regression equation.The
GLMTest
object tests theGLM
object 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
-
object
GZLM
extends GLM
A Generalized Linear Model 'GZLM' can be developed using the
GZLM
object.A Generalized Linear Model 'GZLM' can be developed using the
GZLM
object. It provides factory methods for General Linear Models 'GLM' via inheritance and for proper Generalized Linear Models:LogisticRegression
- logistic regression,PoissonRegression
- Poisson regression,ExpRegression
- Exponential regression, -
object
GZLMTest
extends App
The
GZLMTest
object tests theGZLM
object using the following regression equation.The
GZLMTest
object tests theGZLM
object 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
-
object
HierClusteringTest
extends App
The
HierClusteringTest
object is used to test theHierClustering
class. -
object
KMeansClusteringTest
extends App
The
KMeansClusteringTest
object is used to test theKMeansClustering
class.The
KMeansClusteringTest
object is used to test theKMeansClustering
class. > run-main scalation.analytics.KMeansClusteringTest -
object
KalmanFilterTest
extends App
The
KalmanFilterTest
object is used to test theKalmanFilter
class.The
KalmanFilterTest
object is used to test theKalmanFilter
class.- See also
en.wikipedia.org/wiki/Kalman_filter > run-main scalation.analytics.KalmanFilterTest
-
object
LogisticFunction
The
LogisticFunction
object contains Activation functions. -
object
MarkovClusteringTest
extends App
The
MarkovClusteringTest
object is used to test theMarkovClustering
class.The
MarkovClusteringTest
object is used to test theMarkovClustering
class.- See also
www.cs.ucsb.edu/~xyan/classes/CS595D-2009winter/MCL_Presentation2.pdf
-
object
MarkovClusteringTest2
extends App
The
MarkovClusteringTest2
object is used to test theMarkovClustering
class. -
object
NMFactorizationTest
extends App
The
NMFactorizationTest
object to testNMFactorizationTest
class. -
object
NeuralNetTest
extends App
The
NeuralNetTest
object is used to test theNeuralNet
class.The
NeuralNetTest
object is used to test theNeuralNet
class. For this test, the initial weights are used for used for prediction. -
object
NeuralNetTest2
extends App
The
NeuralNetTest2
object is used to test theNeuralNet
class.The
NeuralNetTest2
object is used to test theNeuralNet
class. For this test, training data is used to fit the weights before using them for prediction.- See also
http://www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf
-
object
NonLinRegressionTest
extends App
The
NonLinRegressionTest
object tests theNonLinRegression
class: y = f(x; b) = b0 + exp (b1 * x0).The
NonLinRegressionTest
object tests theNonLinRegression
class: y = f(x; b) = b0 + exp (b1 * x0).- See also
www.bsos.umd.edu/socy/alan/stats/socy602_handouts/kut86916_ch13.pdf Answers: sse = 49.45929986243339 fit = (VectorD (58.606566327280426, -0.03958645286504356), 0.9874574894685292) predict (VectorD (50.0)) = 8.09724678182599 FIX: check this example
-
object
PerceptronTest
extends App
The
PerceptronTest
object is used to test thePerceptron
class.The
PerceptronTest
object is used to test thePerceptron
class. For this test, the initial weights are used for used for prediction. -
object
PerceptronTest2
extends App
The
PerceptronTest2
object is used to test thePerceptron
class.The
PerceptronTest2
object is used to test thePerceptron
class. For this test, training data is used to fit the weights before using them for prediction.- See also
http://www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf
-
object
PoissonRegressionTest
extends App
The
PoissonRegression
object tests thePoissonRegression
class.The
PoissonRegression
object tests thePoissonRegression
class.- See also
http://www.cookbook-r.com/Statistical_analysis/Logistic_regression/ Answer: b = (-8.8331, 0.4304), n_dev = 43.860, r_dev = 25.533, aci = 29.533, pseudo_rSq = 0.4178
-
object
PoissonRegressionTest2
extends App
The
PoissonRegressionTest2
object tests thePoissonRegression
class.The
PoissonRegressionTest2
object tests thePoissonRegression
class.- See also
www.stat.wisc.edu/~mchung/teaching/.../GLM.logistic.Rpackage.pdf
statmaster.sdu.dk/courses/st111/module03/index.html
-
object
PolyRegressionTest
extends App
The
PolyRegressionTest
object testsPolyRegression
class using the following regression equation.The
PolyRegressionTest
object testsPolyRegression
class using the following regression equation.y = b dot x = b_0 + b_1*t + b_2*t^2.
-
object
PrincipalComponentsTest
extends App
The
PrincipalComponentsTest
object is used to test thePrincipalComponents
class.The
PrincipalComponentsTest
object is used to test thePrincipalComponents
class.- See also
www.ce.yildiz.edu.tr/personal/songul/file/1097/principal_components.pdf > run-main scalation.analytics.PrincipalComponentsTest
-
object
Probability
extends Error
The
Probability
object provides methods for operating on univariate and bivariate probability distributions of discrete random variables 'X' and 'Y'.The
Probability
object provides methods for operating on univariate and bivariate probability distributions of discrete random variables 'X' and 'Y'. A probability distribution is specified by its probability mass functions (pmf) stored either as a "probability vector" for a univariate distribution or a "probability matrix" for a bivariate distribution.joint probability matrix: pxy(i, j) = P(X = x_i, Y = y_j) marginal probability vector: px(i) = P(X = x_i) conditional probability matrix: px_y(i, j) = P(X = x_i|Y = y_j)
In addition to computing joint, marginal and conditional probabilities, methods for computing entropy and mutual information are also provided. Entropy provides a measure of disorder or randomness. If there is little randomness, entropy will close to 0, while when randomness is high, entropy will be close to, e.g., 'log2 (px.dim)'. Mutual information provides a robust measure of dependency between random variables (contrast with correlation).
- See also
scalation.stat.StatVector
-
object
ProbabilityTest
extends App
The
ProbabilityTest
object is used to test theProbability
object. -
object
ProbabilityTest2
extends App
The
ProbabilityTest2
provides upper bound for 'entropy' and 'entropy_k'. -
object
QuadraticFitTest
extends App
The
QuadraticFitTest
object is used to test theQuadraticFit
class for a two dimensional case. -
object
QuadraticFitTest2
extends App
The
QuadraticFitTest2
object is used to test theQuadraticFit
class for a three dimensional case. -
object
QuadraticFitTest3
extends App
The
QuadraticFitTest3
object is used to test theQuadraticFit
class for a three dimensional case with noise. -
object
RandomGraphTest
extends App
The
RandomGraphTest
object is used to test theRandomGraph
class. -
object
RegTechnique
extends Enumeration
The
RegTechnique
object defines the implementation techniques available. -
object
RegressionTest
extends App
The
RegressionTest
object testsRegression
class using the following regression equation.The
RegressionTest
object testsRegression
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 > run-main scalation.analytics.RegressionTest
-
object
RegressionTest2
extends App
The
RegressionTest2
object testsRegression
class using the following regression equation.The
RegressionTest2
object testsRegression
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. > run-main scalation.analytics.RegressionTest2
-
object
RegressionTest3
extends App
The
RegressionTest3
object tests the multi-collinearity method in theRegression
class using the following regression equation.The
RegressionTest3
object tests the multi-collinearity method in theRegression
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 > run-main scalation.analytics.RegressionTest3
online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html
-
object
Regression_WLSTest
extends App
The
Regression_WLSTest
object testsRegression_WLS
class using the following regression equation.The
Regression_WLSTest
object testsRegression_WLS
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
-
object
ResponseSurfaceTest
extends App
The
ResponseSurfaceTest
object is used to test theResponseSurface
class. -
object
RidgeRegressionTest
extends App
The
RidgeRegressionTest
object testsRidgeRegression
class using the following regression equation.The
RidgeRegressionTest
object testsRidgeRegression
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
-
object
RidgeRegressionTest2
extends App
The
RidgeRegressionTest2
object testsRidgeRegression
class using the following regression equation.The
RidgeRegressionTest2
object testsRidgeRegression
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.
-
object
RidgeRegressionTest3
extends App
The
RidgeRegressionTest3
object tests the multi-collinearity method in theRidgeRegression
class using the following regression equation.The
RidgeRegressionTest3
object tests the multi-collinearity method in theRidgeRegression
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
-
object
SimpleRegressionTest
extends App
The
SimpleRegressionTest
object to testSimpleRegression
class: 'y = b dot x = (b_0, b_1) dot (1, x_1)'.The
SimpleRegressionTest
object to testSimpleRegression
class: 'y = b dot x = (b_0, b_1) dot (1, x_1)'.- See also
http://www.analyzemath.com/statistics/linear_regression.html
-
object
SimpleRegressionTest2
extends App
The
SimpleRegressionTest2
object to testSimpleRegression
class:The
SimpleRegressionTest2
object to testSimpleRegression
class:y = b dot x = b_0 + b_1*x_1.
- See also
http://mathbits.com/mathbits/tisection/Statistics2/linear.htm
- object SimpleTest extends App
-
object
TranRegressionTest
extends App
The
TranRegressionTest
object testsTranRegression
class using the following regression equation.The
TranRegressionTest
object testsTranRegression
class using the following regression equation.log (y) = b dot x = b_0 + b_1*x_1 + b_2*x_2.
> run-main scalation.analytics.TranRegressionTest
-
object
TrigRegressionTest
extends App
The
TrigRegressionTest
object testsTrigRegression
class using the following regression equation.The
TrigRegressionTest
object testsTrigRegression
class using the following regression equation.y = b dot x = b_0 + b_1*t + b_2*t^2.