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CollinearityTest
Returns the pvalue of the multicollinearity test (i.e. whether one variable can be linearly predicted from the others with a nontrivial degree of accuracy).
Syntax
X
is the independent variables data matrix, such that each column represents one variable.
Mask
is the boolean array to select a subset of the input variables in X. If missing, all variables in X are included.
Method
is the statistics to compute (1 = Condition Number (default), 2 = VIF, 3 = Determinant, 4 = Eigenvalues).
Method  Description 

1  Condition Number (Kappa) 
2  Variance Inflation Factor (VIF) 
Column Index
is a switch to designate the explanatory variable to examine (not required for condition number).
Remarks
 The sample data may include missing values.
 Each column in the input matrix corresponds to a separate variable.
 Each row in the input matrix corresponds to an observation.
 Observations (i.e. row) with missing values are removed.
 In the variance inflation factor (VIF) method, a series of regressions models are constructed, where one variable is the dependent variable against the remaining predictors.

Where:
 is the coefficient of determination of a regression of explanator on all the other explanators.
 A tolerance of less than 0.20 or 0.10 and/or a VIF of 5 or 10 and above indicates a multicollinearity problem.
 The condition number () test is a standard measure of illconditioning in a matrix; It will indicate that the inversion of the matrix is numerically unstable with finiteprecision numbers (standard computer floats and doubles).

Where:
 is the maximum eigenvalue.
 is the minimum eigenvalue.
 As a rule of thumb, a condition number () greater or equal to 30 indicates a severe multicollinearity problem.
 The CollinearityTest function is available starting with version 1.60 APACHE.
Examples
References
 Farrar Donald E. and Glauber, Robert R (1967). "Multicollinearity in Regression Analysis: The Problem Revisited". The Review of Economics and Statistics 49(1):92107.