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ChowTest
Returns the pvalue of the regression stability test (i.e. whether the coefficients in two linear regressions on different data sets are equal).
Syntax
Y1
is the response or the dependent variable data array of the first data set (one dimensional array of cells (e.g. rows or columns)).
X1
is the independent variables data matrix of the first data set, such that each column represents one variable.
Y2
is the response or the dependent variable data array of the second data set (one dimensional array of cells (e.g. rows or columns)).
X2
is the independent variables data matrix of the second data set, such that each column represents one variable.
Mask
is the boolean array to select a subset of the explanatory variables in the model. If missing, all variables in X are included.
Intercept
is the regression constant or the intercept value (e.g. zero). If missing, an intercept is not fixed and will be computed from the data set.
Return_type
is a switch to select the return output (1 = pvalue (default), 2 = test statistics, 3 = standardized residuals).
Method  Description 

1  pvalue 
2  test statistics 
Remarks
 The data sets may include missing values.
 Each column in the explanatory (predictor) matrix corresponds to a separate variable.
 Each row in the explanatory matrix and corresponding dependent vector correspond to one observation.
 Observations (i.e. row) with missing values in X or Y are removed.
 Number of observation of each data set must be larger than the number of explanatory variables.
 In principle, the Chow test constructs the following regression models:
 Model 1 (Data set 1):

Model 2 (Data set 2):

Model 3 (Data sets 1 + 2):
 Model 1 (Data set 1):

The Chow test hypothesis:
Where:
 is the null hypothesis^{i}.
 is the alternate hypothesis.
 is the ith coefficient in the jth regression model (j=1,2,3).
 The Chow statistics are defined as follows:
Where:
 is the sum of the squared residuals.
 is the number of explanatory variables.
 is the number of nonmissing observations in the first data set.
 is the number of nonmissing observations in the second data set.
 The Chow test statistics follow an Fdistribution with , and degrees of freedom.
 The ChowTest function is available starting with version 1.60 APACHE.
Examples
References
 Chow, Gregory C. (1960). "Tests of Equality Between Sets of Coefficients in Two Linear Regressions". Econometrica 28 (3): 591â€“605.