int __stdcall NDK_PCR_PARAM ( double **  X,
size_t  nXSize,
size_t  nXVars,
LPBYTE  mask,
size_t  nMaskLen,
double *  Y,
size_t  nYSize,
double  intercept,
double  alpha,
WORD  nRetType,
WORD  nParamIndex,
double *  retVal 

Calculates the regression coefficients values for a given input variable.

status code of the operation
Return values
NDK_SUCCESS  Operation successful
NDK_FAILED  Operation unsuccessful. See Macros for full list.
[in] X is the independent variables data matrix, such that each column represents one variable
[in] nXSize is the number of observations (i.e. rows) in X
[in] nXVars is the number of variables (i.e. columns) in X
[in] mask is the boolean array to select a subset of the input variables in X. If missing (i.e. NULL), all variables in X are included.
[in] nMaskLen is the number of elements in mask
[in] Y is the response or the dependent variable data array (one dimensional array)
[in] nYSize is the number of elements in Y
[in] intercept is the constant or the intercept value to fix (e.g. zero). If missing (NaN), an intercept will not be fixed and is computed normally
[in] alpha is the statistical significance of the test (i.e. alpha)
[in] nRetType is a switch to select the return output:
  1. Value (default),
  2. Std. Error
  3. t-stat
  4. P-Value
  5. Upper Limit (CI)
  6. Lower Limit (CI))
[in] nParamIndex is a switch to designate the target parameter (0 = intercept (default), 1 = first variable, 2 = 2nd variable, etc.).
[out] retVal is the calculated parameter value or statistics.
  1. The underlying model is described here.
  2. \[\mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\varepsilon\] \[\hat{\boldsymbol\beta} = (\mathbf{X}^{\rm T}\mathbf{X})^{-1} \mathbf{X}^{\rm T}\mathbf{y} = \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i \mathbf{x}^{\rm T}_i \,\big)^{-1} \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i y_i \,\big).\] Where:
  • \(\hat{\boldsymbol\beta}\) is the estimated regression coefficients.
  • 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 in X or Y are removed.
  • The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
  • The MLR_PARAM function is available starting with version 1.60 APACHE.
Header SFSDK.H
* Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
* Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848