NDK_MLR_PARAM

int __stdcall NDK_MLR_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 OLS regression coefficients values.

Returns
status code of the operation
Return values
NDK_SUCCESS  Operation successful
NDK_FAILED  Operation unsuccessful. See Macros for full list.
Parameters
[in] X is the independent (explanatory) variables data matrix, such that each column represents one variable.
[in] nXSize is the number of observations (rows) in X.
[in] nXVars is the number of independent (explanatory) variables (columns) in X.
[in] mask is the boolean array to choose the explanatory variables in the model. If missing, all variables in X are included.
[in] nMaskLen is the number of elements in the "mask."
[in] Y is the response or the dependent variable data array (one dimensional array of cells).
[in] nYSize is the number of observations in Y.
[in] intercept is the constant or intercept value to fix (e.g. zero). If missing (i.e. NaN), an intercept will not be fixed and is computed normally.
[in] alpha is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
[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)):
  1. Value (mean)
  2. Std error
  3. Test score
  4. P-value
  5. Upper limit of the confidence interval
  6. Lower limit of the confidence interval
[in] nParamIndex is a switch to designate the target parameter (0=intercept (default), 1=first variable, 2=2nd variable, etc.).
[out] retVal is the computed statistics of the regression coefficient.
Remarks
  1. \[ \mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\varepsilon \] \[\hat{\boldsymbol\beta} = (\mathbf{X}^{\rm T}\mathbf{X})^{-1} \mathbf{X}^{\rm T}\mathbf{y} = \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i \mathbf{x}^{\rm T}_i \,\big)^{-1} \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i y_i \,\big)\] Where:
    • \(\hat{\boldsymbol\beta}\) is the estimated regression coefficients.
  2. The sample data may include missing values.
  3. Each column in the input matrix corresponds to a separate variable.
  4. Each row in the input matrix corresponds to an observation.
  5. Observations (i.e. row) with missing values in X or Y are removed.
  6. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
  7. The MLR_PARAM function is available starting with version 1.60 APACHE.
Requirements
Header SFSDK.H
Library SFSDK.LIB
DLL SFSDK.DLL
Namespace:  NumXLAPI
Class:  SFSDK
Scope:  Public
Lifetime:  Static
int NDK_MLR_PARAM ( double[]  pXData,
double[]  nXSize,
UIntPtr  nXVars,
byte[]  mask,
UIntPtr  nMaskLen,
double[]  pYData,
UIntPtr  nYSize,
double  intercept,
double  alpha,
short  nRetType,
short  ParamIndex,
ref double  retVal 
)

Calculates the OLS regression coefficients values.

Return Value

a value from NDK_RETCODE enumeration for the status of the call. 

NDK_SUCCESS  operation successful
Error  Error Code
Parameters
[in] pXData is the independent (explanatory) variables data matrix, such that each column represents one variable.
[in] nXSize is the number of observations (rows) in pXData.
[in] nXVars is the number of independent (explanatory) variables (columns) in pXData.
[in] mask is the boolean array to choose the explanatory variables in the model. If missing, all variables in pXData are included.
[in] nMaskLen is the number of elements in the "mask."
[in] pYData is the response or the dependent variable data array (one dimensional array of cells).
[in] nYSize is the number of observations in pYData.
[in] intercept is the constant or intercept value to fix (e.g. zero). If missing (i.e. NaN), an intercept will not be fixed and is computed normally.
[in] alpha is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
[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)):
  1. Value (mean)
  2. Std error
  3. Test score
  4. P-value
  5. Upper limit of the confidence interval
  6. Lower limit of the confidence interval
[in] nParamIndex is a switch to designate the target parameter (0=intercept (default), 1=first variable, 2=2nd variable, etc.).
[out] retVal is the computed statistics of the regression coefficient.
Remarks
  1. \[ \mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\varepsilon \] \[\hat{\boldsymbol\beta} = (\mathbf{X}^{\rm T}\mathbf{X})^{-1} \mathbf{X}^{\rm T}\mathbf{y} = \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i \mathbf{x}^{\rm T}_i \,\big)^{-1} \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i y_i \,\big)\] Where:
    • \(\hat{\boldsymbol\beta}\) is the estimated regression coefficients.
  2. The sample data may include missing values.
  3. Each column in the input matrix corresponds to a separate variable.
  4. Each row in the input matrix corresponds to an observation.
  5. Observations (i.e. row) with missing values in X or Y are removed.
  6. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
  7. The MLR_PARAM function is available starting with version 1.60 APACHE.
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI
Class SFSDK
Scope Public
Lifetime Static
Package NumXLAPI.DLL
Examples

	
References
* 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