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

Returns an array of cells for the i-th principal component (or residuals).

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] nRetType is a switch to select a fitness measure (1 = R-Square (default), 2 = Adjusted R Square, 3 = RMSE, 4 = LLF, 5 = AIC, 6 = BIC/SIC ).
  1. R-square (coefficient of determination)
  2. Adjusted R-square
  3. Regression Error (RMSE)
  4. Log-likelihood (LLF)
  5. Akaike information criterion (AIC)
  6. Schwartz/Bayesian information criterion (SIC/BIC)
[out] retVal is the calculated goodness of fit measure
  1. The underlying model is described here.
  2. The coefficient of determination, denoted \(R^2\), provides a measure of how well observed outcomes are replicated by the model. \[R^2 = \frac{\mathrm{SSR}} {\mathrm{SST}} = 1 - \frac{\mathrm{SSE}} {\mathrm{SST}}\]
  3. The adjusted R-square (denoted \(\bar R^2\)) is an attempt to take account of the phenomenon of the \(R^2\) automatically and spuriously increasing when extra explanatory variables are added to the model. The \(\bar R^2\) adjusts for the number of explanatory terms in a model relative to the number of data points. \[\bar R^2 = {1-(1-R^{2}){N-1 \over N-p-1}} = {R^{2}-(1-R^{2}){p \over N-p-1}} = 1 - \frac{\mathrm{SSE}/(N-p-1)}{\mathrm{SST}/(N-1)}\] Where:
    • \(p\) is the number of explanatory variables in the model.
    • \(N\) is the number of observations in the sample.
  4. The regression error is defined as the square root for the mean square error (RMSE): \[\mathrm{RMSE} = \sqrt{\frac{SSE}{N-p-1}}\]
  5. The log likelihood of the regression is given as: \[\mathrm{LLF}=-\frac{N}{2}\left(1+\ln(2\pi)+\ln\left(\frac{\mathrm{SSR}}{N} \right ) \right )\] The Akaike and Schwarz/Bayesian information criterion are given as: \[\mathrm{AIC}=-\frac{2\mathrm{LLF}}{N}+\frac{2(p+1)}{N}\] \[\mathrm{BIC} = \mathrm{SIC}=-\frac{2\mathrm{LLF}}{N}+\frac{(p+1)\times\ln(p+1)}{N}\]
  6. The sample data may include missing values.
  7. Each column in the input matrix corresponds to a separate variable.
  8. Each row in the input matrix corresponds to an observation.
  9. Observations (i.e. row) with missing values in X or Y are removed.
  10. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
  11. The MLR_GOF 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