# NDK_MLR_PRFTest

 int __stdcall NDK_MLR_PRFTest ( double ** X, size_t nXSize, size_t nXVars, double * Y, size_t nYSize, double intercept, LPBYTE mask1, size_t nMaskLen1, LPBYTE mask2, size_t nMaskLen2, double alpha, WORD nRetType, double * retVal )

Calculates the p-value and related statistics of the partial f-test (used for testing the inclusion/exclusion variables).

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] Y is the response or 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] mask1 is the boolean array to choose the explanatory variables in model 1. If missing, all variables in X are included. [in] nMaskLen1 is the number of elements in "mask1." [in] mask2 is the boolean array to choose the explanatory variables in model 2. If missing, all variables in X are included. [in] nMaskLen2 is the number of elements in "mask2." [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 = P-Value (default), 2 = Test Stats, 3 = Critical Value.) [out] retVal is the calculated test statistics/
Remarks
1. The underlying model is described here.
2. Model 1 must be a sub-model of Model 2. In other words, all variables included in Model 1 must be included in Model 2.
3. The coefficient of determination (i.e. $$R^2$$) increases in value as we add variables to the regression model, but we often wish to test whether the improvement in R square by adding those variables is statistically significant.
4. To do so, we developed an inclusion/exclusion test for those variables. First, let's start with a regression model with $$K_1$$ variables:
$Y_t = \alpha + \beta_1 \times X_1 + \cdots + \beta_{K_1} \times X_{K_1}$ Now, let's add a few more variables $$\left(X_{K_1+1} \cdots X_{K_2}\right)$$: $Y_t = \alpha + \beta_1 \times X_1 + \cdots + \beta_{K_1} \times X_{K_1} + \cdots + \beta_{K_1+1} \times X_{K_1+1} + \cdots + \beta_{K_2} \times X_{K_2}$
5. The test of the hypothesis is as follows:
$H_o : \beta_{K_1+1} = \beta_{K_1+2} = \cdots = beta_{K_2} = 0$ $H_1 : \exists \beta_{i} \neq 0, i \in \left[K_1+1 \cdots K_2\right]$
6. Using the change in the coefficient of determination (i.e. $$R^2$$) as we add new variables, we can calculate the test statistics:
$\mathrm{f}=\frac{(R^2_{f}-R^2_{r})/(K_2-K_1)}{(1-R^2_f)/(N-K_2-1)}\sim \mathrm{F}_{K_2-K_1,N-K2-1}$ Where:
• $$R^2_f$$ is the $$R^2$$ of the full model (with added variables).
• $$R^2_r$$ is the $$R^2$$ of the reduced model (without the added variables).
• $$K_1$$ is the number of variables in the reduced model.
• $$K_2$$ is the number of variables in the full model.
• $$N$$ is the number of observations in the sample data.
7. The sample data may include missing values.
8. Each column in the input matrix corresponds to a separate variable.
9. Each row in the input matrix corresponds to an observation.
10. Observations (i.e. row) with missing values in X or Y are removed.
11. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
12. The MLR_ANOVA function is available starting with version 1.60 APACHE.
Requirements
 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_MLR_PRFTest ( double ** pXData, UIntPtr nXSize, UIntPtr nXVars, double[] pYData, UIntPtr nYSize, double intercept, byte[] mask1, UIntPtr nMaskLen1, byte[] mask2, UIntPtr nMaskLen2, double alpha, short nRetType, ref double retVal )

Calculates the p-value and related statistics of the partial f-test (used for testing the inclusion/exclusion variables).

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] pYData is the response or 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] mask1 is the boolean array to choose the explanatory variables in model 1. If missing, all variables in X are included. [in] nMaskLen1 is the number of elements in "mask1." [in] mask2 is the boolean array to choose the explanatory variables in model 2. If missing, all variables in X are included. [in] nMaskLen2 is the number of elements in "mask2." [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 = P-Value (default), 2 = Test Stats, 3 = Critical Value.) [out] retVal is the calculated test statistics/
Remarks
1. The underlying model is described here.
2. Model 1 must be a sub-model of Model 2. In other words, all variables included in Model 1 must be included in Model 2.
3. The coefficient of determination (i.e. $$R^2$$) increases in value as we add variables to the regression model, but we often wish to test whether the improvement in R square by adding those variables is statistically significant.
4. To do so, we developed an inclusion/exclusion test for those variables. First, let's start with a regression model with $$K_1$$ variables:
$Y_t = \alpha + \beta_1 \times X_1 + \cdots + \beta_{K_1} \times X_{K_1}$ Now, let's add a few more variables $$\left(X_{K_1+1} \cdots X_{K_2}\right)$$: $Y_t = \alpha + \beta_1 \times X_1 + \cdots + \beta_{K_1} \times X_{K_1} + \cdots + \beta_{K_1+1} \times X_{K_1+1} + \cdots + \beta_{K_2} \times X_{K_2}$
5. The test of the hypothesis is as follows:
$H_o : \beta_{K_1+1} = \beta_{K_1+2} = \cdots = beta_{K_2} = 0$ $H_1 : \exists \beta_{i} \neq 0, i \in \left[K_1+1 \cdots K_2\right]$
6. Using the change in the coefficient of determination (i.e. $$R^2$$) as we add new variables, we can calculate the test statistics:
$\mathrm{f}=\frac{(R^2_{f}-R^2_{r})/(K_2-K_1)}{(1-R^2_f)/(N-K_2-1)}\sim \mathrm{F}_{K_2-K_1,N-K2-1}$ Where:
• $$R^2_f$$ is the $$R^2$$ of the full model (with added variables).
• $$R^2_r$$ is the $$R^2$$ of the reduced model (without the added variables).
• $$K_1$$ is the number of variables in the reduced model.
• $$K_2$$ is the number of variables in the full model.
• $$N$$ is the number of observations in the sample data.
7. The sample data may include missing values.
8. Each column in the input matrix corresponds to a separate variable.
9. Each row in the input matrix corresponds to an observation.
10. Observations (i.e. row) with missing values in X or Y are removed.
11. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
12. The MLR_ANOVA function is available starting with version 1.60 APACHE.
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static 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
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