NDK_MLR_PRFTest

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
Class	SFSDK
Scope	Public
Lifetime	Static
Package	NumXLAPI.DLL

Examples