2.1.11.16 ocmath_multiple_linear_regression

1 Description
2 Syntax
3 Parameters
4 Return
5 Examples
6 Remark
7 See Also
8 Header to Include
9 Reference

Description

Function to perform multiple linear regression.

Syntax

OCMATH_API int ocmath_multiple_linear_regression(const double* pX, UINT nOSizeN, UINT nVSizeM, const double* pY, const double* pWT, UINT nWTSize, const LROptions* psLROptions, FitParameter* psFitParameter, UINT nFitSize, RegStats* psRegStats = NULL, RegANOVA* psRegANOVA = NULL, double* pCov = NULL,  double* pCorr = NULL, uint nCovCorrRowSize = 0, uint nCovCorrColSize = 0, double* pH = NULL, double* pSE = NULL)

Parameters

pX: [Input] matrix containing data points of the independent variables
nOSizeN: [Input] the number of observations, nOSizeN>=2
nVSizeM: [Input] the total number of independent variables in the data set, nVSizeM>=1
pY: [Input] vector containing data points of dependent variable, size of pY = nOSizeN
pWT: [Input] vector containing weight of the data, all date in pWT should not less than zero
nWTSize: [Input] the size of the weight, should be the same as nOSizeN
psLROptions: [Input] struct for linear regression options
psFitParameter: [Output] pointer to structs to receive information on each fitting parameter
nFitSize: [Input] the size of psFitParameter, should be nVSizeM + 1
psRegStats: [Output] pointer to struct containing Regression statistics
psRegANOVA: [Output] pointer to struct containing ANOVA statistics
pCov: [Output] pointer to covariance matrix of estimate
pCorr: [Output] pointer to correlation matrix of estimate
nCovCorrRowSize: [Input] row size of Covariance and Correlation matrix, which should be nVSizeM + 1
nCovCorrColSize: [Input] column size of Covariance and Correlation matrix, which should be nVSizeM + 1
pH: [Output] pointer to diagonal element of H, leverage Size of the pH should be nOSizeN
pSE: [Output] pointer to standard error of mean predicted values. Size of the pSE should be nOSizeN

Return

Returns STATS_NO_ERROR on successful exit and a non-zero STATS error code on failure.

Error Codes:

STATS_ERROR_SETTING(-151): when psLROptions->Confidence<0 or psLROptions->Confidence > 1.

STATS_INPUT_NULL_POINTER(-156): pX is NULL or pY is NULL.

STATS_ERROR_WEIGHT_DIFF_SIZE(-174): if nWTSize is not 0, nWTSize should equal to nOSizeN

STATS_PARAMS_ARRAY_TOO_SMALL(-98): nCovCorrRowSize < nVSizeM + 1 or nCovCorrColSize < nVSizeM + 1, or nFitSize < nVSizeM.

STATS_ERROR_DATA_PTS_LESS_THAN_PARA_NUM(-212): the number of input data cannot less than the number of parameters.

Other error code please refer to g02dac.

Examples

EX1

void ocmath_multiple_linear_regression_ex1()
{
	Worksheet wks = Project.ActiveLayer();
	if( !wks )
		return; // please make sure a worksheet with data is active 
	
	DataRange dr;
	dr.Add("X", wks, 0, 0, -1, 2);
	dr.Add("Y", wks, 0, 3, -1, 3);
	
	matrix mX;	
	dr.GetData(mX, 0, 0);
	
	vector vY;
	dr.GetData(&vY, 1);
	
	// prepare input and output variables
	UINT nOSizeN = mX.GetNumRows();
	UINT nVSizeM = mX.GetNumCols();
	
	LROptions stLROptions;
	stLROptions.UseReducedChiSq = 1;
	
	FitParameter stFitParameters[4]; // should be nVSizeM+1
	UINT nFitSize = nVSizeM+1;
	
	RegStats stRegStats;
	RegANOVA stRegANOV;
	
	// calculate
	int nRet = ocmath_multiple_linear_regression(mX, nOSizeN, nVSizeM, vY, NULL, 0, &stLROptions, 
				stFitParameters, nFitSize, &stRegStats, &stRegANOV);
				
	if( nRet != STATS_NO_ERROR )
	{	
		out_str("Error");
		return;
	}
	
	// output the parameter value to Script Window
	for(int nn = 0; nn < nFitSize; nn++)
		printf("Param %d=%g\n", nn+1, stFitParameters[nn].Value);
	
	// output statistics results to Result Log
	Tree tr;
	TreeNode trResult = tr.AddNode("MR");
	TreeNode trStats = trResult.AddNode("Stats");
	trStats += stRegStats;
	
	TreeNode trANOVA = trResult.AddNode("ANOVA");
	trANOVA += stRegANOV;
	
	string str;
	tree_to_str(trResult, str);
	Project.OutStringToResultsLog(str);	
}

Remark

The function finds a QR decomposition of X. If R is of full rank, solution is obtained from the QR decomposition. If R is not full rank, a solution is obtain by means of a singular value decomposion(SVD) of R. If R is not full rank, STATS_ERROR_RANK_DEFICIENT is returned in addition to the solutions. The computational engine is the NAG function nag_regsn_mult_linear (g02dac).