func

Regression, ANOVA and Null Hypothesis Calculations using functional approach

Classical Linear Regression Model

void linreg_clrm(double *x,double *y, int N, double* b,
	double *var,double *res,double alpha,double *anv,
	double* ci_lower, double* ci_upper);

/*
 * Classic Linear Regression Model
 * y = b[0] + b[1] * x + u
 * x,y and res are all of same length - N
 * where res is the residual
     *
 * alpha is used to determine confidence interval limits
 * for a given 100*(1-alpha) % confidence interval
 * 
 * 
 * Alpha takes values between  0 and 1.
 * 
 * For 95% confidence interval, the value of alpha is 0.05
 * For 90% confidence interval, the value of alpha is 0.10 etc.
 */ 

/*
 * Parameters ( b is a double vector of length 2)
 * b[0] - beta1
 * b[1] - beta2
 */ 

/* Variances ( var is a double vector of length 5)
 * var[0] - variance of residuals
 * var[1] variance beta1
 * var[2] variance beta2
 * var[3] covariance beta1,beta2
 * var[4] r^2 Goodness of Fit
 */
 
 /*
  * ANOVA ( anv is a double vector of length 7)
  * 
  * anv[0] - TSS Total Sum Of Squares
  * anv[1] - ESS Explained Sum Of Squares
  * anv[2] - RSS Residual Sum Of Squares
  * anv[3] - degrees of freedom of ESS
  * anv[4] - degrees of freedom of RSS
  * anv[5] - F Statistics = (anv[1] / anv[3]) / (anv[2] / anv[4])
  * anv[6] - P value associated with anv[5] used to reject/accept 
  * zero hypothesis
  */ 

 /* ci_lower and ci_upper (Confidence Interval Lower and Upper Limits)
  * ( double vectors of length 3)
  * ci_lower[0] - CI Lower Limit corresponding to b[0]
  * ci_lower[1] - CI Lower Limit corresponding to b[1]
  * ci_lower[2] - CI Lower Limit corresponding to var[0] (sigma^2)
  * ci_upper[0] - CI Upper Limit corresponding to b[0]
  * ci_upper[1] - CI Upper Limit corresponding to b[1]
  * ci_upper[2] - CI Upper Limit corresponding to var[0] (sigma^2)
  */

void zerohyp_clrm(int N,double *b, double *var, double *tval, double *pval) {

Zero Hypothesis Test for CLRM
 N is the length of the data series. b and var are parameters/variances obtained from linreg_clrm function. tval and pval are double vectors of length 2 each containing Student's T values and the corresponding probability distribution values.

Multiple Regression Model

void linreg_multi(int p, double *x, double *y, int N, double* b, double *sigma2,
	double *xxti, double *R2, double *res, double alpha, double *anv,
	double* ci_lower, double* ci_upper);

/*
 * Multiple Regression Model
 * y = b[0] + b[1] * x1 + .. + b[p-1]* xp-1 + u
     * p is the total number of parameters (p >= 2 for multiple Regression)
 * y and res are all of same length - N
 * where res is the residual
     * x is of length (p-1) * N
 * alpha is used to determine confidence interval limits
 * for a given 100*(1-alpha) % confidence interval
 * 
 * 
 * Alpha takes values between  0 and 1.
 * 
 * For 95% confidence interval, the value of alpha is 0.05
 * For 90% confidence interval, the value of alpha is 0.10 etc.
 */ 

/*
 * Parameters ( b is a double vector of length 2)
 * b[0] - beta1
 * b[1] - beta2
 */ 

/* Variances ( var is a double vector of length 5)
 * sigma2 - variance of residuals
 * xxti - Variance-Covariance Matrix of size p*p
 * R2[0] and R2[1] - R2 is double vector of length 2. r^2 Goodness of Fit and adjust r^2
 */
 
 /*
  * ANOVA ( anv is a double vector of length 7)
  * 
  * anv[0] - TSS Total Sum Of Squares
  * anv[1] - ESS Explained Sum Of Squares
  * anv[2] - RSS Residual Sum Of Squares
  * anv[3] - degrees of freedom of ESS
  * anv[4] - degrees of freedom of RSS
  * anv[5] - F Statistics = (anv[1] / anv[3]) / (anv[2] / anv[4])
  * anv[6] - P value associated with anv[5] used to reject/accept 
  * zero hypothesis
  */ 

 /* ci_lower and ci_upper (Confidence Interval Lower and Upper Limits)
  * ( double vectors of length p+1)
  * ci_lower[0] to ci_lower[p-1] corresponding to b[0],...,b[p-1]
  * ci_lower[p] - CI Lower Limit corresponding to sigma2 (sigma^2)
  * ci_upper[0] to ci_upper[p-1] corresponding to b[0],...,b[p-1]
  * ci_upper[p] - CI Upper Limit corresponding to sigma2 (sigma^2)
  */

void zerohyp_multi(int N,double *b,int p, double *varcovar, double *tval, double *pval)

Zero Hypothesis Test for Multiple Regression Model
 N is the length of the data series and p is the total number of parameters. b and varcovar are parameters/Variance-Covariance Matrices obtained from linreg_multi function. tval and pval are double vectors of length 2 each containing Student's T values and the corresponding probability values.