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)
  */