Function File: [b, bint, r, rint, stats] = regress (y, X, [alpha])

Multiple Linear Regression using Least Squares Fit of y on X with the model y = X * beta + e.

Here,

• y is a column vector of observed values
• X is a matrix of regressors, with the first column filled with the constant value 1
• beta is a column vector of regression parameters
• e is a column vector of random errors

Arguments are

• y is the y in the model
• X is the X in the model
• alpha is the significance level used to calculate the confidence intervals bint and rint (see `Return values' below). If not specified, ALPHA defaults to 0.05

Return values are

• b is the beta in the model
• bint is the confidence interval for b
• r is a column vector of residuals
• rint is the confidence interval for r
• stats is a row vector containing:
  • The R^2 statistic
  • The F statistic
  • The p value for the full model
  • The estimated error variance

r and rint can be passed to rcoplot to visualize the residual intervals and identify outliers.

NaN values in y and X are removed before calculation begins.