Statistics: regress

### Function Reference: `regress`

statistics: [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.

See also: regress_gp, regression_ftest, regression_ttest

Source Code: regress