linear_regression(1) simple linear regression and prediction

## SYNOPSIS

linear_regression [-h] [-v] [-i string] [-r string] [-l double] [-m string] [-o string] [-p string] [-t string] -V

## DESCRIPTION

An implementation of simple linear regression and simple ridge regression using ordinary least squares. This solves the problem

```  y = X * b + e
```
where X (--input_file) and y (the last column of --input_file, or --input_responses) are known and b is the desired variable. If the covariance matrix (X'X) is not invertible, or if the solution is overdetermined, then specify a Tikhonov regularization constant (--lambda) greater than 0, which will regularize the covariance matrix to make it invertible. The calculated b is saved to disk (--output_file).

Optionally, the calculated value of b is used to predict the responses for another matrix X' (--test_file):

```   y' = X' * b
```
and these predicted responses, y', are saved to a file (--output_predictions). This type of regression is related to least-angle regression, which mlpack implements with the 'lars' executable.

## OPTIONS

--help (-h)
Default help info.
--info [string]
Get help on a specific module or option. Default value ''.
--input_file (-i) [string]
File containing X (regressors). Default value ''.
--input_responses (-r) [string]
Optional file containing y (responses). If not given, the responses are assumed to be the last row of the input file. Default value ''.
--lambda (-l) [double]
Tikhonov regularization for ridge regression. If 0, the method reduces to linear regression. Default value 0.
--model_file (-m) [string]
File containing existing model (parameters). Default value ''.
--output_file (-o) [string]
File where parameters (b) will be saved. Default value 'parameters.csv'.
--output_predictions (-p) [string]
If --test_file is specified, this file is where the predicted responses will be saved. Default value 'predictions.csv'.
--test_file (-t) [string]
File containing X' (test regressors). Default value ''.
--verbose (-v)
Display informational messages and the full list of parameters and timers at the end of execution.
--version (-V)
Display the version of mlpack.