Regression Class

The Regression class is an abstract class for user defined classes that can be used in the regression model. The class linear_regression implemented in opus_core computes outcome $Y$ as a linear combination of given data $X$ and coefficients $\beta$ : $y_n = \sum_{j=1}^J \beta_j x_{nj}$ . Here, $J$ denotes the number of variables entering the regression and $n$ is an index for observations. The run() method takes a 2-d array of data (of size number of observations $\times$ number of variables) and a 1-d array of coefficients as arguments and returns a 1-d array of outcome.

A child class of linear_regression, called linear_regression_with_normal_error, adds normaly distributed random errors to the outcome: $y_n = \sum_{j=1}^J \beta_j x_{nj} + \delta_n$ where $\delta_n \sim N(\mu_n, \sigma_n^2)$ . $\mu_n$ and $\sigma_n^2$ , respectively, can be passed to the run() method in its argument resources (dictionary) as entries 'linear_regression_error_mean' and 'linear_regression_error_variance', respectively. Both can be specified either as a single value or as an array of size number of observations. By default, $\delta_n \sim N(0, 1)$ for all $n$ .