Details

Let be a vector of input variables and be the response. For each , the linear regression model has the format [Hastie2009]:

Here , , are referred to as independent variables, and are referred to as dependent variables or responses.

Simple Linear Regression
(if there is only one explanatory variable)
Multiple Linear Regression
(if the number of explanatory variables )

Let be a set of training data, . The matrix

X

of size contains observations , ,

j = 1, ldots, p

of independent variables.

To estimate the coefficients one these methods can be used:

Normal Equation system
QR matrix decomposition

Linear regression based prediction is done for input vector using the equation for each .

Usage of Training Alternative

Create a Linear Regression model builder using a constructor with the required number of responses and features.
Use the
setBeta
method to add the set of pre-calculated coefficients to the model. Specify random access iterators to the first and the last element of the set of coefficients [ISO/IEC 14882:2011 §24.2.7]_.
If your set of coefficients does not contain an intercept,
interceptFlag
is automatically set to
False
, and to
True
, otherwise.
Use the
getModel
method to get the trained Linear Regression model.
Use the
getStatus
method to check the status of the model building process. If
DAAL_NOTHROW_EXCEPTIONS
macros is defined, the status report contains the list of errors that describe the problems API encountered (in case of API runtime failure).

If after calling the

getModel

method you use the

setBeta

method to update coefficients, the initial model will be automatically updated with the new coefficients.