c01. Introduction and review of univariate general linear models
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few data analytic techniques command a position of greater importance 

multiple regression analysis

the purpose of the investigator is to study the relationship between the variables

fitting regression models to data allows the analyst the ability to account for or explain variation
in a criterion variable as a function of one or more predictor variables.

the general linear model is an extension of regression models to accommodate both qualitative
and quantitative predictor variables.

subsumes

the breadth of coverage of possible analyses afforded 

distinguished

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Review of Univariate Linear Model Analysis
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the main goal of the linear model is to evaluate relationships in order to
explain variability in a response variable as a fuction of some specified model
and an error of prediction:

.. math::

   Response = Model + Error

Univariate regression models can be expressed mathematically as a regression function,

.. math::

   Y = \beta_0 + \beta_1 X_1 + \varepsilon

for a simple model with a single predictor variable. 

For a more complex model with multiple predictors, we may write

.. math::

   Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + ... + \beta_q X_q + \varepsilon


disturbance -

The :math:`X_j` explanatory variables, j=1,2, ..., q, can be either continuous or categorical.