In Chapter 9, you
learned to describe the association between two variables by using a
simple graphical technique in a two-dimensional (*x*,
*y*) plane. You also learned to quantify the
*bivariate relationship* by computing a correlation
coefficient. You may have been surprised by how easy it was to relate the
mathematical relationship between two variables, especially for simple
cases such as *r* = 1.00, where a perfect correlation
can be graphically described by a straight line, with a specific slope and
intercept.

It is possible to take the relationship one step further and use
characteristics, such as the *slope* and
*intercept*, to build a functional
*mathematical model*, and determine the precise
deviation from the model for observed data. In this approach, the
correlation coefficient and the *coefficient of
determination* still have an important role to play; however,
the use of *linear regression* to test the
*goodness of fit* of observed data to a theoretical
model goes one step further in being able to characterize existing data,
and predict values of dependent variables from independent variables. This
process occurs literally by simple algebraic operations, such as
substitution.

Linear regression is an extremely valuable technique, which is often used for prediction in models where no experimental control has been applied to the collection of data. For example, you may want to determine the relationship between training and performance ...

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