Databases Reference
In-Depth Information
6
Regression Analysis
Regression analysis is a form of prediction modeling that uses selected input
attribute values to predict an output value. The difference between classification
(covered in chapter 5) and regression analysis is in the output data type. In
classification,
the output or predicted type is nominal;
in regression the
predicted type is continuous numeric.
The Regression Model
A formal definition of the regression model is:
Y
i
¼ f ðX
1
i
; X
2
i
; X
pi
Þþ
e
i
where:
Y
i
is the value of the output variable for the
i
th
observation
X
1
i
is the value of the first input variable for the
i
th
observation
X
pi
is the value of the
p
th
input variable for the
i
th
observation
is the random error term for the
i
th
observation.
e
i
The error term is included for two reasons.
1. In most data collection processes there are imprecisions and errors in
measurement.
2. The model as defined is not complete. It is an abstraction of the real world.
There are very likely to be additional inputs that influence the output yet are
not included in the model and the form of the function itself may not
accurately represent real world processes.
