model the relationship between one or more independent or predictor variables and a dependent or response variable
Regression analysis

__Prediction__

(Numerical)
prediction is similar to classification ^{}

^{·
}construct a model^{}

·
use model to predict continuous or ordered value
for a given input

Prediction is different from classification^{}

·
Classification refers to predict categorical class
label

·
Prediction models continuous-valued functions

Major method for prediction: regression^{}

^{ }

·
model the relationship between one or more *independent* or predictor variables and a
*dependent *or response variable

Regression analysis^{}

^{ }

·
Linear and multiple regression

·
Non-linear regression

·
Other regression methods: generalized linear model,
Poisson regression, log-linear models, regression trees

**Linear Regression**

__Linear regression__: involves a response variable y
and a single predictor variable x^{}

^{ }

y = w_{0} + w_{1} x^{}

^{ }

where w_{0} (y-intercept) and w_{1}
(slope) are regression coefficients^{}

^{ }

__Method of least squares__:
estimates the best-fitting straight line^{}

·
__Multiple linear regression__:
involves more than one predictor variable

·
Training data is of the form (**X _{1}**, y

_{·
}Ex. For 2-D data, we may have: y = w_{0} + w_{1} x_{1}+ w_{2} x_{2}

·
Solvable by extension of least square method or
using SAS, S-Plus

·
Many nonlinear functions can be transformed into
the above

**Nonlinear Regression**

^{o
}Some nonlinear models can be modeled by a
polynomial function^{}

^{ }

^{o
}A polynomial regression model can be transformed
into linear regression model. For example,^{}

^{o
}y = w_{0} + w_{1} x + w_{2}
x^{2} + w_{3} x^{3}^{}

^{ }

^{o
}convertible to linear with new variables: x_{2}
= x^{2}, x_{3}= x^{3}^{}

^{ }

^{o
}y = w_{0} + w_{1} x + w_{2}
x_{2} + w_{3} x_{3}^{}

^{ }

^{o
}Other functions, such as power function, can also
be transformed to linear model^{}

^{ }

^{o
}Some models are intractable nonlinear (e.g., sum of
exponential terms)^{}

o
possible to obtain least square estimates through
extensive calculation on more complex formulae

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Data Warehousing and Data Mining : Association Rule Mining and Classification : Prediction |

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