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Table of Contents Multivariate Data Modeling MLR Introduction | |
See also: linear/non-linear models, simple regression, stepwise regression, estimation of new observations |
Multiple linear regression (MLR) is similar to simple regression, the only difference being the use of more than one input variable. In order to calculate the relationship between n input variables x_{i} and the target variable y we could use the linear equation
y = a_{0} + a_{1}x_{1} + a_{2}x_{2} + ... + a_{n}x_{n} + e
or
The parameter e defines the error, or the residual, with a mean
value of zero. This equation defines a hyperplane in n-dimensional space.
The parameters of this plane have to be adjusted so that the plane optimally
fits the data. In order to obtain the best fit, the parameters a_{0}
to a_{n} are adjusted such that the sum of the squared errors is
minimized. The assumptions are
the same as for simple regression. The estimated parameters can again be
discussed by using the ANOVA table.
Last Update: 2006-Jän-17