Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Multivariate Data Modeling MLR Introduction  
See also: linear/nonlinear models, simple regression, stepwise regression, estimation of new observations, Weighted Regression, MLR and Collinearity  
Multiple Linear Regression  Introduction
Multiple linear regression (MLR) is similar to simple linear 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} + ε or The parameter e defines the error, or the residual, with a mean of zero. This equation defines a hyperplane in ndimensional 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.


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Last Update: 20121008