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==Multiple and multivariate regression==

==Multiple and multivariate regression==

The most important extension of the two-variable case is to situations involving more than two variables. When there is still one dependent variable but many predictor variables, the fitting technique is called ''multiple linear regression.'' When there are also more than one dependent variable, the approach is called ''multivariate regression'' (see [[Multivariate data analysis]]). The methods of simple bivariate regression extend directly to these multivariate situations. A typical geological application of multiple regression is the prediction of fold thickness from various geometric attributes, as given by the following equation:

The most important extension of the two-variable case is to situations involving more than two variables. When there is still one dependent variable but many predictor variables, the fitting technique is called ''multiple linear regression.'' When there are also more than one dependent variable, the approach is called ''multivariate regression'' (see [[Multivariate data analysis]]). The methods of simple bivariate regression extend directly to these multivariate situations. A typical geological application of multiple regression is the prediction of [[fold]] thickness from various geometric attributes, as given by the following equation:

:<math>\text{Thickness } = a+b~(\text{attitude}) + c~(\text{tightness}) + d~(\text{asymmetry}) </math>

:<math>\text{Thickness } = a+b~(\text{attitude}) + c~(\text{tightness}) + d~(\text{asymmetry}) </math>