In practice, it is not uncommon to use both LDA and PCA in combination: e.g., PCA for dimensionality reduction followed by an LDA.
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Linear Regression is a linear approach for modelling the relationship between a scalar dependent variable y and one or more independent variables denoted X. The case of one independent variable is called Simple Linear Regression. For more than one independent variable, the process is called Multiple Linear Regression.
Random Forests are an ensemble learning method for classification, regression and other tasks, that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees.