What does 'linear function' in linear regression mean exactly?

I would be careful in asking this as an "R linear regression" question versus a "linear regression" question. Formulas in R have rules that you may or may not be aware of. For example: http://wiener.math.csi.cuny.edu/st/stRmanual/ModelFormula.html. read more

These functions need not be linear in the explanatory variables, [math]x_1[/math] and [math]x_2[/math]. Clearly the [math]x_1^2x_2[/math] function is not linear. The word “linear” in linear regression refers to the fact that these functions are combined together using a linear combination. read more

Second, it’s not “instead of”. Linear regression is part of the generalized linear model. The GLM is a generalization of linear regression. Third, GLM offers a lot more flexibility in terms of what you can model. Linear regression requires that the dependent variable be continuous (or nearly so). read more