Linear regression models

In the context of linear statistical modelling, 'linear' means linear in the parameters (coefficients), not the explanatory variables. The explanatory variables can be transformed (say, ), but the model will still be linear if the coefficients remain linear. When the overall function (Y) remains a sum of terms that are each an X variable multiplied by a coefficient, the function Y is said to be linear in the coefficients. A non-linear model has a non-constant slope. (A tutorial on Simple Linear Regression.)