Refers to any model where a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.

A linear model is any model where a random variable, $Y$, is related to one or more random variables, $X$, by a function that is linear in a finite number of parameters. That is, the parameters being estimated are all coefficients. Note that it does not matter if the resulting function looks like a straight line.

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