What does linear stand for in linear regression?

In R, if I write

lm(a ~ b + c + b*c) 

would this still be a linear regression?

How to do other kinds of regression in R? I would appreciate any recommendation for textbooks or tutorials?

Answer

Linear refers to the relationship between the parameters that you are estimating (e.g., $\beta$) and the outcome (e.g., $y_i$). Hence, $y=e^x\beta+\epsilon$ is linear, but $y=e^\beta x + \epsilon$ is not. A linear model means that your estimate of your parameter vector can be written $\hat{\beta} = \sum_i{w_iy_i}$, where the $\{w_i\}$ are weights determined by your estimation procedure. Linear models can be solved algebraically in closed form, while many non-linear models need to be solved by numerical maximization using a computer.

Attribution
Source : Link , Question Author : suprvisr , Answer Author : Charlie

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