# what does linear regression actually mean?

Wikipedia gives the following definition for linear regression:

In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variable) denoted X. The case of one explanatory variable is called simple linear regression.

What does the name actually mean? I.e. what do the 'linear' and 'regression' parts of the name actually stand for?

• Popular question without like 7+ upvotes, nice work guys I like this SE. This isn't a question that shows research effort. (I'm totally serious.) – Alec Teal Jul 28 '15 at 15:11

• Just to emphasize the linear part, linear regression is linear in the parameters not necessary the data. That is the model y= $\beta_{0} +\beta_{1}x^{100} +\epsilon$ is a linear model but the model y= $\beta_{0} +\beta_{1}^{2}x +\epsilon$ is not. – Nick Thieme Jul 28 '15 at 14:49
"Linear" refers to the type of the model, $$y=\beta_0 + \beta_1 x_1 + \beta_2 x_2 +\ldots + \beta_m x_m.$$ to understand the meaning of "linear" without going to higher dimensions, let's have just one $x$ and assume $\beta_0=0$. Then above formula reduces to,
$$y= \beta_1 x_1$$ as you see this is a line with slop of $\beta_1$ in 2D space. This models simply means, by knowing a coefficient, $\beta_1$ and having some values for $x_1$, then you can find (maybe predict with some uncertainty) the value of the left hand side (usually called response variable). This procedure is called regression in literature.