Linear Regression is a method for modelling a relationship between a dependent variable and independent variables. These models can be fit with numerous approaches. The most common is least squares, where we minimize the mean square error between the predicted values $\hat{y} = \textbf{X}\hat{\beta}$ and actual values $y$: $\left(y\textbf{X}\beta\right)^{2}$.
We can also define the problem in probabilistic terms as a generalized linear model (GLM) where the pdf is a Gaussian distribution, and then perform maximum likelihood estimation to estimate $\hat{\beta}$.
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