# Supervised Model-based Numeric-Value Prediction Task

• As a result of an experiment, four $(x, y)$ data points were obtained, $(1, 6),$ $(2, 5),$ $(3, 7),$ and $(4, 10)$ (shown in red in the picture on the right). It is desired to find a line $y=\beta_1+\beta_2 x$ that fits "best" these four points. In other words, we would like to find the numbers $\beta_1$ and $\beta_2$ that approximately solve the overdetermined linear system \begin{alignat}{3} \beta_1 + 1\beta_2 &&\; = \;&& 6 & \\ \beta_1 + 2\beta_2 &&\; = \;&& 5 & \\ \beta_1 + 3\beta_2 &&\; = \;&& 7 & \\ \beta_1 + 4\beta_2 &&\; = \;&& 10 & \\ \end{alignat} of four equations in two unknowns in some "best" sense.