Consider a collection of data points
\begin{equation*}
(x_1,y_1), (x_2,y_2), ... , (x_n,y_n)
\end{equation*}
and a general linear function
\begin{equation*}
f(x) = mx + b.
\end{equation*}
It is possible that each of the given data points are exactly "interpolated" by the linear function so that
\begin{equation*}
f(x_k) = y_k
\end{equation*}
for k = 1, 2, ... , n. However, in general this is unlikely since even three points are not likely to be colinear. However, you may notice that the data points exhibit a linear tendency or that the underlying physics might suggest a linear model. If so, you may find it easier to predict values of y for given values of x using a linear approximation. Here you will investigate a method for doing so called "linear regression", "least-squares", or "best-fit line".