# One-Dimensional Linear Regression

The simple linear regression algorithm is a closed-form solution to a least-squared distance minimization problem. Here is demonstrated the one-dimensional case of simple linear regression.

$$
\min_{\alpha,\beta} \sum_{i=1}^{n} (y_i - \alpha - \beta x_i)^2
$$

*Click and drag* the black points to affect the regression. *Double click* to
add or remove points. The blue point in the center represents the geometric
average, through which the fit always passes through.

In this problem, the least-squared distance considered includes only the vertical component. This is what makes the problem “one-dimensional”, even though the visualization of the problem is two-dimensional.