A Better Linear Model Than Regression-Line for Data-Mining Applications

Abstract

The regression-line for a set of data-points $p_i = (x_i, y_i), 1 \le i \le N$ and $N > 2$, lacks the rotation-property in the sense that if each $p_i$ is rotated by an angle $\theta$ around the origin then the regression-line does not rotate by the same angle $\theta$ except for the special case when all $p_i$’s are collinear. This makes the regression-line unsuitable as a linear model of a set of data points for applications in data mining and machine learning. We present an alternative linear model that has the rotation property. In many ways, the new model is also more appealing intuitively as we show with examples. The computation of the new linear model takes the same O(N) time as that for the regression-line.