APPENDIX 1 Uncertainty on the line of least squares fit

If all the experimental points were exactly on the line, σm would be 0, since we would know the slope exactly. A non-zero value arises from the fact that one or more points deviate from the line. Each experimental point (xi yi) makes its own contribution to the uncertainty in m. In line with the principle of least squares we are concerned with the sum of the squares of the separate contributions.