When the relationship between two physical variables, such as voltage and current, can be expressed as y = bx where b is a constant. b may be estimated by least squares, or by averaging the values of b obtained for each x-y data pair. We show for data gathered in an experiment, as well as through Monte Carlo simulation and mathematical analysis, that the least squares approach to determining the standard deviation in b is superior. Specifically, we show that when random errors are confined to the y quantity, the standard deviation in b found using least squares is smaller than that obtained using the point by point approach. Consequently, least squares is favoured whenever the conditions for which it is valid are satisfied. It is argued that Monte Carlo simulation, as carried out by students, is an attractive approach by which they may be convinced of the value of the least squares over a point by point analysis.