Fitting straight lines to experimental data

Abstract

The problem associated with use of statistical methods for determining a best linear relationship of the form Y = AX +B have been examined for a condition quite prevalent with experimental research, i.e., when the values of both variables are subject to essentially unknown errors. Under this condition standard least-squares regression analysis underestimates the value of the slope A. A very simple method for determining the best value of the slope and intercept has been introduced which can be used when errors are present in both variables. With this proposed method, the calculated slope is equal to the standard error of Y divided by the standard error of X (with the appropriate sign) and the intercept is found from the mean values of X and Y, i.e., B = Y - AX. The best estimate of the slope is also equal to the slope found with the conventional regression method divided by the absolute value of the correlation coefficient. The line determined with the suggested method can be considered to be a line of symmetry through the data.