A LEAST-SQUARES-BASED METHOD FOR DETERMINING THE RATIO BETWEEN 2 MEASURED QUANTITIES

A numerical procedure to find the ratio between two measured quantitie s is discussed in the framework of the least-squares method with error s in both coordinates. Constant, as well as variable, amounts of stati stical uncertainties are considered for each variable along their meas ured range. Analytical solutions for particular cases are given. The v ariance of the ratio is given as a closed analytical expression valid for the general case. Limiting cases of the presented results are comp ared with those obtained using classical least-squares expressions. A comparison with the weighted average method is also discussed.