Abstract
AbstractThe general equation to a straight line of best fit to observational data of two related variates x and y is obtained by minimizing the general expression \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{i = 1}^n {(y_i - ax_i - b)^2 } $\end{document} ϕ(a) involving the departures of both variates from the time. It is shown that the only expression for ϕ (a) which produces consistent results with change of unit is ϕ (a) = constant. ak, where k depends on the relative errors (ex, ey) in measurements of the two variates.The line of best fit is shown to be where c is obtained from the equation (k + 2) c2 – 2 (k + 1) rc + k = 0, in which r is the coefficient of correlation between x and y, and k is a given function of ex and ey. The usual regression lines and line with a slope equal to the geometric mean of the slopes of the two regression lines, arise as special cases of the general equation. Examples are given to show general application.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Quarterly Journal of the Royal Meteorological Society
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
