IF a number n of readings are taken of a dependent variable y for various values of the independent variable x we frequently need to determine a reasonably satisfactory curve to express the relation between the two variables; preferably we should be able to give an equation for this curve. We know that the observations will be subject to random errors due to various causes; we therefore expect the curve not to go through all the points representing the observations, but to lie evenly among these points. If the curve is expected to be a straight line, we may be able to determine it with sufficient accuracy by eye. The ‘least-squares’ technique for finding the equation of the best-fitting curve C for which y is a polynomial of degree m in x is well known. If m is small, the curve Cm will be smooth, but may not fit very well; if m=n−1, the fit is perfect, but Cm is likely to have several oscillations which do not correspond to reality. If m has an intermediate value, there will be some oscillations and a fair fit; increasing m rapidly increases the complexity of the equations determining Cm, and the unreliability of Cm from the statistical point of view.


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    Titel :

    Fitting Curves to Experimental Data by Least Squares


    Untertitel :

    An Examination of the Method of Plotting Experimental Results


    Beteiligte:
    Head, J.W. (Autor:in) / Oulton, G.M. (Autor:in)

    Erschienen in:

    Erscheinungsdatum :

    01.09.1957


    Format / Umfang :

    3 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



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