The greatest limitation of the method of curve fitting by the principle of least squares is the choice of the mathematical curve to be fitted to the given data. The choice of a particular curve for describing the given data requires great skill, intelligence and expertise. The graph of the give data enables us to have a fairly good idea about the type of the curve to be fitted. The graph will clearly reveal if the trend is linear or curvilinear. If the graph exhibits a curvilinear trend then further approximations to the type of trend curve can be obtained on plotting the data on a semi – logarithmic scale. A careful study of the graph obtained on plotting the data on arithmetic or semi logarithmic scale often provides adequate basis for selecting the type of the curve. The various types of curves that may be used to describe the given data in practice are:
yx= a+ bx
yx= a+ bx +cx2
yx= a0+ a 1 x+ a 2 x2+……………..+ a 1 xk
yx= ab x
Log yx =log a + c x log b = A + Bcx
For deciding about the type of curve to be fitted to a given set of data, the following points may be helpful:
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