Statistics Course Help With Selection Of Type Of Curve To Be Fitted
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:
- (i) A straight line
yx= a+ bx
- (ii) Second degree parabola:
yx= a+ bx +cx2
- (iii) Kth degree polunomicla:
yx= a0+ a 1 x+ a 2 x2+……………..+ a 1 xk
- (iv) Exponential curve:
yx= ab x
- è Log yx = Log a+ x Log b = A+ Bx
- (v) Second degree curve fitted to logarithms:
- è Log yx =log a + x log b + x2 log c
- è Log yx = A+ Bx+ Cx2
- (vi) Growth curves
- (a) (Modified exponential curve)
- (b) (Gompertz curve)
Log yx =log a + c x log b = A + Bcx
- (c) ( logistic curve)
For deciding about the type of curve to be fitted to a given set of data, the following points may be helpful:
- (i) When the y x series is found to be increasing by equal absolute amounts, the straight line curve is used. In this case, the graph of the data will give a straight line graph.
- (ii) The logarithmic straight line (exponential curve) is used when the series is increasing or decreasing by a constant percentage rather than a constant absolute amount. In this case, the data plotted on a semi – logarithmic scale will give a straight line graph.
- (iii) Second degree curve fitted to logarithms may be tried if the data plotted on a semi- logarithmic scale is not a straight line graph but shows curvature, being concave either upward or downward.
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