Curve-Fitting, Cubic Spline and Approximation
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Let there be two variables x and y which give us a set of n pairs of numerical values
(x1, y1), (x2, y2).......(xn, yn). In order to have an approximate idea about the relationship of these
two variables, we plot these n paired points on a graph thus, we get a diagram showing the
simultaneous variation in values of both the variables called scatter or dot diagram. From
scatter diagram, we get only an approximate non-mathematical relation between two variables.
Curve fitting means an exact relationship between two variables by algebraic equations, infact
this relationship is the equation of the curve. Therefore, curve fitting means to form an equation
of the curve from the given data. Curve fitting is considered of immense importance both from
the point of view of theoretical and practical statistics.