Curve fitting of exponential curve

Curve fitting

1. Curve Fitting of Exponential Curve Divyang R. Rathod

2. Definition Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. It is a statistical technique use to drive coefficient values for equations that express the value of one(dependent) variable as a function of another (independent variable)

3. Curve fitting There are two general approaches for curve fitting: Least squares regression: Data exhibit a significant degree of scatter. The strategy is to derive a single curve that represents the general trend of the data. Interpolation: Data is very precise. The strategy is to pass a curve or a series of curve through each of the points.

4. Curve fitting

5. Curve fitting There are 3 cases of curve fitting Fitting of Linear Curve Fitting of Quadratic Curve Fitting of Exponential and logarithmic Curves

6. Fitting of Exponential and logarithmic Curves Let (x i, y i ), I = 1, 2, …, n be the set of n values and let the relation between x and y be y = ab. Taking logarithm on both the sides of the sides of the equation , Putting , x = X, and , Y = A + BX  

7. This is a linear equation in X and Y. The normal equations are, Solving these equations, A and B, and, hence, a and b can be found. The best fitting exponential curve is obtained by substituting the values of a and b in the equation . Similarly, the best fitting exponential curves for the relation and can be obtained.  

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