Curve fitting When data is given for discrete

Curve fitting When data is given for discrete values a long continuum , we may require estimates at points between the discrete values. Curve are fitted to such data obtain intermediate estimates it is also used to replace a complicated function. 1. Least –Square –Regression. 2. Interpolation.

Least- squares regression F(X) Used for data that exhibitions noise error. (does not intersect every point ) X

Interpolation Used for very precise data when curve passes directly through each points The values between points are estimated

Types of Interpolation F(x) The first type is : Linear Interpolation x

Types of Interpolation F(X) Interpolation The second type is : Curvilinear Interpolation Extrapolation X Extrapolation : Goes beyond limits of the data. Interpolation : Goes within limits of the data

Statistics Review 1. Arithmetic Mean ( ): Is the location of the center of the distribution of the data. Sum of in divided data points Number of points

2. Standard derivation ( ): Is a measure of spread for sample a bout the mean Total sum of the squares of the residuals between data points and the mean

2. Variance ( ): Degree of freedom If (n-1) values are know , the remaining value is known also:

3. Coefficient of Variation (C. V): It is a normalized measure of the spread.