Numerical Curve Fitting The Method of Least Squares Regression

Numerical Curve Fitting The Method of Least Squares (Regression) 

Graphical techniques have lost fevor because of the availability of computers and software packages that make numerical procedures much less tedious than graphical techniques. Furthermore, numerical procedures are less subjective and are usually more accurate than graphical procedures. The method of least squares is a numerical procedure for finding a continuous fimction to represent a set of data points. Our data points are represented by ordered pairs of numbers, (j i, yi), fe, y2), (x3, ys), etc. where x is the independent variable. We assume that there is some fimction 

We define the residual for the ith data point as the difference between the measured value and the value of the function at that point  

This is a set of simultaneous equations, one for each parameter. For some families of functions, these simultaneous equations are nonlinear equations and are solved by successive approximations. For linear functions or polynomial functions, the equations are linear equations, and we can solve them by the methods of Chapter 10. 

In the method of linear least squares or linear regression, we find the linear function that best fits our points. If we have a nonlinear function, we might have a theory that produces a linear dependence linearize) by changing variables. The family of linear functions is given by 

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