Nonlinear Curve Fitting

    Use the change of variables    on all the data points and obtain

          for  .  

Fit the points   with a "least squares line" of the form  .  

Comparing the equations    we see that  .  Thus

        

are used to construct the coefficients which are then used to "fit the curve"  

            

to the given data points    in the xy-plane.

Data Linearization Method for a Power Function Curve Fitting.  

    Fit the curve    to the data points  .  

Taking the logarithm of both sides we obtain  ,  thus

        .  

Introduce the change of variable  .  Then the previous equation becomes  

          

which is a linear equation in the variables X and Y.  

    Use the change of variables    on all the data points and obtain

          for  .  

Fit the points   with a "least squares line" of the form  .  

Comparing the equations    we see that  .  Thus

        

are used to construct the coefficients which are then used to "fit the curve"  

            

to the given data points    in the xy-plane.