Module

for

Nonlinear Curve Fitting

Data Linearization Method for Exponential 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.

Computer Programs  Nonlinear Curve Fitting  Nonlinear Curve Fitting

Example 1.  Fit the curve    to the data points  .
Solution 1.

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.

Example 2.  Fit the curve    to the data points  .
Solution 2.

Example  3.  Often times a  scientist must decide which formula "fits" the data best.
3 (a).  Find both the "exponential fit" and "power fit" for the data points  .
3 (b).  Discuss how this was accomplished and what transformations were used in the process.
3 (c).  Determine which curve fits the data best.
Solution 3.

Old Lab Project (Nonlinear Curve Fitting  Nonlinear Curve Fitting).  Internet hyperlinks to an old lab project.

Research Experience for Undergraduates

Nonlinear Curve Fitting  Nonlinear Curve Fitting  Internet hyperlinks to web sites and a bibliography of articles.

Download this Mathematica Notebook Nonlinear Curve Fitting

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(c) John H. Mathews 2004