Fitting Nonlinear Data to a Linear Equation: Manual Calculation Process

In summary, the speaker is completing an experiment where they need to extrapolate data using nonlinear curve fitting. They have 3 data sets and are required to fit them to a specific equation. They are looking for a hint on how to manually calculate the curve fitting process without using software. The suggested approach is to plug in the data pairs for x and y and solve the linear system of equations to find the unknowns A, B, and C. It is clarified that the problem is linear in the unknowns, but nonlinear in the known x values.
  • #1
Doctor_Doom
14
0
Hey guys I'm completing an experiment and I'm required to extrapolate data by performing nonlinear curve fitting.

I have 3 sets of data: (x1, y1); (x2, y2); (x3, y3).

I'm required to fit the above mentioned sets of data to the following equation :

[PLAIN]http://img245.imageshack.us/img245/8121/37594905.png

In order to gain maximum marks manual operations would be required. Thus I would prefer if someone could provide me with an initial hint on how to start a manual calculation process.

I'm assuming that performing the calculations manually for the curve fitting would not be a huge task due to the fact that there are only 3 sets of data points.

So I'm hoping someone could provide me with the starting hint on how to perform the manual (NO SOFTWARE USED) calculations for the curve fitting of the above equation.
 
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  • #2
Just plug in your data pairs for x and y, and solve the linear system of this three equations for A, B, C.

ehild
 
  • #3
Additionally, the problem isn't nonlinear. The equation is linear in the unknowns A, B, C as implied in ehild's reply. It is nonlinear in x, but the x's are known.
 

Related to Fitting Nonlinear Data to a Linear Equation: Manual Calculation Process

1. What is nonlinear curve fitting?

Nonlinear curve fitting is a statistical technique used to find the best-fit curve for a set of data points that does not follow a linear trend. It involves finding the optimal parameters for a nonlinear equation that can effectively model the data.

2. When is nonlinear curve fitting used?

Nonlinear curve fitting is used when the relationship between the independent and dependent variables in a dataset is not linear. It is commonly used in fields such as physics, chemistry, biology, and economics to analyze and predict complex relationships between variables.

3. How is nonlinear curve fitting different from linear regression?

The main difference between nonlinear curve fitting and linear regression is that nonlinear curve fitting uses nonlinear equations to model the data, while linear regression uses linear equations. Nonlinear curve fitting is also more flexible and can capture complex relationships between variables, whereas linear regression can only model linear relationships.

4. What are the advantages of using nonlinear curve fitting?

Nonlinear curve fitting allows for more accurate predictions and can capture complex relationships between variables that linear regression cannot. It also provides more flexibility in choosing the model equation and can handle a wider range of data types, including non-normally distributed data.

5. What are some common methods for performing nonlinear curve fitting?

There are various methods for performing nonlinear curve fitting, including the Gauss-Newton method, Levenberg-Marquardt algorithm, and the trust region method. These methods use iterative processes to find the optimal parameters for the nonlinear equation that best fits the data.

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