Nonlinear Regression Curve Fitting

In summary, the conversation is about a person seeking help with fitting data to the Drude-Smith model for conductivity. They have a large set of data points and need values for fitting parameters. They plan to use algebra to split the equation into real and imaginary components, but are unsure how to fit it. They mention using MATLAB and suggest starting with the mathworks website for help.
  • #1
Yosty22
185
4
This isn't a precise homework question, but this seemed like the most reasonable place to post. If not, please feel free to move it.

I have a large set of data points that should fit to a known equation (the Drude-Smith model for conductivity)

The equation the data should fit to is: σ(ω) = (ε0ωp2τ)/(1-iωτ) * [1+Σ(cn)/(1-iωτ)].

I have all of the data, so I have hundreds of data points for σ(ω). I need to have values for other fitting parameters, namely ωp, cn, and τ. To make it solvable, I figure I can do some algebra on the above equation to split it into real and imaginary components, then let ωp be constant. Then, I technically have 2 "equations" (1 real 1 imaginary)and 2 "unknowns" (cn and τ). However, I am unsure how to fit this. Any help would be appreciated.

Note: I will be using MATLAB.
 
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  • #2
Yosty22 said:
This isn't a precise homework question, but this seemed like the most reasonable place to post. If not, please feel free to move it.

I have a large set of data points that should fit to a known equation (the Drude-Smith model for conductivity)

The equation the data should fit to is: σ(ω) = (ε0ωp2τ)/(1-iωτ) * [1+Σ(cn)/(1-iωτ)].

I have all of the data, so I have hundreds of data points for σ(ω). I need to have values for other fitting parameters, namely ωp, cn, and τ. To make it solvable, I figure I can do some algebra on the above equation to split it into real and imaginary components, then let ωp be constant. Then, I technically have 2 "equations" (1 real 1 imaginary)and 2 "unknowns" (cn and τ). However, I am unsure how to fit this. Any help would be appreciated.

Note: I will be using MATLAB.

Did you start with the mathworks website? http://www.mathworks.com/help/stats/nonlinear-regression-1.html

Do you already have any code written?
 

1. What is nonlinear regression curve fitting?

Nonlinear regression curve fitting is a statistical method used to model the relationship between two or more variables that are not linearly related. It involves finding the best-fitting curve that describes the relationship between the variables, rather than a straight line. This technique is commonly used in data analysis and is particularly useful when the relationship between the variables is complex or nonlinear.

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

The main difference between nonlinear regression curve fitting and linear regression is the type of relationship being modeled. Linear regression is used when the relationship between the variables is linear, meaning one variable is directly proportional to the other. Nonlinear regression, on the other hand, allows for more complex relationships that cannot be described by a straight line.

3. What are the advantages of using nonlinear regression curve fitting?

Nonlinear regression curve fitting allows for a more flexible and accurate representation of complex relationships between variables. It also allows for better prediction and estimation of values beyond the range of the observed data. Additionally, it can handle outliers and non-normal data better than linear regression.

4. What are some common techniques used for nonlinear regression curve fitting?

There are several techniques used for nonlinear regression curve fitting, including the Gauss-Newton method, the Levenberg-Marquardt algorithm, and the Nelder-Mead algorithm. These methods use different approaches to find the best-fitting curve, such as minimizing the sum of squared errors or maximizing the likelihood function.

5. How do I know if nonlinear regression curve fitting is appropriate for my data?

Nonlinear regression curve fitting is appropriate when there is a clear nonlinear relationship between the variables being studied. This can be determined by visually examining the data or by performing a statistical test to check for linearity. Additionally, it is important to have a sufficient amount of data to accurately estimate the parameters of the model.

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