Help Me Find Df & k Values Using Non-Linear Regression

[ayildirim10]

Dear everybody,
I wave an equation with datas and want to regress in non linear form with plot.
Would you help me to solve the equation bellow by any softwares, please?
The data, the equation and parameters are given bellow. I want to fit the data to non-linear equation to find Df and k values.
I just need help.
Your sincerely,,

M=Mo + (Mo - Ms)*Pi*8*r*Ms*
a [Sum[((k*r^2 + Pi^2*a n^2)*k*r^2*t -
Pi^2*r^2*a n^2 - (Pi^2*r^2*a) n^2*
Exp[-t*(k*r^2 + a*Pi^2 n^2)/r^2])/(k*r^2 + n^2 a*Pi^2)^2]


n=1000
ms=146.5
mo=11.58
r=0.003975

t m
0 11.58
30 72.61
60 97.89
90 106.05
120 109.63
150 117.02
180 119.57
210 125.99
240 129.56
270 132.85

 

[Dale]

Your equation looks incomplete

 

[quicknote]

Dear [Name],

Thank you for reaching out for help with your non-linear regression problem. I will do my best to guide you in finding the Df and k values using the given data and equation.

First, it is important to note that non-linear regression requires specialized software to fit the data to the equation. Some commonly used software for non-linear regression include R, MATLAB, and Python. You can also use online tools such as Wolfram Alpha or GraphPad Prism.

To begin, let's break down the equation and understand the parameters given. The equation you provided is a non-linear function with two unknown parameters, Df and k. The data given consists of two variables, t and m, which represent time and mass, respectively.

To fit the data to the equation, we will use the method of least squares, which minimizes the sum of the squared differences between the observed and predicted values. This can be done using the software mentioned above.

Once you have chosen your preferred software, you can input the equation and data to perform the non-linear regression. The software will provide you with the best-fit values for Df and k, as well as a plot showing how well the equation fits the data.

I hope this helps you in finding the Df and k values using non-linear regression. If you need further assistance, please feel free to reach out again.

Best,