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Data Science Mathematics Wolfram Language

Fitting a data set to an equation to get constants

math p

Posted 10 years ago

Hi, I have a data set with y and x. I have an equation that I want to fit this data to y=a/b(1-e^bx). Can someone tell me how do I plot the data to this equation to get the constants a and b. For a better explanation: Generally when we are given x and y, we can plot this data and use either excel or mathematica etc to get either a linear, polynomial or exponential fit. From those fitted equations we can extrapolate data. In this case, I have a small data set, and I know the function that I want the data to be fit in. From the fit data I want to get the constants in the equation so that I can extrapolate the data. Thanks,

POSTED BY: math p

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David Keith

Posted 10 years ago

In Mathematica, the base of the natural log is E, not e. In[1]:= eq = -36 - 23.1 E^(-39.36 b) + 59.1 E^(-19.38 b) == 0; In[2]:= sol = Solve[eq, b, Reals] During evaluation of In[2]:= Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result. >> Out[2]= {{b -> -0.0209738}, {b -> 0.}} In[3]:= eq /. sol Out[3]= {True, True} However, it would help you get a good response if you would post your code and data. Attaching a notebook and a spreadsheet or CSV file would be good. Best regards, David

In Mathematica, the base of the natural log is E, not e.

In[1]:= eq = -36 - 23.1 E^(-39.36 b) + 59.1 E^(-19.38 b) == 0;

In[2]:= sol = Solve[eq, b, Reals]

During evaluation of In[2]:= Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result. >>

Out[2]= {{b -> -0.0209738}, {b -> 0.}}

In[3]:= eq /. sol

Out[3]= {True, True}

However, it would help you get a good response if you would post your code and data. Attaching a notebook and a spreadsheet or CSV file would be good.

Best regards, David

POSTED BY: David Keith

Jesse Friedman

Jesse Friedman, Wolfram Research

Posted 10 years ago

Is FindFit what you're looking for?

POSTED BY: Jesse Friedman

math p

Posted 10 years ago

Hi, David Thank you very much for the help. Appreciate it. Best wishes,

POSTED BY: math p

David Keith

Posted 10 years ago

Hi math, There are a number of syntax errors you will find corrected below. (Look up FindFit in the help system!) Best, David In[1]:= xData = {19.38, 39.36, 58.62, 78.6, 99, 119.4, 138.6, 158.4, 199.2, 219, 239.4, 259.8, 278.4, 299.4}; yData = {23.1667, 59.1667, 147, 176.667, 228.333, 266.667, 300, 330, 401.667, 413.333, 425, 415, 408.333, 446.667}; In[2]:= (* FindFit wants pairs ) data = Transpose@{xData, yData}; In[3]:= ( the model is an expression for the dependent variable in \ terms of the independent and parameters. Note the space in b x, and \ also the curly braces for lists ) solution = FindFit[data, (a/b)(1 - E^(-b x)), {a, b}, x] Out[3]= {a -> 2.91944, b -> 0.00494724} In[4]:= Show[ListPlot[data, PlotStyle -> Red], Plot[(a/b)(1 - E^(-b x)) /. solution, {x, 19, 450}]] Attachments:*

Hi math,

There are a number of syntax errors you will find corrected below. (Look up FindFit in the help system!)

Best, David

In[1]:= xData = {19.38, 39.36, 58.62, 78.6, 99, 119.4, 138.6, 158.4, 
  199.2, 219, 239.4, 259.8, 278.4, 299.4}; yData = {23.1667, 59.1667, 
  147, 176.667, 228.333, 266.667, 300, 330, 401.667, 413.333, 425, 
  415, 408.333, 446.667};

In[2]:= (* FindFit wants pairs *)
data = Transpose@{xData, yData};

In[3]:= (* the model is an expression for the dependent variable in \
terms of the independent and parameters. Note the space in b x, and \
also the curly braces for lists *)
solution = FindFit[data, (a/b)*(1 - E^(-b x)), {a, b}, x]

Out[3]= {a -> 2.91944, b -> 0.00494724}

In[4]:= Show[ListPlot[data, PlotStyle -> Red], 
 Plot[(a/b)*(1 - E^(-b x)) /. solution, {x, 19, 450}]]

enter image description here

POSTED BY: David Keith

math p

Posted 10 years ago

I used this for Mathematica FindFit[{{19.38`, 39.36`, 58.62`, 78.6`, 99, 119.4`, 138.6`, 158.4`, 199.2`, 219, 239.4`, 259.8`, 278.4`, 299.4`}, {23.16666667`, 59.16666667`, 147, 176.6666667`, 228.3333333`, 266.6666667`, 300, 330, 401.6666667`, 413.3333333`, 425, 415, 408.3333333`, 446.6666667`}}, (y - ((a/b)*(1 - e^(-bx)))), (a, b), (x, y)] Thanks,

I used this for Mathematica

FindFit[{{19.38`, 39.36`, 58.62`, 78.6`, 99, 119.4`, 138.6`, 158.4`, 
   199.2`, 219, 239.4`, 259.8`, 278.4`, 299.4`}, {23.16666667`, 
   59.16666667`, 147, 176.6666667`, 228.3333333`, 266.6666667`, 300, 
   330, 401.6666667`, 413.3333333`, 425, 415, 408.3333333`, 
   446.6666667`}}, (y - ((a/b)*(1 - e^(-bx)))), (a, b), (x, y)]

Thanks,

POSTED BY: math p

math p

Posted 10 years ago

POSTED BY: math p

math p

Posted 10 years ago

I tried Findfit, but in vain. When I take the ratio of 2 x and 2 y's, I get the following equation to solve -36 - 23.1`e^(-39.36` b) + 59.1`e^(-19.38` b) == 0, b but Solve was unable to solve the system with inexact coefficients or the \ system obtained by direct rationalization of inexact numbers present \ in the system. Since many of the methods used by Solve require exact \ input, providing Solve with an exact version of the system may help.

POSTED BY: math p

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