Fit• Fit[data, funs, vars] finds a least-squares fit to a list of data as a linear combination of the functions funs of variables vars. • The data can have the form {{ ,  , ... ,  }, { ,  , ... ,  }, ... }, where the number of coordinates x, y, ... is equal to the number of variables in the list vars.
• The data can also be of the form { ,  , ... }, with a single coordinate assumed to take values 1, 2, ... .
• The argument funs can be any list of functions that depend only on the objects vars. • Fit[{ ,  , ... }, {1, x, x^2}, x] gives a quadratic fit to a sequence of values  . The result is of the form  +  x +  x^2, where the  are real numbers. The successive values of x needed to obtain the  are assumed to be 1, 2, ... .
• Fit[{{ ,  }, { ,  }, ... }, {1, x, x^2}, x] does a quadratic fit, assuming a sequence of x values  .
• Fit[{{ ,  ,  }, ... }, {1, x, y}, {x, y}] finds a fit of the form  +  x +  y.
• Fit always finds the linear combination of the functions in the list forms that minimizes the sum of the squares of deviations from the values  .
• See also: Interpolation, LocateMinimum, SolveEquation.
Examples Using InstantCalculatorsHere are the InstantCalculators for the Fit function. Enter the parameters for your calculation and click Calculate to see the result.
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You will have to evaluate the following cells in this example to generate the data used for the plots. Here is a table of the fifteenth through the twentieth Fibonacci numbers. Here is a plot of this data.
This gives a quadratic fit to the data.
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Here is a plot of the quadratic fit.
This shows the quadratic fit superimposed on the original data.
Clear the variable definitions. This gives a table of the values of an exponential function for x from 1 to 10 in steps of 1.
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This fit recovers the original functional form.
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If you include other functions in the list, Fit determines that they occur with small coefficients.
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Clear the variable definition.
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