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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 InstantCalculators

Here are the InstantCalculators for the Fit function. Enter the parameters for your calculation and click Calculate to see the result.

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.

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.

This fit recovers the original functional form.

If you include other functions in the list, Fit determines that they occur with small coefficients.

Clear the variable definition.



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