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 Documentation / Mathematica / Built-in Functions / Numerical Computation / Data Manipulation  /
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 .
  • Exact numbers given as input to Fit are converted to approximate numbers with machine precision.
  • See the Mathematica book: Section 1.6.6Section 3.8.1.
  • See also Implementation NotesA.9.44.25MainBookLinkOldButtonDataA.9.44.25.
  • See also: Interpolation, InterpolatingPolynomial, Solve, PseudoInverse, QRDecomposition, FindMinimum.
  • Related packages: Statistics`NonlinearFit`, Statistics`LinearRegression`.

    Further Examples

    You will have to evaluate all the cells in this example to regenerate the data used for the plots.
    Here is a table of the first 20 primes.

    In[1]:=

    Here is a plot of this data.

    Evaluate the cell to see the graphic.

    In[2]:=

    This gives a quadratic fit to the data.

    In[3]:=

    Here is a plot of the quadratic fit.

    Evaluate the cell to see the graphic.

    In[4]:=

    This shows the quadratic fit superimposed on the original data. The quadratic fit is better than the linear one.

    Evaluate the cell to see the graphic.

    In[5]:=

    This gives a table of the values of an exponential function for x from 1 to 10 in steps of 1.

    In[6]:=

    Out[6]=

    This fit recovers the original functional form.

    In[7]:=

    Out[7]=

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

    In[8]:=

    Out[8]=

    You can use Chop to get rid of the terms with small coefficients.

    In[9]:=

    Out[9]=

    In[10]:=