BUILT-IN MATHEMATICA SYMBOL

# 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.

## DetailsDetails

• The data can have the form , where the number of coordinates , , ... 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[{f1, f2, ...}, {1, x, x^2}, x] gives a quadratic fit to a sequence of values . The result is of the form , where the are real numbers. The successive values of needed to obtain the are assumed to be 1, 2, ... . »
• Fit[{{x1, f1}, {x2, f2}, ...}, {1, x, x^2}, x] does a quadratic fit, assuming a sequence of values . »
• Fit[{{x1, y1, f1}, ...}, {1, x, y}, {x, y}] finds a fit of the form . »
• Fit always finds the linear combination of the functions in the list funs 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. »

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Here is some data:

Find the line that best fits the data:

 Out[2]=

Find the quadratic that best fits the data:

 Out[3]=

Show the data with the two curves:

 Out[4]=