# Fit

Fit[data,funs,vars]

finds a leastsquares fit to a list of data as a linear combination of the functions funs of variables vars.

# Details

• 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 fi. The result is of the form a0+a1x+a2x^2, where the ai are real numbers. The successive values of x needed to obtain the fi are assumed to be 1, 2, . »
• Fit[{{x1,f1},{x2,f2},},{1,x,x^2},x] does a quadratic fit, assuming a sequence of x values xi. »
• Fit[{{x1,y1,f1},},{1,x,y},{x,y}] finds a fit of the form a0+a1x+a2y. »
• 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 fi. »
• Exact numbers given as input to Fit are converted to approximate numbers with machine precision. »

# Examples

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## Basic Examples(1)

Here is some data:

 In[1]:=

Find the line that best fits the data:

 In[2]:=
 Out[2]=

Find the quadratic that best fits the data:

 In[3]:=
 Out[3]=

Show the data with the two curves:

 In[4]:=
 Out[4]=