To begin a curve fitting problem, you will first need to provide data. The data can be specified as a collection of points, or as separate collections of $x$-values and $y$-values.  

You may want to import data from a file using Tools>Assistants>Import Data....  For more information on importing data, see the Importing Data section of the Tutorial on Data Manipulation.

If you want to define the data in Maple, you can list the pairs of data, or define a 2-column Array or Matrix containing the data.

After you have provided the data, select the data and choose Curve Fitting>Interactive Curve Fitting from the Context Panel.

You will be asked to provide a name for the independent variable. Then the assistant opens with the data loaded.

Alternatively, you can use the CurveFitting[Interactive] command to call the Curve Fitting Assistant.

$\mathrm{CurveFitting}\[\mathrm{Interactive}\]\left(\left[\left[-5\,5\right]\,\left[0\,2\right]\,\left[4\,0\right]\right]\right)$

Note: It is possible to launch the Curve Fitting Assistant directly from the Tools>Tutors>Statistics menu.  You will then have an opportunity to import the data.  In the Curve Fitting Assistant's first window, click the Import button to use Maple's Import Assistant:

However, this method is less practical because after you close the Curve Fitting Assistant, you cannot review the data or access it for further analysis.

After the data is imported into the Curve Fitting Assistant you can explore different curve fitting methods.  The following data is used in this section:

$\left[1\, 2\, 3\, 4\, 5\, 6\, 7\, 8\right]\, \left[4\, 10\, 22\, 44\, 102\, 190\, 300\, 436\right]$

This window displays a plot of the points, an indication of the vertical range of the plot, and a selection of relevant curve fitting commands to the right.  At the bottom of the window there is a box that displays the interpolant found with the selected curve fitting algorithm.

Note: Rational interpolation is only available if the data contains no decimal values.  Thiele interpolation is available if the dependent variable values in the data are unique.

For the rational interpolation and splines options, sliders allow you to control the maximum degree of the numerator and denominator used in the rational interpolant, or the degree of the spline being used during the curve fitting procedure.

The least squares section provides an input box where you can specify an expression in terms of $x$.  The parameters will be fit by the Least Squares command with values according to this procedure.  Only expressions that are linear in terms of the parameters are allowed.

In this example, enter the expression a*x^2+b*x+c.  Then click the Plot button for the least squares method to see the result.

Click Done to return the interpolant for the least-squares approximation.

$\left[1\, 2\, 3\, 4\, 5\, 6\, 7\, 8\right]\, \left[4\, 10\, 22\, 44\, 102\, 190\, 300\, 436\right]$$\stackrel{\text{curve fitting assistant}}{\to }$$\frac{346}{7}-\frac{1018}{21}x\+\frac{253}{21}{x}^2$

For more information on the least-squares fitting command, see CurveFitting[LeastSquares].

The Curve Fitting Assistant allows you to explore different curve fitting algorithms and easily see the plot of the resulting curve.  This interface also allows for experimenting with setting different settings for the curve fitting procedure.  When you find the curve that you are looking for, you can choose to return the interpolant (equation) or the plot when you finish using the assistant.

The Task Templates show you how to perform this task in Maple using polynomial, rational, spline, B-spline, least squares approximation, or Thiele's continued fraction interpolation methods.  

Insert a Task into a worksheet and replace the placeholders with your information.  (See Using Tasks for details.)

Example: Polynomial Interpolation   Here, the task was inserted with the Insert Default Content button.  This inserts the title and description as well as the example.   To replace the placeholders, place your cursor at the beginning of the first execution group and press tab.  Replace the highlighted data with your data.  Press tab to move to the next placeholder ($x$) and replace with a variable name of your choice. Polynomial Interpolation   Calculate the interpolated polynomial of specified data points. This produces a polynomial of degree n, where n is one less than the number of data points.   Enter a list of data points. >  $\left[\left[\mathrm{-5}\,5\right]\,\left[0\,2\right]\,\left[4\,0\right]\right]$ $\left[\left[-5\,5\right]\,\left[0\,2\right]\,\left[4\,0\right]\right]$ (1)   Specify the independent variable, and then calculate the interpolated polynomial. >  $p:=\mathrm{CurveFitting}\left[\mathrm{PolynomialInterpolation}\right]\left(\,x\right)$ $p:=\frac{1}{90}{x}^2-\frac{49}{90}x\+2$ (2) >  $$ For example, the data gets replaced with 5 new data points and called the variable $t$.   The returned curve is a polynomial of degree 4. >  $\left[\left[0\,0\right]\,\left[2\,-3\right]\,\left[3\,3\right]\,\left[4\,0\right]\,\left[5\,5\right]\right]$ $\left[\left[0\,0\right]\,\left[2\,-3\right]\,\left[3\,3\right]\,\left[4\,0\right]\,\left[5\,5\right]\right]$ (3) >  $p:=\mathrm{CurveFitting}\left[\mathrm{PolynomialInterpolation}\right]\left(\,t\right)$ $p:=\frac{11}{12}{t}^4-10t^3\+\frac{421}{12}{t}^2-39t$ (4) >  $$ Example: Least Squares Approximation   Here, in addition to specifying the data points and the variable name, you can also specify the format of the function to be returned.   The Task shows $a{x}^2\+bx\+c$.  Other examples include $ax\+b$ and  $a^3 x\+b x$. $$ Least Squares Approximation   Calculate a least squares approximation using specified data points.   Least Squares Fit of Data by a Specified Curve List of Data Points: >  $\left[\left[2\,-1\right]\,\left[4\,3\right]\,\left[6\,-7\right]\,\left[7\,5\right]\,\left[9\,-2\right]\right]$ $\left[\left[2\,-1\right]\,\left[4\,3\right]\,\left[6\,-7\right]\,\left[7\,5\right]\,\left[9\,-2\right]\right]$ (5) Fitting Curve: >  $a x^2\+b x\+c$ $a{x}^2\+bx\+c$ (6) Independent Variable: >  $x$ $x$ (7) Least Squares Curve: >  ${\mathrm{CurveFitting}}_{}\left[\mathrm{LeastSquares}\right]\left(\,\,\mathrm{curve}\=\right)\;$ $-\frac{6315}{5071}\+\frac{5975}{10142}x-\frac{669}{10142}{x}^2$ (8)

The Bézier Curves Task Template is an interactive template.  As you draw points, the curve fitting is calculated and shown.

The Interpolation with Equispaced Points Task Template is also interactive: