Add graph by least squares fit

Graph window	Edit menu
Add Graph by Least Squares Fit

Perform a least squares fit, i.e. fit the best line, through values that are available in the table.

Before you can use this option, the graph window should already display a point graph of 2 value columns of a table. For more information, see Create a graph.

This dialog box appears:

when you choose the Add Graph Least Squares Fit command from the Edit menu in a graph window;
when you click the arrow next to the Add Graph button in the toolbar of the graph window, and choose the Least Squares Fit command;
when you use the right mouse button in the white space of the Graph Management pane, and choose the Add Graph Least Squares Fit command from the context-sensitive menu.

Dialog box options:

X-column:	Select a value column which contains the independent variable. This is the same column that is probably used for the X-values in the current point graph.
Y-column:	Select a value column which contains the dependent variable. This is the same column that is probably used for the Y-values in the current point graph.
Function:	Select a function that should be used to calculate the least squares fit. The following functions are available: Exponential, Logarithmic, Polynomial, Power Law, and Trigonometric. For more information, see below.
Nr. of terms:	When using the Polynomial or Trigonometric function, specify the number of terms that the function should use.

The least squares fit is calculated and the result is directly shown as a line graph in the graph window.

The resulting least squares fit equation is shown in the Graph Options - Least Squares Fit dialog box.

Available functions:

Exponential:	y = a * e^bx
Logarithmic:	y = a * log(b* x)
Polynomial:	y = a + b* x + c* x² + d* x³ + ...
Power Law:	y = a * x^b
Trigonometric:	y = a + b * cos(x) + c * sin(x) + ...

Examples:

Example 1:

The values of column ColX and column ColY1 are used to create a Graph from Columns (the red points in Figure 1 below). Then, by adding a Graph by Least Squares Fit, in this case using a polynomial function with 2 terms, the 'best' fit is found through these points (the black line in Figure 1 below).

The resulting formula is Y = 49.101 + 1.276 * X and can be viewed on the Graph Options - Least Squares Fit dialog box.

Fig. 1: A least squares fit using a polynomial function. The Least Squares Fit line is defined by Y = 49.101 + 1.276 * X

Example 2:

The values of column ColX and column ColY2 are used to create a Graph from Columns (the red points in Figure 1 below). Then, by adding a Graph by Least Squares Fit, in this case using an exponential function, the 'best' fit is found through these points (the black line in Figure 1 below).

The resulting formula is Y = 42.341302790409 * exp(0.007566547732 * X) and can be viewed on the Graph Options - Least Squares Fit dialog box.

Fig. 2: A least squares fit using an exponential function. The Least Squares Fit line is defined by Y = 42.341302790409 * exp(0.007566547732 * X)

Tips:

To modify the appearance or the name of the least squares fit graph, double-click the least squares fit layer in the Graph Management pane: the Graph Options - Least Squares Fit dialog box will appear.
The resulting least squares fit equation is shown in the Graph Options - Least Squares Fit dialog box.
You can also perform a least squares fit on columns in a table, where the resulting Y-value will be written into a new output column. In the table window, choose the Least Squares command from the Columns menu. For more information, see Table window : Least squares fit.
To adapt the title, the X-axis, or the Y-axis (left or right) of the graph, double-click the appriopriate item in the Graph Management pane or in the graph window itself: the Title, X-axis, Y-axis (left), or the Y-axis (right) dialog box will appear.

The grid lines of the graph can be modified in the X-axis and Y-axis dialog boxes.

To create a new graph in a new graph window, choose Create Graph from the File menu in the graph window: the Create Graph dialog box will appear.
To save the contents of a graph window as a graph, choose Save or Save As from the File menu in the graph window.

Graph window

Add Graph by Least Squares Fit