Graph Options - Least Squares Fit

Graph window	Graph Management
Graph Options - Least Squares Fit

Modify the name, the appearance (i.e. display options), view the resulting least square fit formula, and/or select another function to recalculate the selected graph by least squares fit.

This dialog box appears:

when you double-click an existing graph by least squares fit in the Graph Management pane;
when you click an existing graph by least squares fit with the right mouse button in the Graph Management pane, and select Graph Options from the context-sensitive menu.

Dialog box options:

Name:	Optionally, modify the name of this graph by least squares fit. The name of the graph layer is visible in the Graph Management pane and in the legend of the graph window.
Line type:	Select a line type in which the graph by least squares fit should be displayed.
Color:	Select a color with which the graph should be displayed. To define your own color, click the little create button or select the 'Custom' item at the bottom of the list; then, the Windows Color dialog box will appear.
Support line:	For line types Single, Dot, Dash, Dash Dot, Dash Dot Dot and Symbol: Select this check box when an extra support line should be drawn below the selected line type. Subsequently, specify the color of the support line in the Background Color list box in this dialog box. Clear this check box when the line should be drawn in a single color.
Background color:	When a support line is specified for line types Single, Dot, Dash, Dash Dot, Dash Dot Dot or Symbol: select an extra color for the support line. For line types Double, Triple or Blocked, select an extra color for the inner part of a double, triple or blocked line.
Line width (mm):	Specify the line width (mm) with which the graph should be drawn in the graph window and in which the graph should be printed. When you accept the default line width of 0.0, the line will be drawn as fine as possible (hair line), i.e using a width of 1 pixel on the screen, and a width of 1 dot on a printer. When a support line is specified, this option refers to the line width of the support line; the selected line type will be drawn as fine as possible.
Block distance (mm):	For line type Blocked: Type a value for the distance between the blocks (mm).
	For line type Symbol: Click the Symbol button to select a symbol, a symbol size, and a rotation. You can use simple symbols or a symbol from any installed symbol font. The Line Symbols dialog box will appear.
Symbol distance (mm):	For line type Symbol: Specify a value for the distance between the symbols.
Function:	Optionally, select another function to recalculate the least squares fit. The following functions are available: Exponential, Logarithmic, Polynomial, Power Law, and Trigonometric. For more information, see the Add Graph Least Squares Fit dialog box.
Nr. of terms:	When using the Polynomial or Trigonometric function, specify the number of terms that the function should use.
Least Squares Fit equation:
	View the resulting formula of the (previous) least squares fit calculation.

Tips:

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 add another graph from formula to the current graph window, choose Add Graph from Formula from the Edit menu in the graph window or click the arrow next to the Add Graph button in the toolbar of the graph window, and choose the Least Squares Fit command; the Add Graph Least Squares Fit dialog box will appear.
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.
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.

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 in 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)

Graph window

Graph Options - Least Squares Fit