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Chapter 161

Scatter Plots
Introduction
The x-y scatter plot is one of the most powerful tools for analyzing data. NCSS includes a host of features to
enhance the basic scatter plot. Some of these features are trend lines (least squares) and confidence limits,
polynomials, splines, loess curves, border box plots, and sunflower plots. Following are examples of scatter plots
that you can create with this procedure. Instructions on how to create each are given later.

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Scatter Plots

Data Structure
A scatter plot is constructed from two variables. A third variable may be used to divide the first two variables into
groups (e.g., age group or gender). No other constraints are made on the input data. Note that rows with missing
values in one of the selected variables are ignored.

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Scatter Plots

Procedure Options
This section describes the options available in the Scatter Plot procedure.

Variables Tab
This panel specifies which variables are in the scatter plot.

Variables
Vertical Variable(s)
Enter one or more vertical variables. If more than one variable is entered, the number of plots is determined by the
Overlay option.
Horizontal Variable(s)
Enter one or more horizontal variables. If more than one variable is entered, the number of plots is determined by
the Overlay option.
Grouping (Symbol) Variable
This variable may be used to separate the observations into groups. For example, you might want to use different
plotting symbols to distinguish observations from different groups. You designate the grouping variable here.
Each unique value of this column is plotted with a different symbol. The symbols are selected by clicking on the
plot format button and then clicking on the symbol format button.
Data Label Variable
A data label is text that is displayed beside each point. A column containing the data labels is specified here. The
values may be text or numeric. The data labels will not be shown unless you activate them by clicking the plot
format button and checking “Labels.”
Plot Overlay
This option is used when multiple vertical and/or horizontal variables are entered to specify whether to overlay
specified plots onto a single plot. Possible choices are:

• None
No plots are overlaid. Each combination of horizontal and vertical plots produces its own separate plot.

• Multiple Vertical
All vertical variables are combined onto one plot. A separate plot is drawn for each horizontal variable.

• Multiple Horizontal
All horizontal variables are combined onto one plot. A separate plot is drawn for each vertical variable.

• Series of Paired
Each sequential pair of horizontal and vertical variables is combined onto one plot.

• Series: No Overlay
A series of plots are drawn using each vertical and horizontal variable in sequence. The first vertical variable
is matched with the first horizontal variable, the second vertical with the second horizontal, and so on.

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Format Options
Variable Names
This option selects whether to display only variable’s name, label, or both.
Value Labels
This option selects whether to display only values, value labels, or both. Use this option if you want the group
variable to automatically attach labels to the values (like 1=Yes, 2=No, etc.).

Scatter Plot Format

Format
Click the format button to change the plot settings (see Scatter Plot Window Options below).
Edit During Run
Checking this option will cause the Scatter Plot Format window to appear when the procedure is run. This allows
you to modify the format of the graph with the actual data.

Symbol Size Options

Symbol Size Variable
This optional variable can be used to specify a proportional size for the data points.

Scatter Plot Window Options

This section describes the specific options available on the Scatter Plot window, which is displayed when the
Scatter Plot button is clicked. Common options, such as axes, labels, legends, and titles are documented in the
Graphics Components chapter.

Scatter Plot Tab

Symbols Section
You can modify the shape, color, and size of the plot symbols. To change them, click the Symbol Format button
to display the Symbol Format window. Here are some of the graphics effects that can easily be achieved.

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Linear Regression Section

You can add regression lines, residuals, confidence limits, confidence bands, prediction limits, and probability
ellipses to the plot using the options available in this section. The technical details of how these items are
calculated are presented in the Linear Regression and Correlation chapter.

Estimation Section
With these options, you can set the resolution of any curved lines (such as confidence limits and polynomial fits).
You can also force the regression line to pass through the origin.

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Data Point Labels Section

You can display data labels next to the symbols.

More Lines Tab

Alternative Linear Regression Lines Section

You can add other types of regression lines to the plot using the options available in this section. A popular
alternative to linear regression is curvi-linear regression. Other possible lines are orthogonal (principal
components) regression, robust regression through the medians, and robust regression through the quartiles.

Smooth Lines Section

You can add loess smooth and median smooth lines using the options available in this section.
The loess smooth line is documented in the Linear Regression and Correlation chapter.
The median smooth is analogous to the moving average. It is computed using running medians instead of running
means.

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Connect Data Points Section

You can connect the symbols with a line. Along with setting the format of the connecting line, this section also
lets you specify the order in which the points are connected. The connection can be done with a straight line or a
curved spline.

45º Line
You can connect the symbols with a line. Along with setting the format of the connecting line, this section also
lets you specify the order in which the points are connected. The connection can be done with a straight line or a
curved spline.

Points-to-Axis Tab

Tick Marks for each Data Point Section

You can display a tick mark along each axis for each point.

Lines from each Data Point Section

You can display a line between the data point and an axis.

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Bars from each Data Point Section

You can display bars between data points and an axis.

Mean Extension Lines Section

You can display horizontal and vertical lines at the group means.

Border Plots Tab

X and Y Axis Sections

You can display box plots, density plots, dot plots, and histograms in the border of each axis.

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Sunflower Tab

Sunflower Density Section

You can display a sunflower grid over the points on the plot. This technique was developed for when you have
many, many overlapping points on the plot. Instead of showing the points, flowers are shown in which the number
of petals is proportional to the number of points falling in the grid cell.

Titles, Legend, X Axis, Y Axis, Grid Lines, and Background Tabs

Details on setting the options in these tabs are given in the Graphics Components chapter.

Example 1 – Creating a Scatter Plot

This section presents an example of how to generate a simple scatter plot. The data used are from the Size dataset.
We will create a scatter plot of variables Weight versus Height.
You may follow along here by making the appropriate entries or load the completed template Example 1 by
clicking on Open Example Template from the File menu of the Scatter Plots window.

1 Open the Size dataset.

• From the File menu of the NCSS Data window, select Open Example Data.
• Click on the file Size.NCSS.
• Click Open.

2 Open the Scatter Plots window.

• Using the Graphics menu or the Procedure Navigator, find and select the Scatter Plots procedure.
• On the menus, select File, then New Template. This will fill the procedure with the default template.

3 Specify the variables.

• Double-click in the Vertical Variable(s) text box. This will bring up the variable selection window.
• Select Weight from the list of variables and then click Ok. “Weight” will appear in the Vertical
Variable(s) box.
• Double-click in the Horizontal Variable(s) text box. This will bring up the variable selection window.
• Select Height from the list of variables and then click Ok. “Height” will appear in the Horizontal
Variable(s) box.

4 Run the procedure.

• From the Run menu, select Run Procedure. Alternatively, just click the green Run button.

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Scatter Plot Output

Example 2 – Scatter Plot with a Regression Line and Prediction

Limits
This section presents an example of how to generate a simple scatter plot with a regression line and prediction
limits. The data used are from the Size dataset. We will create a scatter plot of variables Weight (Y) versus Height
(X).
You may follow along here by making the appropriate entries or load the completed template Example 2 by
clicking on Open Example Template from the File menu of the Scatter Plots window.

1 Open the Size dataset.

• From the File menu of the NCSS Data window, select Open Example Data.
• Click on the file Size.NCSS.
• Click Open.

2 Open the Scatter Plots window.

• Using the Graphics menu or the Procedure Navigator, find and select the Scatter Plots procedure.
• On the menus, select File, then New Template. This will fill the procedure with the default template.

3 Specify the variables.

• Double-click in the Vertical Variable(s) text box. This will bring up the variable selection window.
• Select Weight from the list of variables and then click Ok. “Weight” will appear in the Vertical
Variable(s) box.
• Double-click in the Horizontal Variable(s) text box. This will bring up the variable selection window.
• Select Height from the list of variables and then click Ok. “Height” will appear in the Horizontal
Variable(s) box.

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4 Turn On the Regression Line and Prediction Limits

• Click the Scatter Plot Format button. This will bring up the scatter plot format window.
• Check the Regression Line box to turn on the display of the regression line.
• Check the Prediction Limits – Fill box to turn on the display of the prediction limits shaded region.
• Click the OK button to save the updated settings and close the Scatter Plot Format window.

5 Run the procedure.

• From the Run menu, select Run Procedure. Alternatively, just click the green Run button.

Scatter Plot Output with Regression Line and Predicition Limits

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Example 3 – Scatter Plot with a Regression Line, Prediction

Limits, and Border Plots
This section presents an example of how to generate a simple scatter plot with a regression line, prediction limit,
and border plots (box plots and dot plots). The data used are from the Size dataset. We will create a scatter plot of
variables Weight (Y) versus Height (X).
You may follow along here by making the appropriate entries or load the completed template Example 3 by
clicking on Open Example Template from the File menu of the Scatter Plots window.

1 Open the Size dataset.

• From the File menu of the NCSS Data window, select Open Example Data.
• Click on the file Size.NCSS.
• Click Open.

2 Open the Scatter Plots window.

• Using the Graphics menu or the Procedure Navigator, find and select the Scatter Plots procedure.
• On the menus, select File, then New Template. This will fill the procedure with the default template.

3 Specify the variables.

• Double-click in the Vertical Variable(s) text box. This will bring up the variable selection window.
• Select Weight from the list of variables and then click Ok. “Weight” will appear in the Vertical
Variable(s) box.
• Double-click in the Horizontal Variable(s) text box. This will bring up the variable selection window.
• Select Height from the list of variables and then click Ok. “Height” will appear in the Horizontal
Variable(s) box.

4 Turn On the Regression Line and Prediction Limits

• Click the Scatter Plot Format button. This will bring up the scatter plot format window.
• Check the Regression Line box to turn on the display of the regression line.
• Check the Prediction Limits – Fill box to turn on the display of the prediction limits shaded region.

5 Turn On the Border Plots

• Click the Border Plots tab button. This will bring up the border plots window.
• Check the X Axis – Box Plot box to turn on the display of the horizontal box plot.
• Check the X Axis – Density Plot box to turn on the display of the horizontal density plot.
• Check the X Axis – Dot Plot box to turn on the display of the horizontal dot plot.
• Check the Y Axis – Box Plot box to turn on the display of the vertical box plot.
• Check the Y Axis – Density Plot box to turn on the display of the vertical density plot.
• Check the Y Axis – Dot Plot box to turn on the display of the vertical dot plot.
• Click the OK button to save the updated settings and close the Scatter Plot Format window.

6 Run the procedure.

• From the Run menu, select Run Procedure. Alternatively, just click the green Run button.

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Scatter Plot Output with Regression Line, Predicition Limits, and Border
Plots

Example 4 – Scatter Plot with a Loess Line

This section presents an example of how to generate a simple scatter plot with a Loess line. The data used are
from the Size dataset. We will create a scatter plot of variables Weight (Y) versus Height (X).
You may follow along here by making the appropriate entries or load the completed template Example 4 by
clicking on Open Example Template from the File menu of the Scatter Plots window.

1 Open the Size dataset.

• From the File menu of the NCSS Data window, select Open Example Data.
• Click on the file Size.NCSS.
• Click Open.

2 Open the Scatter Plots window.

• Using the Graphics menu or the Procedure Navigator, find and select the Scatter Plots procedure.
• On the menus, select File, then New Template. This will fill the procedure with the default template.

3 Specify the variables.

• Double-click in the Vertical Variable(s) text box. This will bring up the variable selection window.
• Select Weight from the list of variables and then click Ok. “Weight” will appear in the Vertical
Variable(s) box.
• Double-click in the Horizontal Variable(s) text box. This will bring up the variable selection window.
• Select Height from the list of variables and then click Ok. “Height” will appear in the Horizontal
Variable(s) box.

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4 Turn On the Loess Line

• Click the Scatter Plot Format button. This will bring up the scatter plot format window.
• Click the More Lines tab to bring up the More Lines options.
• Check the Loess box to turn on the display of the Loess line.
• Click the OK button to save the updated settings and close the Scatter Plot Format window.

5 Run the procedure.

• From the Run menu, select Run Procedure. Alternatively, just click the green Run button.

Scatter Plot Output with Loess Line

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Example 5 – Scatter Plot with 3D Symbols of Varying Sizes and

Gradient Interior
This section presents an example of how to generate a scatter plot with 3D symbols of varying sizes and a
gradient-filled interior background. The data used are from the FISHER dataset. We will create a scatter plot of
variables SepalLength (Y) versus SepalWidth (X) by Iris (G).
You may follow along here by making the appropriate entries or load the completed template Example 5 by
clicking on Open Example Template from the File menu of the Scatter Plots window.

1 Open the Fisher dataset.

• From the File menu of the NCSS Data window, select Open Example Data.
• Click on the file Fisher.NCSS.
• Click Open.

2 Open the Scatter Plots window.

• Using the Graphics menu or the Procedure Navigator, find and select the Scatter Plots procedure.
• On the menus, select File, then New Template.

3 Specify the variables.

• Double-click in the Vertical Variable(s) text box.
• Select SepalLength from the list of variables and click Ok.
• Double-click in the Horizontal Variable(s) text box.
• Select SepalWidth from the list of variables and click Ok.
• Double-click in the Grouping (Symbol) Variable text box.
• Select Iris from the list of variables and click Ok.

4 Change the Symbols

• Click the Scatter Plot Format button.
• Click the Scatter Plot tab to bring up the Scatter Plot options.
• Click the Symbol Format button at the top of the window to bring up the Symbols Format window.
• Click on the right side of symbol 1 (the red circle) to display the Preset Symbols.
• Select the red 3D symbol in row 7 column 3.
• Click on the right side of symbol 2 (the blue circle).
• Select the blue 3D symbol in row 7 column 8.
• Click on the right side of symbol 3 (the green circle).
• Select the green 3D symbol in row 7 column 6.
• Click the Change All button to bring up the Change All Symbol Properties window.
• Check the Symbol Size and Border Width boxes to display those options.
• Change the Symbol Size to 135.
• Change the Border Width to 1.
• Click OK.
• Click symbol 2 (the blue 3D circle) to display the Symbols Format (Group 2) window.
• Change the Symbol Size to 200.
• Click OK.

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5 Change the Background Color of the Plot Interior

• The Scatter Plot Format window should still be open from step 4. If not, click the Scatter Plot Format
button.
• Click the Background tab to bring up the Background Color options.
• Click the Interior – Specify Fill button to the right of the Fill check box. This will cause the Color Fill
Selection window to be displayed.
• Click on the Quick Fills button at the top of the window.
• Select the light blue gradient in row 6 column 7.
• The Gradient Stops options will now be displayed.
• Click on the right side of the Color button (it is light blue).
• Select the light blue color in row 1 column 7.
• Click OK.
• Click the OK button to save the updated settings and close the Scatter Plot Format window.

6 Run the procedure.

• From the Run menu, select Run Procedure. Alternatively, just click the green Run button.

Scatter Plot Output with 3D Symbols and Gradient Background

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Example 6 – Scatter Plot with Probability Ellipse

This section presents an example of how to generate a scatter plot with overlaid probability ellipses. The data used
are from the FISHER dataset. We will create a scatter plot of variables SepalLength (Y) versus SepalWidth (X) by
Iris (G).
You may follow along here by making the appropriate entries or load the completed template Example 6 by
clicking on Open Example Template from the File menu of the Scatter Plots window.

1 Open the Fisher dataset.

• From the File menu of the NCSS Data window, select Open Example Data.
• Click on the file Fisher.NCSS.
• Click Open.

2 Open the Scatter Plots window.

• Using the Graphics menu or the Procedure Navigator, find and select the Scatter Plots procedure.
• On the menus, select File, then New Template.

3 Specify the variables.

• Double-click in the Vertical Variable(s) text box.
• Select SepalLength from the list of variables and click Ok.
• Double-click in the Horizontal Variable(s) text box.
• Select SepalWidth from the list of variables and click Ok.
• Double-click in the Grouping (Symbol) Variable text box.
• Select Iris from the list of variables and click Ok.

4 Add the Probability Ellipses

• Click the Scatter Plot Format button.
• Click the Scatter Plot tab to bring up the Scatter Plot options.
• Check both the Probability Ellipse box and the corresponding Fill box (to its right).
• Click OK.

5 Run the procedure.

• From the Run menu, select Run Procedure. Alternatively, just click the green Run button.

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Scatter Plot Output with Probability Ellipses

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