### 4.2.1. X-Y-Z Scatter Plot

Three columns are selected by clicking on [__X__ axis],
[__Y__ axis] and [__Z__ axis]. Each axis can have the Scale Type Log base 10, Log base e, log based to any user-defined value,
reciprocal, logit, probit, gompit (cloglog) or loglog. It is also possible to
draw bivariate projection plots on X-Y, X-Z and Y-Z planes, error bars in any direction, fit linear regression planes and polynomial surfaces. Contours can be drawn for fitted surfaces.

**Interactive Data Points****:** When the graph is still in Graphics Editor (i.e. before it is sent to Excel or Word), the data
points plotted by this procedure are linked with the data in data matrix (see 2.3.2.3. Interactive Data Points). Move the mouse pointer over a data point and press down the right mouse
button. A tooltip-like information panel will be displayed about that point
until you release the right mouse button. If you are running UNISTAT in Stand-Alone Mode, the row of Data Processor containing this point
will also be highlighted. If the delete key is pressed while highlighting a
point, this point will be excluded from the plot and the graph will be redrawn.
In Stand-Alone Mode, it is also possible to select a row of the
spreadsheet to highlight the points on the graph which belong to this row.

**Missing Values:** Any point with at least one missing
value is treated as missing.

**Unequal Column Lengths:** Columns with different lengths
can be selected for X, Y and Z axes. Any triplet with at least one *no data*
value will be considered as missing.

The Edit options specific to this procedure are as follows:

#### 4.2.1.1. Viewpoint

As in all 3D Plots, you can alter the viewpoint and perspective options for the unit cube (see 2.3.4.6. 3D Viewpoint and Perspective).

#### 4.2.1.2. Contours

When a surface is fitted on the data, contour curves can also be drawn (see 2.3.4.7. Contours).

#### 4.2.1.3. X-Y-Z Points

**Line: **If the Line Type
option is set to Line, then the consecutive x-y-z
points will be connected with straight lines. There is another Line field in the Planes
dialogue, which is used for drawing bivariate projection plots on reference planes (see 4.2.1.4. Planes).

**Symbol: **Hundreds of different types of symbols can be
selected for the x-y-z points (see 2.3.4.5.3. Symbols).
Again, this is not to be confused with the Symbol
field for the Planes dialogue.

**Point Labels****: **Point Labels will be drawn alongside the x-y-z points. As in X-Y Plots, the text for Row Labels are used. If no Row Labels have been entered then the row numbers will be displayed.

#### 4.2.1.4. Planes

This dialogue controls how UNISTAT will draw bivariate plots on X-Y, X-Z and Y-Z planes, connect x-y-z points to reference Planes, and draw symmetric and asymmetric error bars on x-y-z points in any one of six directions.

Click on the desired tab to control the parameters for each plane.

**Line: **This frame is similar to the one in X-Y Plots (see 4.1.1.1.1. Line), except
that the Curve and Frame
options are not available for Line Type.

**Symbol:** Hundreds of different types of Symbols can be selected for the x-y points.

**Point Labels****: **Point Labels will be drawn alongside the x-y points for the
selected plane. As in X-Y Plots, the text for Row Labels are used. If no Row Labels have been entered then the row numbers will be
displayed.

**Connect X-Y-Z Points:** If this box is checked, then
each x-y-z point will be connected to the currently selected plane with a
perpendicular line. On entry, this box will be checked for the X-Y plane.

**Error Bar****s:** This will control error bars in the direction perpendicular to the selected plane. For instance, when the Symmetric Bars option is selected for the X-Y Plane,
then the up and down error bars will be drawn in the positive and negative Z
directions.

One or two data columns containing a dispersion measure
(e.g. standard error, standard deviation) can be selected from the Variable Selection
Dialogue. Error bars can be symmetric, in which case only one column is selected by clicking on [Err __v__ert],
or they can be asymmetric in which case the column containing up-pointing bars
is selected by clicking on [Err __u__p] and the one containing
down-pointing bars is selected by clicking on [Err __d__own]. Although
the *up* and *down* options make sense for the Z direction, they must
be interpreted as *left* and *right* or *in* and *out* for
the X and Y directions.

In Stand-Alone Mode, columns containing means and standard errors for a range of data columns can be generated using the Range Statistics procedure in Data Processor. In Excel Add-In Mode, you can use one of Summary Statistics or Sample Statistics procedures with Output variables in rows option to create data for standard errors or standard deviations.

When calculating the minimum and maximum axis values the program will take error bars into consideration.

#### 4.2.1.5. Surface Fitting

The Edit → Surface Fitting option provides access to three surface fitting options: Linear Regression Plane, Polynomial Surface and Weighted Averages Surface. In the first two cases you will have the option of fitting with or without a constant term.

Residual bars, i.e. the lines connecting each data point to the fitted surface can also be drawn. It is possible to control the colour and thickness of residual bars and whether they are to be displayed or not.

Coefficients of the fitted plane,
as well as its R-squared and standard error values will be displayed in the
legend object. However, since there may be up to 15 coefficients for the
polynomial surface fit, they will not be displayed in the legend. In Stand-Alone Mode, it is also possible to run interpolations on the fitted curve, without having to retype these coefficients, using the Data
Processor’s Reg function (see 3.4.2.6.3. UNISTAT Functions). The same coefficients will also be saved automatically in the file
POLYCOEF.TXT, in the order of constant term (if any), *X^1, X^2, …,Y^1,
Y^2, …, Y^r* for a degree *r* polynomial.

**Linear Regression Plane****:** Output includes R-squared, standard error of regression and the equation of
the plane fitted. When a log option is selected for an axis, the fitted values
calculated using the Data Processor’s Reg
function (see 3.4.2.6.3. UNISTAT Functions) must be transformed back to the original coordinates.

**Polynomial Surface:** The
degree of X and Y variables can be determined independently and the constant
term included or omitted. You must ensure that values of X and Y variables are
not too large to cause a number overflow, particularly with higher degree
polynomials.

Logarithmic and other nonlinear scaling options on X, Y and Z axes are available for polynomial surface fitting, but the contour curves will not be drawn. Coefficients of the fitted equation will be saved to the file POLYCOEF.TXT. It is also possible to run interpolations using the Data Processor’s Reg function (see 3.4.2.6.3. UNISTAT Functions).

**Weighted Average:** For each vertex of the mesh, the Z
value of each point is weighted by the inverse square of its distance from the
vertex, to form an average value for the fitted surface at this vertex.