Linear Regression Analysis

If you have followed the directions for looking at the native sample file, you should have a screen that shows two windows, the main (graph) window and the data window. Note that the data window is a "Dockable" window, which can either float free or be attached to the main window. The default is for it to float free, so you should have something that looks like this :  Note that clicking on the double-window icon on the top of the "Regression Statistics" window will dock it to the main window.

Looking first at the main window, we see that it displays the scattergram of the two chosen fields. At the bottom of the window is an "Odometer", which shows the position of the cursor when it is over the graph. This is useful for finding the values of a point on the screen. If the "Delta" box is checked, the odometer will be zeroed when you click the mouse anywhere in the graph, and the odometer will then report the distance from that point. 

The fields shown in the data window are:

Mean and SD (Standard Deviation): These are computed for each axis.

Regression Data: The regression slope (Y/X) and regression intercept are shown, along with their standard deviations.

Correlation Statistics: The Standard Error of the Mean for Y is shown, both in relative and absolute terms. Pearson's r-value, "student" t-value and the p-value are also given.

Just below the box are menus for setting the plot mark, plot color and line type. Experiment with them to see what happens. After you choose some new settings, click on the "Apply" button for them to take effect. Note that all data sets are shown in the graph window (in this case, there is only one), but only a single set is shown in the "Regression Statistics" window. If there is more than one data set, its statistics can be seen by selecting the set from the upper selection menu. 

Zooming In:

A portion of interest in the graph may be selected by simply left-clicking, holding and dragging to outline an area to be expanded:

The graph axes will be reset to approximately the bounds chosen. Note that nothing will happen if too small an area is selected. To look at a very tiny area, you will need to select more than one time in succession.

This is the area selected as shown above. Note that the sizing algorithm adjusts the axes to rounded values.

Setting Specific Axis Values:

The original window, as created, was auto-scaled to show all of the data points. This often the optimal presentation, but it is also possible to set any axis values.

To do this, choose "Set Axes..." from the "Graph" menu.

To go back to the original axes, choose "Reset Axes" from the "Graph" menu. 

Comparing Data Across Graphs:

An extremely useful capability of DataPlus is the ability to visualize how data from one graph relates to another.  This is possible because the DataPlus console acts as a data server and allows communication between all tools launched from it. NOTE that this only applies if the tools were launched by clicking on their launch buttons; if the tools are started separately, they will perform analyses on their own, separately saved data sets, but they won't be able to communicate with other tools.

To begin, close the regression plot application and open a new data set in the console, "series_2" in the "Samples" folder. Then, select  the X and Y fields as shown ("Population" and "Result") and click the regression launch icon.

Then, create another regression graph by changing the fields to "Pop_2" and Pop_2_Result" and clicking the regression analysis icon. To clear up the screen clutter, you may want to hide the regression data by clicking the upper-right 'Close' icon on the data display panels.

You should now have two graph windows which look like this:

Marking Data:

At first glance, there is no obvious relationship between the populations, but we can use the selection and data marking capabilities of DataPlus to see if there is. First, right-click the mouse button and drag the outline  box as show. Note that the cursor changes to a cross; this shows that you are in a data selection mode. When the mouse button is released, the data points in the selected area are collected and presented in a dialog:

The Mark Dialog contains a list of the data points which were in the selection window. The record identifier, if any, is shown first, followed by the X and Y data coordinates. In this exercise, we will mark those points. 'Mark' is the default selection of the three available in the lower-left menu. Click on the "Mark Color" button (now black), and a color selection panel will appear. Choose red and note the color button changes to red as shown.  This shows the color which will be applied to the selected points. Click on the "OK button.

What happens is that the record keys of the selected data points and the marking information are sent to ALL DataPlus programs currently running which were launched from the DataPlus console. In our case, it is the two regression plot applications plus the DataPlus Console itself.  The other choices are:

Suppress: This removes the point from the graph and from the analysis.

Delete: This also suppreses the point, but if the data set is saved, the record is permanently deleted from that set. Note that this can be very useful for 'cleaning up' a data set. If the DataPlus Console is enabled for marking, and if bad data records are 'Deleted' in one of the analysis tools, the 'deleted' records won't be shipped to any other analysis tools. The deletion can be removed by the 'Unselect' menu item in the 'Data' menu up until the set is saved to a file.

Note now that the points selected on the lower left of the left-most graph are marked in red. Most importantly, note that there are points on the right-most graph which are also marked. These are points from the same record (row). The information here is that the points selected as being low on both the X and Y axes in the first graph are also those which bias the results of the second measurements toward the low side. This trend can be confirmed by selecting the upper-right points of the first graph and marking them green - try it - you will see the upper-biased points of the second graph be marked green as well.

 In the DataPlus Console, there is a selection in the 'Data' menu, "Allow Data Marking". If this is checked, the message directs the applications to mark the chosen data points in the data base itself. When a new application is launched, the selected records will already be marked (or suppressed/deleted).

Using Multiple Data Sets:
 
A number of related sets may be examined in the same graph as long as the axes are the same. (Actually, they don't have to be the same, but since they are plotted on the same axis, it would be very confusing if they were represented totally different things). For example, if experiments are run on two separate days, it is often good to simultaneously examine the results to see any variation. The following example illustrates this:
In the DataPlus Console, open the data file "smallseries" and select "Population" for the X-axis and "Result" for the Y-axis. Then, choose "Import Data..." from the file menu and load the file "Values_2". This is a tab-separated text file which is parsed by the application, which found two fields and 100 data points. The two data sets appear as tabbed panels:

The result should look like this:

Notice that the regression analysis launch icon is dimmed; this is because both data sets must have the X and Y data sets selected. Click on the "Values_2" tab and set the fields as shown.. Then, click the regression analysis button, and a display showing both sets of data will appear, and each have their own set of regression data and regression lines:

Only one set of statistics is shown at a time. To see a particular set, simply select it from the menu in the "Regression Statistics" menu. If two data sets are closely related, as these are, they can have separate colors or markers. For this instance, choose the green color and  "+" plot mark for "Vaules_2" and click "Apply". All of the data points and the regression line are colored. This can be done with any number of data sets. Please keep in mind this is not the same as marking the records which we did previously; it only applies to the data records currently showing. Also keep in mind that if a 'marked' data point has the same color as a data set, you will not be able to tell the difference!

If you wish to see what the data looks like when analyzed as a single, combined set, choose "Combine Data Sets..." from the "Data" menu. You will receive a warning that this is permanent, so save before doing this if having separate sets is important. Here is the combined set; note that there is now only a single regression line, which represents the linear regression of the combined sets.

Saving and Printing Data

Saving and Printing choices are found in the "File" menu. Printing acts like one would expect. Saving allows the regression plot tool to keep both its data and settings. The file created will not contain all of the fields found in the DataPlus Console and can only be opened by the regression tool. There is also a particularly helpful option "Save As a Picture...", which saves the plot and statistical panels as a '.png' file, which can be pasted into a document. The picture size will be exactly that of the graph portion of the graph window; the odometer is not shown. A separate data panel (just the data itself) will be saved for each data set.

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