# Understanding the least-squares adjustment summary

This topic applies to ArcEditor and ArcInfo only.

After a least-squares adjustment has been run, a summary of the adjustment results is displayed on the Least Squares Adjustment Summary dialog box. If the adjustment completes successfully, "ADJUSTMENT COMPLETED" is displayed at the top of the Least Squares Adjustment Summary dialog box.

If the adjustment failed to complete, the adjustment report will state, "ADJUSTMENT FAILED." Reasons for the adjustment failure are listed under the statistical reports.

## Project Option Settings summary

Under the Project Option Settings summary, information about adjustment input parameters is listed. These parameters include the coordinate system of the data and tolerances used for bearings and distances. If you checked the Treat dependent lines as standard boundary lines option on the Adjust Coordinates dialog box, Dependent data is set to Yes. If there are historical parcels and lines participating in the adjustment, Historical Data is set to Yes. By default, the boundary of the adjustment is not held fixed. Parcels adjacent to adjusted parcels will receive the same adjustments as the adjusted parcels so that the adjusted parcels can be seamlessly integrated back into the parcel fabric.

If running the adjustment using ArcObjects, you can hold the adjustment boundary fixed by setting the FixBoundary property of PerformAdjustment Method on the ICadastralAdjustment Interface to True.

## Adjustment Statistical Summary

Under Adjustment Statistical Summary, statistical information about the adjustment is listed such as the number of control points used, the number of parcels being adjusted, coordinate residuals, and network redundancy.

You can also get a quick overview of the number of lines that are adjusting outside the specified tolerances as well as any close points and line points that have been found. The Parcel Lines, Close Points, and Line Points reports displayed farther down on the Least Squares Adjustment Summary dialog box will list further details about data that exceeds tolerances.

### Number of unknowns and redundancy

The value listed for the number of unknowns under Adjustment Statistical Summary is a measure of the actual work that is going to have to be done by the least-squares adjustment. For each point in the fabric, there are two unknowns, a correction to the x-coordinate and a correction to the y-coordinate. In addition to the corrections to fabric point coordinates, there is also a parcel rotation correction, which is also an unknown.

The bearings and distances of parcel lines are the "knowns" in the adjustment. An equation is generated for each bearing and each distance. If there is a line point sitting on a parcel line, two bearings are generated for that line, which is why the number of bearings is greater than the number of distances. In the example below, the number of bearings is 1,832, the number of distances is 1,482, and the number of unknowns is 1,177 for this particular adjustment.

Redundancy equals the number of bearings plus the number of distances minus the number of unknowns. For example, in the example above, redundancy equals 1,832 + 1,482 - 1,177, which is 2,137. When the redundancy is greater than the number of unknowns, the least-squares adjustment can determine the best solution as well as flag those lines that are statistically suspect. If the redundancy is the same or less than the number of unknowns, the least-squares adjustment cannot perform well and cannot determine the best solution. In the above example, the parcel network is well conditioned, with redundancy being almost twice the number of unknowns.

### Coordinate residuals

Coordinate shift statistics are also displayed under Adjustment Statistical Summary. The point that received the maximum coordinate shift is listed with the average coordinate shift for all points.

A fabric least-squares adjustment should be run repeatedly until the maximum and average coordinate shifts become 0.0 or do not change.

Each time an adjustment is rerun, an adjustment iteration has been performed. You are iterating an adjustment if you click Run on the Adjust Coordinates dialog box or Accept on the Least Squares Adjustment Summary dialog box, then click Run again on the Adjust Coordinates dialog box to run another adjustment iteration. Once OK is clicked on the Adjust Coordinates dialog box, the adjustment is completed with no more iterations. Once the maximum and average coordinate shifts become 0.0 or do not change, the adjustment has converged to an optimal solution.

## Close Points report

The Close Points report lists those points that lie closer to each other than the specified tolerance and do not have dimensions between them. Close points are a good indication of points that mostly likely should be merged into single, common points.

## Line Points report

The Line Points report lists those line points that are offset from their lines at a greater distance than the specified tolerance. Line points that are significantly offset from their adjacent parcel lines indicate data inaccuracies or incorrect parcel joining.

## Parcel Lines report

The Parcel Lines report lists all those lines that have a bearing or distance that adjusted outside the specified tolerances. The adjustment finds a best fit for all parcel points in the network and computes new coordinates for the parcel points. Parcel line shapes are recomputed using the adjusted parcel points. In the Parcel Lines report below, (c-o) stands for computed minus observed. The computed minus observed value is the difference between the distance or bearing of the recomputed line shape and the original distance or bearing attribute on the line (observed). In other words, the Parcel Lines report is reporting how much difference there is between the adjusted line shape and the original recorded bearing and distance of the line attributes.

Only those lines that are adjusting more than the tolerances specified for Bearings and Distances on the Adjust Coordinates dialog box are listed under the Parcel Lines report. To see the adjustments for every line in the network, select the Extended report type on the Adjust Coordinates dialog box.

Lines that have a bearing or a distance that adjusts more than three times the specified tolerances will cause the adjustment to fail. These lines will be marked with a ## in the Parcel Lines report.

## Plan structure constraints

If you checked either the Line points tolerance or Straight lines tolerance option under Plan Structure Constraints on the Adjust Coordinates dialog box, the least-squares adjustment summary will display a report listing the points moved. Plan structure constraints are postprocessing options and are performed after the adjustment has completed.

### Line points forced to their line

A list of line points that have been moved to their adjacent parcel lines is displayed under Linepoints forced to their line. The distance the line point was moved is also included. If line points were found that were offset from their lines at a greater distance than the specified tolerance, these line points are listed as well.

### Straight lines report

When enforcing straight lines, the adjustment postprocessing examines series of points, which are on adjacent parcels that are part of the same plan and which are connected by lines with the same bearing. A vector for the series of points is computed, and the distance between each point in the series and the vector is measured. If the distance is less than the tolerance specified for straight lines, the point is moved onto the vector line and collinearity is enforced.

## Suspect points and lines

After the adjustment, the standard deviation for all the points and lines in the network is calculated. Those points and lines with standard deviations that are greater than three times the standard deviation of the entire adjusted network are reported in the Suspect points and lines report.