Hello, Dear colleagues
Please I need your help,
Could you tell me, what's the interest and why we use the Residuals plot (for statistical study).
It tells you the amount and direction that your control is weakest in. You can use this info to tighten up your control network if the residuals are too high.
Plots of the residuals primarily assist in analysis of a least squares solution and blunder detection. Histograms will show skew and clusters of residuals. Ideally, systematic errors and blunders will not be present in the dataset, leaving you with random error, which in theory should plot as a normal curve. There are some methods to calculate a theoretical cut-off for maximum acceptable size of the residuals, which you can use to decide whether to accept an observation, or remove it from the dataset and re-run the adjustment.
However, standardized residuals (rather than the raw residuals) are generally more useful for determining whether or not an observation is likely a blunder. There are a couple of methods available, such as data snooping and the tau criterion, for computing the cut-off point.
XyHT had an excellent 4-part series on the subject. Here's the first one (has links to the rest of the series at the bottom):
I could not find the post by Jim Frame but a good example of the utility of plotting data is here:
Outlier detection is greatly simplified via the use of graphs. In GPS data processing high-end tools include residual plots to analyze data and detect outliers. While detecting and fixing cycle slips are highly automated nowadays, in the “old days” we had to manually (creating an edit file) fix cycle slips.
As for the the topic of the statistics of residuals, I recommend:
- Allen J Pope paper.
The source of the graphic (that also includes a good discussion of precision v accuracy) is here:
Another example of the utility of plotting from XKCD...