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Linear Regression with Ordinary Least Squares

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field-dog
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@mark-mayer?ÿ

Thank you for posting this! I watched the video several times, and I posted a comment. Mr. Woolley made some interesting comments concerning how subdivisions are surveyed. I like how he added information to his subdivision map concerning his use of least squares adjustment so that future surveyors can retrace him. Excellent!


 
Posted : January 30, 2022 7:03 am
dave-karoly
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Aw SoCal surveying problems amuse me. Would that things up here fit that well.

Iƒ??ve encountered the systematic shift between lot corners and centerline control he talks about but it was more on the order of 3 tenths.


 
Posted : January 30, 2022 12:54 pm
bernardc
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This topic is thoroughly addressed in a British textbook, Engineering Surveying, Sixth Edition, by Schofield and Breach. See chapter 7. 

https://minersmansion.weebly.com/uploads/2/4/8/5/24858079/engineering_surveying_1.pdf

Here's a small excerpt:

7.3 LEAST SQUARES APPLIED TO SURVEYING
In practical survey networks, it is usual to observe more than the strict minimum number of observations
required to solve for the coordinates of the unknown points. The extra observations are ‘redundant’ and
can be used to provide an ‘independent check’ but all the observations can be incorporated into the solution
of the network if the solution is by least squares.


 
Posted : December 1, 2025 3:28 pm
summerprophet
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Posted by: @chris-bouffard

@rover83 absolutely not.?ÿ The determination would be made on the best available evidence, but, as I have said before, The ROW is where where it is if it were improved in accordance with the original intention, and, sometimes the best fit does not comply with the original intentions.

Are you going to hold the best fit, or, the original intentions?

I have done all the above steps, combining linear regression with helmert's, to determine ROW. In this case, it was high rolling hills and some rock bluffs, with original 4' concrete monuments standing 2.5 feet above the ground. Original survey was done via mule train, in 1928, with subsequent ROW plans stamped in 1933. If I take the entire project as a whole, original control varies from the plan by as much as 300 feet. Even reducing to the best 7 or 8 points, leads itself to residuals of 30 feet or more. 

I began mathematical analysis from one end, using helmerts and linear regression (some points were set on the ROW line, without known stationing, so regression needed), and worked ahead to see when things "started to fall of the rails". From this, I was able to determine 5 different regions of 1-2 miles each that independently had between 3 and 10 control points that deviated by about a foot. A win in my book, and likely FAR more representative of the true intent than just plugging ahead and picking either the left or right-side monuments to hold for your control..... or ignoring the monuments and holding center of highway. 

Just saying the ROW is where it is, is ignorant of the multitudes of different states holding different survey laws, and local historic practices of what those have done before you.  There is never a one size fits all rule to determining ROW*. Do your best practice based on available evidence, and document your steps and methods for those that come behind you.

* (Unless dictated by your state law. The steps outlined here might be outright illegal in other states. )

 


 
Posted : December 1, 2025 5:36 pm
MightyMoe
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@summerprophet 

An important issue to consider with ROW's from the early 1900's era and before is the basis of bearings which may not be stated but is often true north. Longer east-west highways may show considerable convergence angles as a grid is laid over them. Once true north is taken into consideration it can help solve many vexing mis-closures that aren't really there. Not only highways but railroad surveys can be enhanced by applying convergence to retracement of the ROWs. GPS gives an option to quickly follow the found evidence and evaluate if true north was applied to the original layout. 


This post was modified 6 months ago by MightyMoe
 
Posted : December 2, 2025 8:37 am

Landbutcher464MHz
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@summerprophet " If I take the entire project as a whole, original control varies from the plan by as much as 300 feet. Even reducing to the best 7 or 8 points, leads itself to residuals of 30 feet or more."

I am curious. Did your final map follow the concrete monuments or not?


 
Posted : December 7, 2025 12:50 pm
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