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Linear Regression with Ordinary Least Squares

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chris-bouffard
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I'm lost on the reasoning for using the best fit on a ROW, the ROW is the ROW and it is where it is, not where it fits best.


 
Posted : December 9, 2021 3:24 pm
Norman_Oklahoma
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@chris-bouffard?ÿ

You find 8 pins along a right of way. You run the best fit and find that they all fall no more than 0.04' this way or that of a best fit line. Except 1 that falls 1.00 off. You apply the virtual hammer to 7 and call it a straight line. The eighth is a 1 foot offset. Done in 5 minutes.?ÿ Sure, you could reach the same conclusion by fussing with it for a couple hours but why would you want to?


 
Posted : December 9, 2021 4:51 pm
rover83
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Posted by: @chris-bouffard

I'm lost on the reasoning for using the best fit on a ROW, the ROW is the ROW and it is where it is, not where it fits best.

I'll ask the same question I asked upthread: would you / do you place angle points at every single monument you find along a ROW that was platted and/or dedicated as a straight line, no matter the positional tolerance or residuals?


 
Posted : December 9, 2021 5:04 pm
chris-bouffard
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@norman-oklahoma I don't think any of us would have a concern with 0.04, that was not my point.?ÿ The ROW became what it is upon dedication and acceptance.?ÿ If your example of 0.04 fits are not in accordance with the original intention at the time of conveyance, that "fit" is meaningless and thr ROW is where it is.

I recently came completed a survey next door to the father of somebody that developed the block that the father built his home on.?ÿ The father objected to a new home being built on the ajacent lot, even though he did not own it.?ÿ He object from the beginning and when the son developed the block, he sought and got approval for a 20 lot subdivision but refused to pay his Surveyor to momument it.

I (my crews) surveyed surveyed the surrounding blocks around the PIQ and determined that pins found on the father's property were somehow shifted by 2', parralell to the road frontage and on my PIQ.?ÿ He claimed the new home violated the minimum side yard set back by that 2' and wanted to be compensated.

In come the Legal Eagles.?ÿ Fortunately, the Town Engineer and Municipal Attorney were able to understand the proofs laid before them and it was a dine deal with the other Surveyor not even replying to multiple calls and certified mailings to participate in the dispute.

The father's house was on a corner, it had two road frontages, both based on an errant filed plan.?ÿ Do we shift one ROW 2', or do we talk about the original intention??ÿ


 
Posted : December 9, 2021 8:47 pm
chris-bouffard
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@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?


 
Posted : December 9, 2021 9:03 pm

rover83
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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'm going to show the right-of-way based upon what the preponderance of evidence indicates, taking into account intent as well as monumentation, occupation and maintenance.

If monuments are original, have been relied upon, and are within acceptable positional tolerance of the dedicated ("intended") line, taking into consideration local methodology at the time of original survey, a best-fit is most likely the equitable solution and the least likely to disturb either public or private rights.

I wasn't really trying to accuse you or anyone else of poor practice, but merely pointing out that (a) right-of-way/corridor surveying is a bit of a different animal than single-parcel surveying, and (b) there's a bit of inconsistency in us saying "hold the monuments" but also saying "we can't hold a best fit line" even when monumentation is within acceptable tolerance (which admittedly can vary with region) and the ROW is presumed (and dedicated) to be straight.

It gets messy at times, and doesn't work 100% of the time, but there's nothing wrong with using mathematics to assist in striking a ROW line.


 
Posted : December 10, 2021 5:09 am
Jim in AZ
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Posted by: @robertusa

I presume you have located property monuments and want to use a best fit line calculation? Why? Why have software determine the r/w line? To call all points ƒ??offline, which is a best fit, is reprehensible. Make and use your own calculation. Some points will be off by a bit and they shouldnƒ??t be considered.

It may be reprehensible, but it's how our DOT does it...


 
Posted : December 10, 2021 8:39 am
mathteacher
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The NCDOT right of way manual is 447 pages. I haven't read it all, but this little snippet on page 82 caught my eye:

We have more lawyers today and folks have less respect or fear of the state than they once had, so abuse isn't as easy as it once was.?ÿ


 
Posted : December 10, 2021 10:57 am
dmyhill
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Posted by: @mathteacher

We have more lawyers today and folks have less respect or fear of the state than they once had, so abuse isn't as easy as it once was.?ÿ

I do not think that is abuse, it sounds practical. Having a road in front of your property improved is generally a benefit to you. I remember one small triangle of land that needed to be used (maybe 100 square feet). I must have laid that out/refreshed stakes, etc half a dozen times over many years. The amount of pain and money to obtain that small portion of property was outlandish. And in the end, it benefited everyone, even the landowner.?ÿ


 
Posted : December 10, 2021 12:50 pm
geeoddmike
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@gary_g?ÿ

I like this one. It is also from XKCD.


 
Posted : December 10, 2021 1:28 pm

mathteacher
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@dmyhill?ÿ

In many cases, I agree with you. But a dairy farmer who woke up one morning to?ÿ find bulldozers splitting one of his pastures 3/4 - 1/4 did not consider that an improvement. Having 1/4 of his pasture on the other side of a road was crippling to his operation.

North Carolina has always favored roads over people and we have an excellent highway infrastructure. Here's one that began with a law passed in 1987 and was resolved by the NC Supreme Court in 2020.

https://www.howardstallings.com/a-big-win-for-property-owners-and-map-act-claimants-in-north-carolina/

It's just best to get these things finalized early so that property rights are not violated.

?ÿ


 
Posted : December 10, 2021 2:49 pm
field-dog
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Posted by: @ashton

It would seem to me that if you hold the endpoints, the line segment is fully determined.

There was one block corner that was out of position by several feet. If I had held that corner as one of the endpoints without checking its position, the line segment would've been incorrect. The only endpoints, which were block corners only, that I held were the ones I had calculated per plat.


 
Posted : January 28, 2022 8:55 pm
field-dog
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Posted by: @mathteacher

It's good to see consistency among the black boxes.

I recently figured out how to use the best fit line (BFL) routine in MAGNET Field. The offset data, using the point to line routine, agrees with Carlson to within thousandths. The BFL routine is totally graphical. You select points on the program's map after you select the routine's icon; the points "light up" after you select them. After you deselect the routine, a purple, dotted polyline appears in-between the points; this is your BFL. You then select the snap to end icon and select each end of the BFL; coordinates are created for each end point. Use the endpoints as the start and end points in the point to line routine.

What I don't like about the BFL routine is:

  1. It doesn't create a report listing left and right offsets from every selected point near the BFL.
  2. It doesn't number the endpoints starting with any particular number; it should prompt me for the number.
  3. It doesn't let me assign a weight to any point.

?ÿ

What I like about the BFL routine is:

  1. It's totally graphical.
  2. It's easy to use.

 
Posted : January 28, 2022 10:27 pm
field-dog
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Posted by: @mathteacher

It also works on curves, as long as an equation can be defined.

I've moved on to the?ÿbest fit curve (BFC) routine in MAGNET Field; I'm having a difficult time learning how to use it. After I create the BFC, I use the?ÿsnap to center to create a point on the center of the curve. I assume the next step is to check the radial distance from that point to the radius point. Since I'm not currently working on a project that involves a curve, I fabricated a project that includes a curve. I created points along the curve that are on radial offsets to the curve. The radial distance from the BFC to the radius point should be ƒ?? 276', but I keep getting 195'. I don't know what I'm doing wrong.

Edit

I must be tired. The only difference between a BFL and a BFC, is that the later involves radial offsets instead of perpendicular offsets. I still need to relate the BFC to the radius point, and every point along the BFC should be the same radial distance. Would I use towards the radius point, or?ÿaway from the radius point to describe a point's relationship to a BFC?


 
Posted : January 28, 2022 10:54 pm
mathteacher
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First things first. Be sure that you know the meanings of?ÿradial distance, radial offset, and?ÿradius point.

This video shows the development of a curve by tangents and offsets. The narrator really is speaking English, I promise. If you follow his diagrams, you can interpret most of his pronunciations, and he's a danged good teacher. Second time through is better than the first. You might also find a perpendicular distance that you didn't realize is perpendicular.

Last, don't look at fitted curves and derived coordinates as being the be-all, end-all to problem solutions. This is pure mathematics; surveying is practiced on the ground. To the extent that pure mathematics can be helpful, it's a reliable aid, a piece of evidence, not the total solution.

Remember, a circle can be uniquely defined in many ways. For example, three non-collinear points define a circle, as does a center and a radius, and any number of computer applications can use either method to produce one.

Be careful and understand fully!

?ÿ

?ÿ


 
Posted : January 29, 2022 2:10 pm

Mark Mayer
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Least Squares for Boundary Resolution (2 of 3)

This Part 15 of a series of videos by David Woolley and the Orange County Chapter of the CLSA. I really like most all of what he has to say.?ÿ


 
Posted : January 29, 2022 3:13 pm
mathteacher
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@mark-mayer?ÿ

He pretty much lost me when he replaced monumented locations with least squares locations on the map, making the map automatically disagree with the ground. Then he says that the monuments were held because they were used to calculate the map coordinates, and that he probably should have said that on the map, but he didn't.

Given that he can't measure with accuracy closer than the least squares positions are to the measured positions, why replace the measured coordinates on the map? Neither is superior to the other, so why deliberately make the map disagree with the ground?

Here, the pure math verifies the accuracy of the measurement. I don't see the value in using it for anything more.

Am I missing something?


 
Posted : January 29, 2022 6:22 pm
Mark Mayer
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Posted by: @mathteacher

Am I missing something?

I think you are missing that the positions of the corners post best fit analysis fall within the error ellipse of the as-tied monument positions. He is talking about a rigorous way to deal with these small variations in coordinate values.?ÿ?ÿ


 
Posted : January 29, 2022 8:35 pm
john-nolton
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@mathteacher?ÿ Sure wish he would quite calling the digit "0" ; "OH".?ÿ Send him an email and tell him that's its?ÿ "ZERO"

?ÿ

JOHN NOLTON


 
Posted : January 29, 2022 8:57 pm
field-dog
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@mathteacher?ÿ

I'm interested in figuring out at what point the offsets from the two tangents intersect on the curve.


 
Posted : January 30, 2022 5:02 am

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