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Paired Sales Analysis & Adjustments
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Posted by Terry,
I like what you are doing. I don’t work rural and farm but is has always been my view that it has to start with a pretty good dollop of land studies, trying get a workable understanding of the size-price relationship before you put those houses or barns on those huge parcels.
Posted by Moe
My point was that bracketing and regression show that “adjustments” tend to be moot and symbolic - a point that no one addressed. A secondary point is that regression offers solutions with suport in seconds with fresh data versus what Mike said he spent “years and years” figuring out the hard way with info that is bound to get stale
You say,
In the first example size and year built did not move together. Here is a second random sample of seven sales, from the same “perfect” market, except that now size and year built are directly related, moving in perfect lockstep. The newer the house, the bigger it is and vice verse. The columns are year, built, size (sf) and price
1 2002 2,300 430,000
2 2000 2,200 418,000
3 1999 2,000 400,000
4 1996 1,900 386,000
5 1995 1,850 380,000
6 1994 1,750 370,000
7 1992 1,700 362,000
Again, the “bracketing” solution says, the same subject (built in 1997 adn containin 1,950 sf) is still in the middle of the pack. This time the uniformity of the size year built relationship allows a tight bracket between sale 3 ($386,000) and sale 4 ($400,000). The subject is somewhere around $393,000. Done! No adjustments!
Because the market reaction in this perfect market to size and year built is still the same, the regression equation still produces $392,000. Done! No adjustments!
For those who like “adjustments” and aren’t happy unless they see that grid, the columns are price, size adj, age adjust, indicated value.
1 430,000 -28,000 -10,000 392,000
2 418,000 -20,000 -6,000 392,000
3 400,000 -4,000 -4,000 392,000
4 386,000 +4,000 +2,000 392,000
5 380,000 +8,000 +4,000 392,000
6 370,000 +16,000 +6,000 392,000
7 362,000 +20,000 +10,000 392,000
So what happened, Moe? Still think size and year built are not independent?
During a power outage?
I like what you are doing. I don’t work rural and farm but is has always been my view that it has to start with a pretty good dollop of land studies, trying get a workable understanding of the size-price relationship before you put those houses or barns on those huge parcels.
Posted by Moe
Everyone is. That's where the utopian idea of "matched pairs" comes from.
My point was that bracketing and regression show that “adjustments” tend to be moot and symbolic - a point that no one addressed. A secondary point is that regression offers solutions with suport in seconds with fresh data versus what Mike said he spent “years and years” figuring out the hard way with info that is bound to get stale
The original question I quoted and answered was one of “support.” If support is beyond the scope of your assignment, then you don’t need pairs either.
You say,
Of course they are
In the first example size and year built did not move together. Here is a second random sample of seven sales, from the same “perfect” market, except that now size and year built are directly related, moving in perfect lockstep. The newer the house, the bigger it is and vice verse. The columns are year, built, size (sf) and price1 2002 2,300 430,000
2 2000 2,200 418,000
3 1999 2,000 400,000
4 1996 1,900 386,000
5 1995 1,850 380,000
6 1994 1,750 370,000
7 1992 1,700 362,000
Again, the “bracketing” solution says, the same subject (built in 1997 adn containin 1,950 sf) is still in the middle of the pack. This time the uniformity of the size year built relationship allows a tight bracket between sale 3 ($386,000) and sale 4 ($400,000). The subject is somewhere around $393,000. Done! No adjustments!
Because the market reaction in this perfect market to size and year built is still the same, the regression equation still produces $392,000. Done! No adjustments!
For those who like “adjustments” and aren’t happy unless they see that grid, the columns are price, size adj, age adjust, indicated value.
1 430,000 -28,000 -10,000 392,000
2 418,000 -20,000 -6,000 392,000
3 400,000 -4,000 -4,000 392,000
4 386,000 +4,000 +2,000 392,000
5 380,000 +8,000 +4,000 392,000
6 370,000 +16,000 +6,000 392,000
7 362,000 +20,000 +10,000 392,000
So what happened, Moe? Still think size and year built are not independent?
moe cohen
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I would caution against using regression in a casual manner unless you know well how to get your variables to be independent. I am not aware of any indepent variables among the ones we use. I suppose as I said that you address the independence issue using the appropriate methods. If you do it was not clear in the post.
Moe
Moe
Austin
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Neat problem Steven: Perfect example of multicollinearity. Both independent variables almost perfectly correlated to each other and to price and using either one or both gives the exact same answer. If you are trying to fool the boys and girls in the peanut gallery you probably succeed. 
PS: That is how I deal with multicollinearity. In the aggregate. Just use either one.
PS: That is how I deal with multicollinearity. In the aggregate. Just use either one.
Austin,
What you said in an earlier post about texts, etc., just containing theory and very little “how to” is true. We are forced to construct our own problems, add things to them and see what comes out so that we can see how the tools work. These samples were from a series I made in 1994.
The funny thing is, I agree with the substance of your last post, except I don’t see the connection between most of it and what I wrote - except that you used numbers from my illustrations.
Also, how could I have been more clear and emphatic that the illustrations were NOT making “adjustments.” I even bolded the text, "the regression equation still produces $392,000. Done! No adjustments"
This one intrigues me. You say,
1 2002 414000
2 2000 418000
3 1999 380000
4 1996 378000
5 1995 384000
6 1994 394000
7 1992 386000
What you said in an earlier post about texts, etc., just containing theory and very little “how to” is true. We are forced to construct our own problems, add things to them and see what comes out so that we can see how the tools work. These samples were from a series I made in 1994.
The funny thing is, I agree with the substance of your last post, except I don’t see the connection between most of it and what I wrote - except that you used numbers from my illustrations.
Yeah, probably, but who said “go outside the data set.” Not me.
Also, how could I have been more clear and emphatic that the illustrations were NOT making “adjustments.” I even bolded the text, "the regression equation still produces $392,000. Done! No adjustments"
This one intrigues me. You say,
Really? I’d like to see that. Here are the first 7 sales. Date and price.
1 2002 414000
2 2000 418000
3 1999 380000
4 1996 378000
5 1995 384000
6 1994 394000
7 1992 386000
Austin
Elite Member
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- Professional Status
- Certified General Appraiser
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- Virginia
Steven:
I have the graph right in front of me of date versus price and the R^2 is almost 96%. Graph it and look at it. Can't get much better than that. Also look at the graph of date versus GLA with an R^2 also of about 96%. I wasn't addressing what you wrote, I was using your examples to show how multicollinearity can be a problem.
I have the graph right in front of me of date versus price and the R^2 is almost 96%. Graph it and look at it. Can't get much better than that. Also look at the graph of date versus GLA with an R^2 also of about 96%. I wasn't addressing what you wrote, I was using your examples to show how multicollinearity can be a problem.
You are not looking at what I just posted. Right off the post without graphing, I can see that the 1994-buit house sold for more than both: the more-recently-built sales in 1995 and 1996; and the older 1992 home. That doesn' line up.
Austin
I see what you mean. Year-built, especially on the second sales set, APPEARS to be a very good price predictor. In fact for all 14 sales, year-built APPEARS to be a good price predictor by "real-world" rules-of-thuimb. This appearance results because this is a perfect market with perfect data. Getting close on “typical market” standards, like saying “96%…can’t get much better than that” misses the point. This is a test case to practice with "tools." there is already a 100% solution. Perhaps, I could/should have said variables "A: and "B" instead of size and year-built. Maybe it would have avoided triggering your personal hypotheses about how these two things work "in the real world" which is not so much tools as value theory.
These perfect-market prices are so consistent that year-built alone, or bracketing or “eyeballing-the-mid-range” or what you like to do (eyeballing the regression line) would probably all point to the low $390.000’s. Heck, we probably can just “average-up” the prices and still hit the low $390,000’s. However, all of that misses all my points.
---------------
- I started by addressing a question of how to “support adjustments” and one possible answer, which was collecting “matched pairs” for “years and years.”
- I tried to offer something faster and/or more reliable. Bracketing of overall price is good way to replace the (perceived) need for “pairs” and “adjustments.” Bracketing can be enhanced by or replaced by regressions, which is still not “adjustments,” but can be used to make adjustment grids for those who like to see them.
- The paired-sales equation is primitive and depends too much on chance creating an opportunity. The basic regression equation (ols) is like an advanced “pairing” equation, that extracts a rate of change when there are no “matched” pairs. I gave a two sub-sets from “perfect” market with no matched pair to show the regression equation can pull out the $80/sf and $2,000/yr rates of change anyway. Had I put in just one matched pair, it would have unlocked the same solution, but regression always unlocks the same solution even when the eye can't see it.
- My 7-sale illustrations gave “supported” solution, extracted right from sales on hand, without, “years and years” of hunting in the dark for pairs for “adjustments” (which, as you point out, may not apply outside the original neighborhood area).
So here is a quandary. The fact is you use regression. You would have, and probably did, come up with a very similar solution to the problem. And yet you are like “totally” ranting dude, about “meaningless” and “misleading” and “totally misleading” and “totally erroneous.”
---------------
Bogeymen and Multicollinearity
Appraisers know what multicollinearity is – or so I thought from years of hearing them address it- even though most of them don’t toss the word around there is a Frisbee contest.
The simplest way to explain the idea is that there are several ways to measure property “size.” For houses, we can measure property size with several variables like, square footage, room count, cubic feet, etc. For land, we measure size with price per acre and price per square foot - or price per hectare or price per square inch.
An example of creating a multicolliearity problem in a land appraisal is an appraiser using the variable of ‘square feet’ (size) and the variable of ‘cubic feet’ (size) on the same adjustment grid or in the same model and triying to adjust or reconcile for both at the same time. Pretty much everybody knows not to do that, right? This also goes to Moe’s comment, that somehow creating this problem is connected to regression, rather than a result of “man-made” error that is independent of adjustment or reconciliation method.
Real estate appraisers do not deal in abstract data, but limited and repetitive types of data. Whether it is SFR’s or some other “class” of property, we use the same limited number of variables over and over – size, condition, location, etc. We know what overlaps with what most of the time. Don’t we?
General property knowledge is that size and year-built measure different things. Even without that knowledge and allowing that markets are fickle, in my illustration, the market reaction is $80 per square foot REGARDLESS of age, and the market depreciates $2,000 per year REGARDLESS of size. Each variable moves with perfect consistency on its own course regardless of what the other one does. If those two ideas are not enough to communicate the independence of these two variables, keep in mind that I constructed the data. I constructed it purposely and specifically to make the two variables independent – and I could have called them “A” and “B” instead of size and year-built.
Multicolinearity is not when the market reacts to two separate property variables and not when we can show the effect of each on price. It is when the market is reacting to one variable and the appraiser gives it two names and "adjusts" twice.
I see what you mean. Year-built, especially on the second sales set, APPEARS to be a very good price predictor. In fact for all 14 sales, year-built APPEARS to be a good price predictor by "real-world" rules-of-thuimb. This appearance results because this is a perfect market with perfect data. Getting close on “typical market” standards, like saying “96%…can’t get much better than that” misses the point. This is a test case to practice with "tools." there is already a 100% solution. Perhaps, I could/should have said variables "A: and "B" instead of size and year-built. Maybe it would have avoided triggering your personal hypotheses about how these two things work "in the real world" which is not so much tools as value theory.
These perfect-market prices are so consistent that year-built alone, or bracketing or “eyeballing-the-mid-range” or what you like to do (eyeballing the regression line) would probably all point to the low $390.000’s. Heck, we probably can just “average-up” the prices and still hit the low $390,000’s. However, all of that misses all my points.
---------------
- I started by addressing a question of how to “support adjustments” and one possible answer, which was collecting “matched pairs” for “years and years.”
- I tried to offer something faster and/or more reliable. Bracketing of overall price is good way to replace the (perceived) need for “pairs” and “adjustments.” Bracketing can be enhanced by or replaced by regressions, which is still not “adjustments,” but can be used to make adjustment grids for those who like to see them.
- The paired-sales equation is primitive and depends too much on chance creating an opportunity. The basic regression equation (ols) is like an advanced “pairing” equation, that extracts a rate of change when there are no “matched” pairs. I gave a two sub-sets from “perfect” market with no matched pair to show the regression equation can pull out the $80/sf and $2,000/yr rates of change anyway. Had I put in just one matched pair, it would have unlocked the same solution, but regression always unlocks the same solution even when the eye can't see it.
- My 7-sale illustrations gave “supported” solution, extracted right from sales on hand, without, “years and years” of hunting in the dark for pairs for “adjustments” (which, as you point out, may not apply outside the original neighborhood area).
So here is a quandary. The fact is you use regression. You would have, and probably did, come up with a very similar solution to the problem. And yet you are like “totally” ranting dude, about “meaningless” and “misleading” and “totally misleading” and “totally erroneous.”
---------------
Bogeymen and Multicollinearity
Appraisers know what multicollinearity is – or so I thought from years of hearing them address it- even though most of them don’t toss the word around there is a Frisbee contest.
The simplest way to explain the idea is that there are several ways to measure property “size.” For houses, we can measure property size with several variables like, square footage, room count, cubic feet, etc. For land, we measure size with price per acre and price per square foot - or price per hectare or price per square inch.
An example of creating a multicolliearity problem in a land appraisal is an appraiser using the variable of ‘square feet’ (size) and the variable of ‘cubic feet’ (size) on the same adjustment grid or in the same model and triying to adjust or reconcile for both at the same time. Pretty much everybody knows not to do that, right? This also goes to Moe’s comment, that somehow creating this problem is connected to regression, rather than a result of “man-made” error that is independent of adjustment or reconciliation method.
Real estate appraisers do not deal in abstract data, but limited and repetitive types of data. Whether it is SFR’s or some other “class” of property, we use the same limited number of variables over and over – size, condition, location, etc. We know what overlaps with what most of the time. Don’t we?
General property knowledge is that size and year-built measure different things. Even without that knowledge and allowing that markets are fickle, in my illustration, the market reaction is $80 per square foot REGARDLESS of age, and the market depreciates $2,000 per year REGARDLESS of size. Each variable moves with perfect consistency on its own course regardless of what the other one does. If those two ideas are not enough to communicate the independence of these two variables, keep in mind that I constructed the data. I constructed it purposely and specifically to make the two variables independent – and I could have called them “A” and “B” instead of size and year-built.
Multicolinearity is not when the market reacts to two separate property variables and not when we can show the effect of each on price. It is when the market is reacting to one variable and the appraiser gives it two names and "adjusts" twice.
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