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E36 M3 (1992-1999) {Euro - S50 B32 321hp @ 7400 rpm} {U.S. - S52 B32 240 hp @ 6000 rpm}
Total Produced: 71,212 - Years Produced: 1992 to 1999


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Old Sun, Oct-07-2012, 10:36:42 PM   #1
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Default E36M3 Regression Analysis - Purchase Price Findings

*****Hello All. Currently (12/15) this data set should probably be considered outdated at this point.

The following is the aggregate of the 67 total data samples that were given. I did end up deleting 2 data samples, due to the numbers being wildly off/car must have been incredibly modified. Again, this is a total of the 95-99 M3s in every fashion available, purchased 2003-2012.

****Variables such as coupe, sedan, vert, or automatic are considered "dummy variables". You only add in (or usually subtract) the variable if your car comes with such option.******

All 67 car's numbers accounted for with no filtering.

Price is a function (fn) = 23235.64 -.06 (mileage) -1802.85 (coupe) -1718.44 (vert) -442.10 (age of vehicle)

Example of my car - 97 M3/4/5 = Price (fn) = 23235.64 -.06 (140,000) -442.10 (15) = $8515.17.


Finding of the regression analysis is that sedans are the more favorable form of the three chassis options. Coupes tend to sell for $1802.85 less and verts sell for $1718.44 less.


I was interested in seeing how much per mile that we usually deduct from an E36M3 purchase. As it shows when I just compare purchase price vs. mileage I get...

Price (fn) = 18183.41 - .07 (per mile)


When just comparing sedans vs. sedans.

Price (fn) = 20183.43 - 0.04 (mileage) - 340.09 (age)

My M345 = Price (fn) = 20183.43 - 0.04 (140,000) -340.09 (15) = $9738.23



Coupe vs coupe.

Price (fn) = 22133.90 - 0.06 (per mile) - 465.11 (age)


Vert vs vert.

Price (fn) = 31164.49 - 0.09 (per mile) - 1019.64 (age)

Interestingly, I was able to compare standard verts and automatic verts too. Although, there was only 1 automatic vert, but Excel feels pretty strongly the deduction is warranted. **I'd think that if a super low mileage - auto vert was sold and used it would through these numbers off a bit.**

Price (fn) = 28059.10 - 0.04 (per mile) -1022.80 (age) -3773.66 (automatic)


Since, I received many samples and the earlier purchases usually had high purchase prices and lower miles, I figured I'd break this down as well. I made three more regressions with 2012-2010, 2009-2008, and 2007-older.

2012 - 2010.

Price (fn) = 16593.86 - 0.05 (per mile) - 2907.51 (coupe) - 2262.52 (vert) + 16.35 (age)

***Notice that the age of the vehicle is actually a positive variable. This is the only place in any of these regressions that it actually comes up as a positive variable....indicator that our cars are going up in prices as compared to all other variables????

This is with 38 out of the 67 samples being involved too.

Although these were purchased in that time.

Amount $$ Mileage
$21,000.00 21,530
$15,500.00 53,989
$15,000.00 78,000
$13,990.00 49,000


2009 - 2008

Price (fn) = 20847.93 - 0.06 (mileage) + 78.47 (sedan) - 317.83 (age)


2007 - older

Price (fn) = 28523.22 - 0.11 (mileage) - 3207.13 (coupe) - 693.56 (sedan) - 421.22 (age)


The above numbers were for the most part just something 'fun' for me to do. They obviously should not be taken as too serious, but plugs your numbers in and see what you think. My car's $8515.17 evaluation is actually pretty close to the sales price, if my car was stock and loved by its owner.

***Also, since these numbers are time sensitive they will not hold for too much longer than next year.





Correlation numbers. Can not really hold too much weight, but it was easy enough to run. The only number that makes obvious sense would be that mileage and year effect the "Amount $$" the most. The difference between the coupe, sedan, and vert's correlation numbers are probably the fact that coupes tend to have more miles than the other options.


............................Amount $$.......................Mileage
Amount $$..................1
Mileage................-0.724035755......................1
coupe..................-0.428279874................0.284461543
sedan....................0.390901637..............-0.158884899
vert.......................0.110946587............ ..-0.24649766
Age of veh.............-0.59844421................0.412945568




Data: http://www.m3forum.net/m3forum/showthread.php?t=422123
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Old Sun, Oct-07-2012, 11:02:38 PM   #2
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

really good job
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Old Mon, Oct-08-2012, 01:24:02 AM   #3
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

wow this is an amazing formula, just tested it with a couple cars ive seen on craiglist as well as mine and such and it gives you a pretty accurate number. I say we make a new rue of thumb with newbies asking what cars are worth, the number of this formula + or - a thousand depending on car condition and history. again i know there are special cars that are going to be modded, built, etc. but this is a very good general price. Great gob OP

but there should be like a -3000 for salvage title or something
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Old Mon, Oct-08-2012, 03:26:34 AM   #4
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Default

VERY cool. Viewing at this on Tapatalk, but will have to give it a closer look when I get to an actual computing machine.

Nice work.
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Old Mon, Oct-08-2012, 03:41:43 AM   #5
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

First post, been lurking for a month or so and this is one thread that is very interesting to me; a thread I can't pass on posting in!

OP, I'd just like to say excellent job on this regression given the amount and nature of the data you were given. I just want to ask a couple questions/critique your methodology but please take no offense in any of this. I am NOT trying to come in here with a "You're doing it wrong" attitude at all!!!!!

1. Did you find linear regression to be the best fitting type of regression for this data set? I'd be curious as to how different types of regression would fit this plot but that could lead to some points of extreme variance, especially over this spread out of a data set. I understand that linear regression is quick and dirty (as I'm pretty sure you meant this to be, obviously nobody can make a crystal ball for car sales), also easiest for you to preform and the average end user of your model to calculate.

2. Why were some variables left out? Let me start here, of the data you collected I agree with your methodology of leaving color out as the only one of the variables you collected but didn't use. Color is definitely a variable that can be left out without any statistically significant change given the amount of unknown variables already present. if people hate a color but want an e36 m3 they are likely to just wait it out until they find one in a desirable color. Also, there will always be a buyer for every color, because everyone likes something different... You'd have to knock me out and drag me into the drivers seat of a dakar, but I'm sure there's a dakar owner out there that wouldn't be caught dead in my "purple" daytona violet.

But what about the other variables that can significantly affect price of the car? here's a couple I think would really help this become even better. The first and most obvious is branded titles. In my opinion, this is the single biggest factor in car price aside from year or mileage. Some people will completely refuse to buy branded titles, while some will see them as a "score" and pick them up. While this entirely personal preference has no bearing on which car is a better value overall (that is up to the individual, and could probably be another thread altogether)... We should all be able to agree that any car with a branded title has less inherent value than the exact same car with a clean title in the same condition.

Another big one I see is mods. I'm sure you thought of this when making your original post asking for data but it would be ridiculous to try to figure out how much X mod adds to the purchase price of X car, and do this for every single e36 mod out there. I think you could, maybe (big maybe), have owners estimate the dollar amount of all mods when they were purchased brand new, so instead of having a crazy number of mods and how much they can weigh on the price individually, just a simple "the car had approx $XXXX.xx in mods when I bought it". This is obviously not going to be extremely accurate, but as it stands now there is no difference to the equation between a heavily modified show car and a 100% stock car. That being said, I definitely realize that this would be difficult to add in and estimate, but it also might be cool to see a baseline of how much mods depreciate when the car switches owners.

I would also like to see dealer vs private owner purchase. Pretty straightforward here, average prices of cars bought from dealers are typically going to be more expensive than cars bought from owners.

3. Why did you truncate/round where you did for cents/mile? When multiplying even the smallest numbers (less than ten cents) by numbers as large as the mileage of car (potentially hundreds of thousands) the rounding/truncating can make all the difference. I'll just explain mathematically so you can see what my thought process is:

Let's assume the car in question has exactly 100k and we are using a $.06/mile formula just to make this simple.

100,000 x .06 = 6000
100,000 x .061 = 6100
100,000 x .062 = 6200
100,000 x .063 = 6300
100,000 x .064 = 6400
...and so on...

What I'm getting at is that if you truncated, these numbers could be off by as much as $999 per 100k miles. I'll go ahead and assume you rounded, meaning your numbers could still be off by as much as $499 per 100k. Being that all of these cars are currently in their teens and none are going backwards in miles, adding just a couple decimals here can increase accuracy by quite a bit.

Before anyone goes out and points it out, I realize there is no such thing as six and one tenth of a cent, however these fractions of a cent can be significant when multiplied out hundreds of thousands of times. If you guys have seen "Office Space" this should make sense haha.

Additional points to note:
- A sample consisting of many cars of various years, body styles, clean and branded titles, colors, transmissions, options, body damage, mods, etc. would need an EXTENSIVE amount of data to cover ALL of the variations in the cars and making it all average out. Meaning, the more variation that can exist in a data set, the more data points, "n" you need to make it approach a normal distribution, look up "central limit theorem" for more explanation. In this example, the number of samples must be MUCH larger than n=67 for it to have statistical significance because of the amount of variation in the data. I do not know how many samples you would need before a normal distribution would be seen, but it would be a lot.

- All of these cars in this regression are in various conditions and/or states of repair, while this is a pretty good estimate, it shouldn't be held as the gospel (and was never meant to be) when pricing an e36 m3

- It's uncommon to find a completely bone stock e36 m3 these days, so this chart is probably going to be a better match for modified car purchases, that have around the average number of mods as the cars in this study. Which is, again, very hard to determine.


One more time I would like to thank the op for doing this as well as getting my brain going on this one, well done!
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Old Mon, Oct-08-2012, 12:08:15 PM   #6
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Sorry, but it seems to be an exercise in mental masturbation.. There is no way you can come up with a formula that is valid. Supply and demand, and vehicle condition are just too unpredictable.
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Old Mon, Oct-08-2012, 12:37:43 PM   #7
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Nice job, I like it. And I don't agree that it's mental masturbation. Maybe if you're looking at individual cars it doesn't make sense, but looking at overall trends it's pretty damn accurate. Cars that sold in the tens of thousands will follow a general trend, and you can expect to find lots under the fat part of the curve, with a few outliers. Use it to get a handle on the market, then go work a deal on a particular car.
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Old Mon, Oct-08-2012, 01:19:22 PM   #8
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Very cool, thanks! although it looks like I overpaid by about $500...I'll chalk it up to "intangibles"

Actually, I wonder how region would factor in - I realize you have way too few data points to accurately model that, but here in SW VA nice M3s are very hard to come by, so I was willing to pay a little more for a clean example (and budge on my search criteria - was really dreaming of an estoril sedan, but so it goes). Very cool project, though!
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Old Mon, Oct-08-2012, 02:35:20 PM   #9
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Quote:
Originally Posted by Mjoyabl3 View Post
First post, been lurking for a month or so and this is one thread that is very interesting to me; a thread I can't pass on posting in!

OP, I'd just like to say excellent job on this regression given the amount and nature of the data you were given. I just want to ask a couple questions/critique your methodology but please take no offense in any of this. I am NOT trying to come in here with a "You're doing it wrong" attitude at all!!!!!



1. Did you find linear regression to be the best fitting type of regression for this data set? I'd be curious as to how different types of regression would fit this plot but that could lead to some points of extreme variance, especially over this spread out of a data set. I understand that linear regression is quick and dirty (as I'm pretty sure you meant this to be, obviously nobody can make a crystal ball for car sales), also easiest for you to preform and the average end user of your model to calculate.

Two reasons. First, I felt that the linear model fit the regression fairly well. All of the variables have roughly the same effect on the price and all of the prices were followed a definite trend. Second, I am most comfortable with the linear model.


2. Why were some variables left out? Let me start here, of the data you collected I agree with your methodology of leaving color out as the only one of the variables you collected but didn't use. Color is definitely a variable that can be left out without any statistically significant change given the amount of unknown variables already present. if people hate a color but want an e36 m3 they are likely to just wait it out until they find one in a desirable color. Also, there will always be a buyer for every color, because everyone likes something different... You'd have to knock me out and drag me into the drivers seat of a dakar, but I'm sure there's a dakar owner out there that wouldn't be caught dead in my "purple" daytona violet.

But what about the other variables that can significantly affect price of the car? here's a couple I think would really help this become even better. The first and most obvious is branded titles. In my opinion, this is the single biggest factor in car price aside from year or mileage. Some people will completely refuse to buy branded titles, while some will see them as a "score" and pick them up. While this entirely personal preference has no bearing on which car is a better value overall (that is up to the individual, and could probably be another thread altogether)... We should all be able to agree that any car with a branded title has less inherent value than the exact same car with a clean title in the same condition.

Another big one I see is mods. I'm sure you thought of this when making your original post asking for data but it would be ridiculous to try to figure out how much X mod adds to the purchase price of X car, and do this for every single e36 mod out there. I think you could, maybe (big maybe), have owners estimate the dollar amount of all mods when they were purchased brand new, so instead of having a crazy number of mods and how much they can weigh on the price individually, just a simple "the car had approx $XXXX.xx in mods when I bought it". This is obviously not going to be extremely accurate, but as it stands now there is no difference to the equation between a heavily modified show car and a 100% stock car. That being said, I definitely realize that this would be difficult to add in and estimate, but it also might be cool to see a baseline of how much mods depreciate when the car switches owners.

I would also like to see dealer vs private owner purchase. Pretty straightforward here, average prices of cars bought from dealers are typically going to be more expensive than cars bought from owners.


Colors: I wish that I was able to run the regression and include the colors as a variable. However, the sample size was not big enough I feared. The major colors that I was coming up with was silver, black, and the different types of blues. I was worried that the one or two techno violets may have had different negative variables that effected their price and then would have thrown off the TV MV price. I'd think that we would need at least 10 samples of each color to accurately come up with a MV for colors. I then was going to switch it to a standard color vs an individual color car....and then came up with no individuals and then realized that I may fall into the same thing that the TV MV would have and would need ~1/6 of the data samples to come up as individual.

Branded titles: I actually came across a few people that willingly wrote that the price included a salvage title and I did not include those in the sample sets. And unless I am mistaken, the rest of the sample sets did not include any more salvage titles...unless someone got a very bad deal on a salvage, or I am missing something. So salvage titles fit into the "not enough data" too.

Mods: If I was wondered things would have been a shitshow without accounting for mods, imagine my fear when accounting for mods. I agree that most E36Ms are somewhat modded these days. However, the modded M3 may actually hurt its price too. Imagine you came across an estoril and it had normally acceptable mods, but mods that you did not care for (ie. funky normally accepted rims or something or an extreme suspension set up). Now, I'd think that modded war would lean towards the - mass market is okay with what has been done, but some may want to start off with as much of a clean slate as possible. I know that if I was looking and the car came with anything other than stock rims they'd better be BBS LMs or I am deducting from the price.

Plus, as I said in the OP, I did delete two samples that must have been modded greatly. The cars had typical/high miles and purchase prices of 140% or so of the typical MV.

**I was not delete happy with the samples either. I deleted two samples and chose not to include another (the salvaged one). I did not want to input any bias at all.

Good point about private sale vs dealership purchases. I did not think of that at the time. I could make arguments either way with where you'd get a better deal/pay more. I can see a PS going for more loot, because the PSer knows his car in and out and is more likely to do the sale themselves. The car would probably have more mods and can be proven that it was taken cared for. But, people usually get beat up at the stealer and may have paid more for a stealer car too. Then, when one is looking for a really good deal, they probably would scour the classifieds/Craigslist for someone's old headache or beater and get the best deal off of a PS.

I'd wrap this up as the average...


****Also, I actually received pretty good R^2 and R-bar^2 numbers with these regressions. I am confident that if I kept on adding in dummy variables I would have lost the R^2 and R-bar^2 numbers that I received and the regressions would have been hurt with their additions.


3. Why did you truncate/round where you did for cents/mile? When multiplying even the smallest numbers (less than ten cents) by numbers as large as the mileage of car (potentially hundreds of thousands) the rounding/truncating can make all the difference. I'll just explain mathematically so you can see what my thought process is:

Let's assume the car in question has exactly 100k and we are using a $.06/mile formula just to make this simple.

100,000 x .06 = 6000
100,000 x .061 = 6100
100,000 x .062 = 6200
100,000 x .063 = 6300
100,000 x .064 = 6400
...and so on...

What I'm getting at is that if you truncated, these numbers could be off by as much as $999 per 100k miles. I'll go ahead and assume you rounded, meaning your numbers could still be off by as much as $499 per 100k. Being that all of these cars are currently in their teens and none are going backwards in miles, adding just a couple decimals here can increase accuracy by quite a bit.

Before anyone goes out and points it out, I realize there is no such thing as six and one tenth of a cent, however these fractions of a cent can be significant when multiplied out hundreds of thousands of times. If you guys have seen "Office Space" this should make sense haha.


I'll be completely honest....I was just thinking dollars and cents and the thousandths and tens of thousandths did not even come to mind. I will update the OP and I thank you for bringing that up.

I will say though that just as I rounded to the tenths, most people that gave their mileage rounded to the nearest thousands, and some may have rounded to the nearest ten-thousands. I had five people out of sixty-seven that actually took it down to the mile. But, nonetheless, you are correct and I will add in the thousandth and ten-thousandth points.


Additional points to note:
- A sample consisting of many cars of various years, body styles, clean and branded titles, colors, transmissions, options, body damage, mods, etc. would need an EXTENSIVE amount of data to cover ALL of the variations in the cars and making it all average out. Meaning, the more variation that can exist in a data set, the more data points, "n" you need to make it approach a normal distribution, look up "central limit theorem" for more explanation. In this example, the number of samples must be MUCH larger than n=67 for it to have statistical significance because of the amount of variation in the data. I do not know how many samples you would need before a normal distribution would be seen, but it would be a lot.

- All of these cars in this regression are in various conditions and/or states of repair, while this is a pretty good estimate, it shouldn't be held as the gospel (and was never meant to be) when pricing an e36 m3

- It's uncommon to find a completely bone stock e36 m3 these days, so this chart is probably going to be a better match for modified car purchases, that have around the average number of mods as the cars in this study. Which is, again, very hard to determine.


One more time I would like to thank the op for doing this as well as getting my brain going on this one, well done!
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Old Mon, Oct-08-2012, 02:48:13 PM   #10
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Quote:
Originally Posted by Richardsperry View Post
Sorry, but it seems to be an exercise in mental masturbation.. There is no way you can come up with a formula that is valid. Supply and demand, and vehicle condition are just too unpredictable.
I said that it was "for the most part" going to be a round and rough estimate. I am not trying to outdo our years of experience in remaking the way people price their cars. However, after just running a KBB and mostly everyone here stating the KBB is horribly wrong when dealing with our cars, I came across this for my car.

Excellent.. 7524
Very good....7174
Good.....6974
Fair.....6049

My regression came up with 8500ish, and 9700ish (sedans only).

Obviously I am happier with my numbers. You can make up your own conclusions, but I'd be shocked if you'd side with KBB's nubmers.


And, supply and demand eh? This accounts for supply and demand because that is where I got the numbers. I said that it would not hold up for too long out, but then maybe we can run this again in a few years and come up with a new price function formula. Actually, this may be a better run than just looking at Autotrader, because if you have ever watched "Pawnstars" you'd know, that asking price and selling price are two different things...these are 67 actual selling prices..meaning the actual market clearing price/equilibrium between supply and demand.
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Discussing E36M3 Regression Analysis - Purchase Price Findings in the E36 M3 (1992-1999) Forum - {Euro - S50 B32 321hp @ 7400 rpm} {U.S. - S52 B32 240 hp @ 6000 rpm}
Total Produced: 71,212 - Years Produced: 1992 to 1999 at BMW M3 Forum.com (E30 M3 | E36 M3 | E46 M3 | E92 M3 | F80/X)