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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 Mon, Oct-08-2012, 05:19:38 PM   #11
bmans
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Quote:
Originally Posted by Mjoyabl3 View Post
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.
I agree with you - until you get to the additional point of "normal distribution" and "central limit theorem". Regression is valid whether the data is normally distributed or not. Evaluation of correctness of the regression is through looking at "residuals" - the difference between the actual value and the predicted value from the equation. The residuals have to conform to the assumption of normality - and a couple other assumptions - to be valid. The number of factors that can be evaluated minimally with n data points is n-1. The more data you have the less margin of error in the results.

If the OP provided the data with all of the factors I would be happy to run the statistical tests and post the results - including the probability that each factor is insignificant.

I teach people how to do this in business on a daily basis and consult with my employer's customers on this type of analysis. I am not an expert with a degree in statistics - I am an engineer and apply statistics from a practical viewpoint. I enjoy doing it and it allows me to generate the income to operate my household - and enjoy my fleet of BMWs.

I am fairly new to the forum and don't want to turn it into a statistical forum as I am learning alot from the many posts I read on here about the M3.
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Old Mon, Oct-08-2012, 11:03:50 PM   #12
Mjoyabl3
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

OP, Don't want to take the time to re-quote so I'll just add your in bold to make it easier

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.

Perfect, I was really just wondering if it there were other regressions that appeared to fit. I'm sure linear would be close in this case even compared to the others.

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.

I totally agree, color doesn't matter for these purposes.

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.

I'm going to have to play devil's advocate here haha. There was no question for salvage title in the original poll, so there might be some salvage titles mixed in. However, If you're going to keep that out of the equation it's a moot point.

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.

Truth!!! You're spot on here. After my post I thought about it more and realized how impossible it is to see how those values have a bearing on price. My thought process did not account at all for what mods... I'm in the boat of start with a clean example and would pay more for a clean, stock M than one with $10k of "Stance". Everyone likes something different and it is clear in how many of these you see in that form. Someone out there is drooling over that scraper. Perfect logical analysis here OP.

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.


While I'm sure this is the case, there is no way to be certain what brought the high price. Maybe it was "had to have it" fever. Maybe they just got taken to the cleaner's at the negotiation table. There could also be data points where something else makes the high price point. Look at Richardsperry for example, his price paid is much higher because he purchased the car new. Again, not trying to say/prove anything here at all; This is just two people learning from each other. I just have to point out that the data can't say for sure what caused higher price.

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...


I'm not sure what the data would say but again, without a question on the survey, it's unclear how many of these were dealership cars or PO cars. Going even deeper, you might even want to ask how many POs the car had, a one owner car is definitely going to sell for more than a 5 owner car, but is the rate of depreciation even measurable? Well, we'd have to ask to find out. On something like this, it's really up to you to include it or not and probably isn't a major factor either way.

I just want to stress that decisions should be made on data. I'd even have to critique my original post that said dealership cars sell for more than private cars. I don't know for sure that dealer cars sell for more, just that they are always listed for a substantial ammount more in my area (another assumption, other areas could be different). While it is probably a fair assumption (for me, and in my area) that they usually sell for more, it is still an assumption with no data to back it. They could sell for less but just be listed with haggle room; everyone likes to feel like they are getting a better deal than advertised.

****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.

I figured that your control charts would be pretty good, the formula worked fairly well for a ballpark estimate when I used it.

One more overall thing, I think the more current the data (purchases within the last year or so) the better it would be for extrapolating future purchases or pricing cars currently on sale. I haven't done it, but I'm sure your most current 2-year model ('10-'12) would probably turn in values closest to the actual values, while the overall model would probably price them higher.

Quote:
Originally Posted by 97_4dr_5spd_m3 View Post
What is your educational background?
I have a degree in Operations Management from an accredited university. I've taken applied statistics classes and always been quite interested. FWIW, I don't currently work in this field, but plan to in the future. Regardless, as with every post on every forum, I'm still just some guy on the internet.
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Old Mon, Oct-08-2012, 11:17:40 PM   #13
Mjoyabl3
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

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Originally Posted by bmans View Post
I agree with you - until you get to the additional point of "normal distribution" and "central limit theorem". Regression is valid whether the data is normally distributed or not. Evaluation of correctness of the regression is through looking at "residuals" - the difference between the actual value and the predicted value from the equation. The residuals have to conform to the assumption of normality - and a couple other assumptions - to be valid. The number of factors that can be evaluated minimally with n data points is n-1. The more data you have the less margin of error in the results.

If the OP provided the data with all of the factors I would be happy to run the statistical tests and post the results - including the probability that each factor is insignificant.

I teach people how to do this in business on a daily basis and consult with my employer's customers on this type of analysis. I am not an expert with a degree in statistics - I am an engineer and apply statistics from a practical viewpoint. I enjoy doing it and it allows me to generate the income to operate my household - and enjoy my fleet of BMWs.

I am fairly new to the forum and don't want to turn it into a statistical forum as I am learning alot from the many posts I read on here about the M3.
While the regression fits the data, it does not necessarily mean it is an accurate representation for the entire population. I'd agree that in my post you quoted I didn't explain this part in the best way.

The point I was trying to make: Acording to this site, 71,212 of our beloved e36 m3s were produced. I'm just trying to make the point that 67 is not an accurate representation of our entire population.

So glad others are interested in this project as well!
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Old Tue, Oct-09-2012, 10:14:06 PM   #14
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Nice work! I overpaid. But I already knew that. Still happy.
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Old Thu, Oct-25-2012, 08:22:09 PM   #15
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Bump...Sirius, can we make this a sticky?
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Old Sun, Nov-04-2012, 01:40:44 AM   #16
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

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Originally Posted by 97_4dr_5spd_m3 View Post
Bump...Sirius, can we make this a sticky?
put it in a spreadsheet that does the calculations for us while you're at it.....it makes little sense as it is, need a "for dummies" version that we can simply enter our numbers into and let it spit out figures, math sucks even with a calculator
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Old Fri, Nov-23-2012, 02:54:16 AM   #17
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

I am confused as to if the "price" is supposed to be what I paid or what it was valued at at the time...because they are too very different numbers....or do I use the "price" in the formula? Very confused with the whole thing. If it's not basic math with a calculator it may as well be spanglish to me.
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Old Mon, Nov-26-2012, 01:02:55 AM   #18
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Default Re: E36M3 Regression Analysis - Purchase Price Findings

Fun exercise.

Did you state your r2 or r-bar? If not, what were they?

My guess is you'd have a more accurate model with some additional variables as others have said. I'd say accident history (# of accidents), rust, and some variable for maint history would all have a statistically signif impact. With that said, fewer variables is better for a given accuracy.

Next step - you need another 50-60 people to use your model and report back the results vs. actual price paid. A model that works with the data used to create the model is one thing. A model that works with new data is another. For me, primary model over-estimated by ~$1000 and mileage/year model for coupe underestimated by ~$1000.
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Old Mon, Nov-26-2012, 02:53:35 AM   #19
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If you want good data you need to make a drop down selectable form linked to a database and more clear explanation of things. The OP clearly is ignoring my posts, but why is unclear.

Sent from my SCH-I535 using Tapatalk 2
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Old Mon, Nov-26-2012, 02:45:50 PM   #20
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Quote:
Originally Posted by crqflier View Post
Fun exercise.

Did you state your r2 or r-bar? If not, what were they?

My guess is you'd have a more accurate model with some additional variables as others have said. I'd say accident history (# of accidents), rust, and some variable for maint history would all have a statistically signif impact. With that said, fewer variables is better for a given accuracy.

Next step - you need another 50-60 people to use your model and report back the results vs. actual price paid. A model that works with the data used to create the model is one thing. A model that works with new data is another. For me, primary model over-estimated by ~$1000 and mileage/year model for coupe underestimated by ~$1000.

Still, being within $1000 is pretty solid, all things considered. This model is certainly enough to see if you're in the ball park on a given price.





Quote:
Originally Posted by M3WhiteSedan View Post
If you want good data you need to make a drop down selectable form linked to a database and more clear explanation of things. The OP clearly is ignoring my posts, but why is unclear.

Sent from my SCH-I535 using Tapatalk 2

Maybe he's ignoring you because you're the only person out of everyone who has seen this thread asking him to do even *more* work instead of simply re-reading the very clear instructions in the first post and figuring it out for yourself.

It's clear as day: plug in your personal variables (mileage, age), deduct for vert or coupe and it gives you an approximate value (or price if you're using this as a buying / selling tool). It's not rocket surgery. There are other variations, but that's the basic formula. Takes about 45 seconds with a calculator and that's if you have a hard time with long numbers.

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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)