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10282007, 03:52 AM  #23  
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Off the cuff I would attribute Porsche doing better than others in a similar power to weight region by them being highly focused on doing just that. They build very purposeful sports cars and are good at it. The Cup tires sure don't hurt either. See my post just above about my latest explanation  tires alone! Regression by the way can, and in this case does have everything to do with physics. You have this one so hopelessly wrong (begin back pedaling/foot in mouth, etc.). You are confusing processes  random vs. causal. Here lucid has illustrated a fundamnetal (if obvious) link between time (to cover a distance) and power to weight ratio. Gee, you would think just those terms alone (power, weight, time  the fundamentals of physics) might tell you ther is a lot physics here. In particular the physics is Newtons Laws and most importantly just F=ma. The random process part is that we have a sample of contestants (meaning the cars themselves not the drivers) that have quantifiable and known differences. The results are then confounded a bit by many causal yet unknown and unquantified variables and many random variables as well. However the R^2 value shows you that the physics of cars speeding around a track is evident. Time is stongly correlated to power to weight ratio (or its inverse in this case). If you got an R^2 value of near 0 it would tell you there is no statistical nor causal effects. Time to brush up on the statistics and physics. 

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10282007, 04:03 AM  #24 
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Can't quite get my own laps (around 9:30 in my E46) to fit onto the chart! If I did some analysis, to factor out road tyres, wet track, passengers and luggage, I expect my time would be nearer 7:30  after also somehow factoring out my significant lack of skill

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10282007, 04:58 AM  #25 
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Didn't we already establish that the GTR is on slicks as swamp predicted?
It is stated in the citation to the ring time. Why people are still trying to pretend that it is not on slicks is ridiculous given what we all know and do not know. The regression is no longer even needed to prove that the GTR has an unfair advantage. It was on slicks. period. Swamp prediction #4 (use of race tires)  correct. People trying to pretend GTR has the handling characteristics of a UFO  wrong. People pretending that kg/hp does not predict ring time  wrong (R square says it explains 75% of the variability) People pretending that physics does not relate to this regression  wrong (physics is responsible for our one and only variable  kg/hp, which means it is the sole contributor to our least squares line). Stay in school. Stats is cool. 
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10282007, 05:48 AM  #26 
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The technology in the GTR might explain it amazing lap time, especially it's very advanced awd system which should allow it to way exceed the norm. The CSL is harder to explain, the weight advantages over the M3 and these trick tyres can't explain it's supercar results, the only thing that could explain it is a greater than quoted power output, but how much would be required to meet it's lap time.
Can anyone calculated this? 
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10282007, 08:43 AM  #27  
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Not sure what you mean by the "accuracy of the statistics" here. Statistics are used to deal with variations due to unknown causes. That's the whole point. You obtain a std. error (posted) for the whole population which tells you something about the shape of the distribution. If you have a data point many std. errors away from the expected value, then you have an outlier. Statistics can tell you that accurately. The GTR is an outlier in that sense. That's all the chart/stats is saying. We will probably find out what makes it an outlier in a few weeks. 

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10282007, 08:53 AM  #28 
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If you mean to say correlation does not establish causality, I see what you are saying. But clearly the xaxis is weight/power, and Swamp already said how that's relevant to the laws of physics. So, if you have a solid causal theory that has been demonstrated to work such as F=ma, and if the correlation confirms that relationship, then what do we have on this graph?...

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10282007, 02:31 PM  #29  
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10282007, 02:39 PM  #30  
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Dude you are hilarious! The above emoticons is literal. 

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10282007, 02:44 PM  #31  
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I am waiting anxiously for someone to take all of our work over the the Vette and GTR forums. It will be a total riot in both places 

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10282007, 02:53 PM  #32 
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DCT
Since this discussion is happening in two different threads I wanted to add an important detail I just posted there, with urging from another members good post.
The Nissan DCT will have an affect on lap times and I believe the effect could be in the 510 second range on a 8 minute track. If the DCT effect is this large then this and the tires alone make for a fairly complete explanation of the time and the outlier nature of the point on the plot. They certainly detract from the advanced AWD and torque/traction systems employed in the car (at least as those things relate to track performance  if the car is as good in the winter as hinted that is another story). Bringing it back OT to the M3 if the car ships with Cup+ tires and you also have DCT the time is going to be fantastic! 
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10282007, 03:33 PM  #33  
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10282007, 07:07 PM  #34 
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I added 45 cars ranging from Ford Focus to a Donkervoort D8 RS. As I predicted, the regression line did not change much, the R^2 went up, and the 95% confidence interval got narrower.
Adjusted R^2: 0.85 time=423.05 + 16.59 * kg/hp The red line is the new regression line, and the green line is the old one. Last edited by lucid; 10282007 at 08:05 PM. Reason: update chart (xaxis was cut off at 6) 
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10282007, 07:29 PM  #35 
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Call me thick but the basics of all of this if I understand it right is that cars which are on the line are performing and handling like they should, cars below the line are better handling cars (as this formula is based on an average power/weight vs handling) and finally cars which are above this line aren't as good a handling car as they should be.
If this assumption of mine is right then with the exception of the 335i, CSL and the Z3 all the other Beemers aren't performing as we would have hoped. Bummer. Here's hoping the new M3 lives up to expectations. 
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10282007, 07:49 PM  #36 
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10282007, 07:57 PM  #37  
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Regardless, we can still see that the 480hp GTR is the most extreme outlier here. That doesn't mean that datapoint is bogus. It just means it is an extreme outlier. And, yes, your point about the BMWs seems to be true. 

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10282007, 07:59 PM  #38  
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But there are tons of other factors affecting the stated times. Walter Roehl or whoever achieves ridiculous times in most of the quoted porsche times, while many other stated times are from sportauto, or other drivers. And remember, Bimmers are not the most dedicated sports cars, they are a compromise. To say that a 997 is overperforming and an M3 underperforming should be restated as "an M3 is compromised and has less favorable racing characteristics." (think M5 vs. elise) If the track time is all that matters to you (rather than a backseat) then why would anyone buy a BMW? BMW's are so great because they fall so close to the line, despite being so versatile, comfortable, daily driveable, and luxurious). And the CSL had better tires which supposedly saved it 15ish seconds. So to say it is better is really to say that it had better tires. Put cups on the stock e46 M3 and the time would fall below the line as well. Anyway, I know what you mean. But if you think about it, it makes sense that bimmers would fall above the line (because they are a compromise), when compared with mostly dedicated sports cars. eh? 

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10282007, 08:00 PM  #39  
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Really its that simple and despite how much we all like our BMWs that does not change the fact that they are not in the same league in handling (stock) as many other cars on that list. 

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10292007, 01:34 AM  #40  
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10292007, 10:57 AM  #41 
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My comments weren't directed to start an argument or anything, it was only an observation. The 335i of all the normal BMWs seem to be performing best, might be down to the new chassis or this amazing engine.
As an Audi owner for many years I am coming to the world of BMW a fresh and was always under the impression that they were to driver's choice, outperforming their German rivals in both handling and acceleration, now don't get be wrong here I am over the moon with getting the M3 and it's a much sportier drive than the S5 but I was surprised to see all Audis with the exception of the old RS6 did better than predicted. Is this down to the fact that quattro is easier to obtain a quick lap from or is it extra traction. Sorry for bring this old Audi vs BMW war up that always seem to go on and on. Call me a dick and say not more about it. 
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10292007, 11:34 AM  #42  
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"Mizuno claimed a time of 7minutes 38 seconds, compared with 7:43 for a Porsche 911 GT3 and 7:32 for a Carrera GT, but he was anxious to point out that there had been "two wet patches on the circuit." Indeed, he mentioned the "wet patches" so many times that you wondered why Nissan simply hadn't waited for a dry day. Mizuno reckoned that a time of around 7:30 should have been possible in the dry, but that going much faster would have required handcut slicks, which isn't "real world." Bizarrely, Nissan admitted to having different test drivers for different lapping. While Chief Test Driver Toshio Suzuki operates in the 7:307:40 range, his righthand man is a 7:407:50 man." 

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10292007, 02:09 PM  #43  
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10292007, 09:47 PM  #44  
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Of course mass/power is an important parameter in the equation but this parameter along with tires (to account for traction) ONLY tells you something about straight line perormance (i.e., acceleration). This is Newton's law F=ma. But how is the suspension design affect lap numbers? And how should we account for this in the regression formula? Swamp (and anyone else for that matter) has no clue. BTW, the GT2 is just as much an outlier as the GTR , the few excess seconds beyond the envelope to the regression line cannot be put into context unless we are willing to theorize that the probability distribution of the error residuals is Gaussian (something we don't know anything about either). Let's focus less on BS and more on facts. I expect the regression line fit that was done in this thread to work much better in estimating straight line performance (i.e., 1/4 mile times) than lap times over a very complex track. To say or imply that the GTR lap time is bogus, inflated, trickery etc. based solely on the analysis presented here would be an outright insult to the Nissan engineers who I am sure busted their asses to build this machine. 

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