Regression analysis for kg/hp vs. Ring laptimes

[swamp2]

Originally Posted by coaster

Well swamp it's also possible that none of your four previous points is the case for the GTR. If you hadn't seen the GTR's ring time before you looked at this linear regression chart how would you have explained the GT2's "outlier" status? Probably with the same arguments I bet.

In my eyes and looking at this chart the GTR's time is not that much of an outlier (and neither is the GT2). Now if either was 2X further outside the envelope of all the other cars I would squint hard and be concerned about trickery on Nissan's part.

By the way, regression has nothing to do with "physics". Let's not confuse a least squares fit to some data with the physical laws governing vehicle motion.

Just by a quick look at the graph I'd say the GT2 is about a 16 s outlier and the Nissan is closer to 22. That is a fairly large margin. They do no look that different on the plot until you actually count it up.

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.

[ChrisW]

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

[paulyd]

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.

[footie]

The technology in the GT-R 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?

[lucid]

Originally Posted by enigma

If they did run a "slick" that also has other implications. That the stock suspension was able to run the tire without being overloaded means it must have a very, very good camber curve and a lot of roll stiffness, or the car has been upgraded from stock in some way. Possibly as an unanounced option package al-la the Exige Cup 240.

I agree with Swamp on this one. This car is being marketed to the public as a mass production car. Nissan released this video on purpose. If they made major mods to the car, anything other than tires, they will look pretty stupid in a week or two. They know that.

Originally Posted by enigma

Statistics are great, but not when unknown factors can influence the times by far more than the accuracy of the statistics you are trying to use.

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.

[lucid]

Originally Posted by coaster

By the way, regression has nothing to do with "physics". Let's not confuse a least squares fit to some data with the physical laws governing vehicle motion.

If you mean to say correlation does not establish causality, I see what you are saying. But clearly the x-axis 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?...

[enigma]

Originally Posted by lucid

I agree with Swamp on this one. This car is being marketed to the public as a mass production car. Nissan released this video on purpose. If they made major mods to the car, anything other than tires, they will look pretty stupid in a week or two. They know that.

And what it it was a "competition package" option on the car?

Originally Posted by lucid

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.

What I mean is this. power/weight is just one of many factors. We know what many of the other factors are. Tires, suspension, drivetrain. Now if you had hundreds or throustands of data points I would start to believe you did regress the data you meant to. However, you don't have enough data points to eliminate the other factors like tires from influencing the overall trend line.

[swamp2]

Originally Posted by ChrisW

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

Dude you are hilarious! The above emoticons is literal.

[swamp2]

Originally Posted by chitown08

Why people are still trying to pretend that it is not on slicks is ridiculous given what we all know and do not know.

...

People trying to pretend GTR has the handling characteristics of a UFO - wrong.

...

Stay in school. Stats is cool.

+43, especially the middle comment.

I am waiting anxiously for someone to take all of our work over the the Vette and GT-R forums. It will be a total riot in both places

[swamp2]

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 5-10 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!

[lucid]

Originally Posted by enigma

What I mean is this. power/weight is just one of many factors. We know what many of the other factors are. Tires, suspension, drivetrain. Now if you had hundreds or throustands of data points I would start to believe you did regress the data you meant to. However, you don't have enough data points to eliminate the other factors like tires from influencing the overall trend line.

I don't mean to be offensive, but you don't sound like you understand what a linear regression model does. R^2 and the confidence interval are the revelant parameters for determining if the model holds up or not. Yes, more datapoints might yield even a higher R^2 and tighter confidence intervals, but the ones that came out of this analysis are relatively high to begin with (the confidence interval could be much tighter with more datapoints). There is no qualitative discussion to be had around those issues. It is all numbers. If tires, suspension, and drivetrain differences were to overwhelm the weight/power variable, we should not have seen the numbers that came out of this analysis, and visually, the datapoints would have been all over the place.

[lucid]

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.

[footie]

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.

[enigma]

Originally Posted by footie

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.

Welcome to the world of the McMuffin strut suspension and limited roll stifness.

[lucid]

Originally Posted by footie

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.

I am not sure what you mean handling exactly. But the cars below the line are probably doing much better in breaking, transmission losses, and traction as well as handling. Then there are others variances such as driver and weather and so on.

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.

[paulyd]

Originally Posted by footie

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.

In general you'd be correct.
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?

[enigma]

Originally Posted by lucid

I am not sure what you mean handling exactly. But the cars below the line are probably doing much better in breaking, transmission losses, and traction as well as handling. Then there are others variances such as driver and weather and so on.

Or it could simply be the cars above the line do not handle well by the standards of the cars on that list.

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.

[swamp2]

Originally Posted by lucid

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.

Wow, nice, I figured the slopes and intercepts would be close but I would not have guessed that close. Nice work. We really have the physics locked down here on power to weight ratio. Too bad we don't have more data on things like suspension details, driver, temperature, transmission, redline to see how strong those effects are. Would be really interesting. I would guess though that none would have as high of an R^2 as power to weight!

[footie]

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, out-performing 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.

[jaiman]

Originally Posted by chitown08

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.

Wrong.

"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 hand-cut 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 7:30-7:40 range, his right-hand man is a 7:40-7:50 man."

[lucid]

Originally Posted by jaiman

Wrong.

"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 hand-cut 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 7:30-7:40 range, his right-hand man is a 7:40-7:50 man."

Thanks for the quote. This is good info. Where did you find it?

[coaster]

Originally Posted by footie

The technology in the GT-R might explain it amazing lap time, especially it's very advanced awd system which should allow it to way exceed the norm.

Smartest comment in the bunch. The explanation could easily lie in the suspension design, period.

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.