RESULTS: Statistical Analysis of MPG -- Long
 

REGRESSION ANALYSIS RESULTS:

I’ve had a couple glasses of vodka and pressed a few buttons on the laptop. The Regression Analysis for the set of data is complete. Thank you everyone for contributing and for your suggestions. The results are as follows:

In a nutshell, based on the data provided, the only substantial variables impacting MPG are % Hwy and Driving Style. Yielding an overall Correlation of 79%, this means that these two factors, when combined, explain about 2/3 of the variance between average MPG among RX-8 owners. Relatively speaking, that’s actually very good. Other factors such as using AC, windows open, and Octane also impact MPG, though to a much lesser magnitude. The other variables provided……….no such luck. Model and Tranny I could not use because almost everyone has the 6-Speed GT. One comment regarding Miles to Date. As a particular owner adds miles on their car, it certainly appears that their individual MPG increases, from what I’ve read on other threads. However, when looking across many owners, it is NOT readily apparent that those with fewer miles get worse MPG than those with more miles on their cars. It tends to get washed out by the other, more significant variables. Please see below for the Correlations associated with each of the inputs you provided relative to MPG. The first Correlation factor of 79% for “Regression” is the correlation resulting from including the both % Hwy and Driving Style simultaneously. Also, shown below is an updated MPG vs % Hwy graph

https://www.rx8club.com/attachment.p...tid=5941&stc=1

mod edit : data gathering and discussion thread https://www.rx8club.com/showthread.p...915#post149915

Here's the MPG vs % Hwy graph

https://www.rx8club.com/attachment.p...tid=5942&stc=1

MPG ESTIMATION:

One of the most important outputs of the Regression Analysis is an actual equation that can be used to estimate what someone’s MPG would be, based on their % Hwy and Driving Style. This can be very useful in a couple ways:
1. A current owner can assess, based on their % Hwy and Driving Style if they fall near the Estimated Mileage using the equation. If their MPG is far below the Estimate (say 2 MPG), then either their own estimates of % Hwy or Driving Style may be somewhat off, or some other factors not yet discovered may be coming into play.
2. For a non-RX8 owner who is contemplating getting the car, this Regression equation can be used to Estimate what their MPG might be, given their % Hwy and Driving Style.

Here is the Equation and an Example of how it works:

Estimated MPG = 18.23 + (5.22 * % Hwy) - (1.19 * Driving Style)

Note: For Driving Style ----- Use 1 instead of A, 2 instead of B, 3 instead of C

For someone Driving 80% Hwy with a Driving Style of B (2), the calculation would be
18.23 + (5.22 * 0.80) - (1.19 * 2) = 20.1 Estimated MPG

Below is a graph of each response Actual vs Estimated MPG. To see your data point, get your observation number from the raw data table below the graph.

https://www.rx8club.com/attachment.p...tid=5943&stc=1

Here's the raw data

https://www.rx8club.com/attachment.p...tid=5944&stc=1

One thing to note: Though it looks like % Hwy and Driving Style are the most important determinants of MPG, there certainly may be other variables related to driving conditions/habits which are worth considering. For example, the following have also been suggested:
- Average Highway Cruising Speed
- Average Speed (My favorite preference)
- Altitude
- Updated responses based on more mileage on the cars.

Avg Hwy Cruising Speed may be quite useful. As was pointed out, someone who cruises at 85 mph will get far less MPG than someone cruising at a constant 55 mph. The couple problems with this variable are that for many people (including me), it’s hard to estimate an Avg Hwy Speed. I go anywhere from 55 – 85 depending on traffic, which may yield quite different MPG than someone who just travels at a constant 70 mph. Also, to estimate the average cruising speed would really be a rough ball park number.

I think using Average Speed would probably turn out be the most important variable. It involves NO subjective estimate, and is something which CAN actually be measured. Overall it’s a much better proxy for City/Hwy % driving. One of the biggest problems using % Hwy that I have found while analyzing the data is that it is a subjective estimate, with no hard data behind it. When something is a judgment call, rather than actually measured, it introduces all kinds of problems and judgment error, thus reducing its effectiveness. (That’s also one reason I only included 3 different categories for Driving Style rather than 5 or more).


There are definitely some outliers relative to the estimates, and there is certainly room for improvement. With this idea of improving the analysis, we have to consider a couple things:
1. The ease and feasibility of obtaining the new, reliable information.
2. At this point, people may be sick of this MPG dissection and want to put it to rest.
3. Amount of participation we’ll get.


In conclusion, it looks like significantly improving MPG may be fairly difficult. Based on the data provided, the analysis shows MPG is mostly determined by driving conditions. The roads people drive on (traffic congestion, lights, etc) can’t really be changed, and I would assume people don’t really want to alter their driving style, especially with a car like the RX-8. If anyone has any comments on the analysis or further suggestions regarding understanding the drivers of MPG, I’d really like to hear.

Interesting Finding:

One BIG outlier in the Actual vs Estimate Graph is the last observation (canzoomer). After doing a bit of forum reading a little while ago, I just discovered he's done some significant work on his engine. Both HP and Torque increased substantially. This is likely one major reason for canzoomer's Actual MPG so much less than the Estimated MPG. I was hoping there was some "external" factor unique to canzoomer's situation that would explain such a large deviation. Perhaps the power increase came at the cost of MPG:)

I'm glad I finished my statistic classes to make sense of all the information.

Good work.

Looks like a good correlation. Unfortunately, it does not correlate with the EPA estimates, which suggest a spread of 20-28(!) mpg highway. It seems to me their projections are about 4mpg too high. I wonder if they tested the vehicle before the detuned fuel maps or would be interested in retesting based on this data.

Norton,
This type of analysis is very hard to do with subjective data input such as percent highway driving and driving style. The results are surprisingly good. This looks like it was a "simple" linear correlation of the various factors, one at a time. Do you have any insight as to whether some factors are more important if they are entered as the square of the term, or a combination of factors? For example, the combination of driving style 3 and city driving may be much worse than highway driving and driving style 3. Is the data set good enough to support further analysis?
Ron

that is absolutely beautiful
great work
________
Mercedes-benz 240d specifications

Nubo: You gave me an idea. Based on the regression analysis equation above, I've put together the resultant "REVISED" MPG Estimates. It's actually very simple algebra. Please see the little table below, at the bottom of this post:

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Ron: I couldn't agree with you more regarding the subjective data. Per my comment above regarding subjective data, ............



Ron: The correlation, one factor at a time was only a minor aspect of the entire analysis. More enlightening, I believe, was the regression information which followed where multiple variables were assessed.



Ron: The square of the term I did not try.
I did try a combination of variables. In fact, in the Multivariate Regression analysis, I first started with all the various inputs everyone gave me, looking at them simultaneously. Then I weeded out those variables which were not too significant, and was left with % Hwy and Driving Style as important to determining MPG.

Per your question regarding your example, please see the little table below. I believe the regression model addresses exactly the scenario you describe.



Ron: Well, it's pretty good data. I was hoping to have another 10-20 observations. It would have helped reduce the impact of the few outliers. Also, there is the shortcoming of the subjective data. I suppose there's more that could be done with the data, though I'm not sure what people would want to see/try.

https://www.rx8club.com/attachment.p...tid=5995&stc=1

I stand in awe of this man! Not only a math wiz, but the spelling and grammer! Bravo!

Uhhhh. Wut'd yuo said I wuz doin?

First, excellent statistical analysis project.

Second, it occurs to me you could simply revisit the topic occasionally to collect more inputs as time goes by and accumulated milage increases. When I get an 8 in another few months, and after I've collected some observations, I'll certainly volunteer some data...

Finally, along the lines of using "cruising speed" as a factor, I think you're suspicions are correct. In every car I've owned, I've noted a strong correllation to MPG and speed... on a tank of gas, I've noted probably on the order of 2-3 MPG, depending on my adherence to the speed limits :D

SpacerX:
Sure, I would be very happy to occasionally rerun the model based on new data. If anyone wants to update their response after more mileage has accumulated on their car, please do so. Or, if anyone wants to provide data for the first time, that's fine too. Rerunning and updating everything is a relatively easy job now that the analytical infrastructure is in place........ basically two glasses of vodka, one joint, and a few computer keys to press.

All in all, at this point I feel comfortable that we have determined a couple things, though not too surprising:
1. GrandMa driving improves mileage.
2. Boring highway driving yields the best mileage.

This is true among any car, though perhaps more so with the RX-8. I think the interesting thing is that no other factors were determined to be significant thus far.

:p

Great analysis.

The sticker on my AT reads 18 to 25.

Here's an excerpt from the government's web site regarding the window sticker figures.

"Manufacturers test pre-production prototypes of the new vehicle models and submit the test results to EPA. EPA re-tests about 10% of vehicle models to confirm manufacturer's results. The vehicles are driven by a professional driver under controlled laboratory conditions, on an instrument similar to a treadmill. These procedures ensure that each vehicle is tested under identical conditions; therefore, the results can be compared with confidence."

The window stickers also say
"Results reported to EPA indicate that the majority of vehicles with these estimates [18 - 25] will achieve between
15 and 21 mpg in the city, and between 21 and 29 on the highway."

Fortunately, I've been getting good gas mileage and seem to fit right in with the analysis' conclusions. Because of a speeding ticket I received (that will be dismissed if I don't get any more this year), I have kept the speed within the posted limits via the cruise control.

The slower speed has taught me a lesson about speed vs gas mileage and now that premium gas is quite high, I'll probably continue "taking it easy". One good thing about driving slower than usual -- I see a lot more people oogling my Winning Blue.

Norton deserves an A for effort, but In the end, his lengthy analysis only confirms the obvious. I think most people would have come to that conclusion without much effort.

Hard driving spends more fuel.
Highway driving gives better mileage than city driving (as indicated by all MPG reports).

Tell me I'm wrong, but that's pretty damn obvious.

Norton,
Thanks for your comments. Another potential "independent" variable is the number of cold starts. I did this type of analysis for another car many years ago and a cold start is devastating to the gas mileage. I think that this would be especially bad for the RX-8 since it apparently runs rich at low rpm and apparently even more so at start-up based on all of the flooding comments. Hope that this helps.
Ron
PS
Do you have an estimate of the error band? This is something that is not eassily obtainable from seat of the pants analysis.
PPS
What happens if you exclude data from the analysis that is "bad" for cause?

I have most of my gas slips with calculated mpg @ odo reading with 4600 miles on my car. Another variable is the VIN. Mine is 00502, significantly earlier than those in your study. Would you like to be flooded with more data? cc

If you have more data, sure, post it up. You can use the survey in the "other" similar thread where I was collecting the data. By the way, VIN was collected and considered in the analysis. (Please see the data table in the 4th post of this thread). Turned out no to be significant.

Squidward: Tartar Sauce! Yes, you are correct. I said the same thing ---- However, in addition to the obvious there were some other interesting conclusions:
o We now have an idea of How Much Hard Driving reduces MPG and How Much Hwy Driving improves MPG.
o Given an individual's % Hwy and Driving Style, they can see how they "fit" with the rest of the pack.
o I think it's probably safe to assume the EPA estimates are exaggerated by a couple MPG.
o Importantly, we can safely omit other variables we were wondering about signficantly impacting MPG (eg. VIN).

mngpao: Can you please provide a link for the above quote. I wanted to read up a bit more on this. I found a similar article, but it implied all new models are tested by the EPA. Here's the link.http://autorepair.about.com/library/.../aa022501d.htm
******************************************

Ron: The Standard Error is about 1.5. This is an output of the Regression Analysis, but I didn't think anyone would be interested.
I did try dropping two outliers. The resultant estimates increased about 0.2 MPG. Actually, this is an important point because it illustrates that the Estimate Equation is very stable. By the way, I also added 2 new observations.... No change to the results though, other than decreasing the Standard Error.

great

Now, that regression of .22 on octane, what octane is best for MPG?

Well, I don't know what you can do with my info, but my RX-8 is for weekend fun (I have other cars and trucks for day-to-day). I go to redline most times off the line in town(1st only), use 97 octance, and hit over 100mph at least once every time I hit the freeway (but not for long), and I get about 15 mpg. I hate the gas mileage, but if I could ever stop hitting the gas pedal, I could probably approximate the EPA, or get close.

But you know what ? I really don't care, because those few minutes over legal are so fun !!!!

AND last week, I was actually driving sane, doing 40 in a 35, coming up to a light that was green, a minivan in the RED lighted left turn lane that was STOPPED decided to get in my lane about 30 feet in front of me, and I swerved to avoid her ! Any other car I have driven, including my Corvette (maybe...)would have rolled. I got sideways rubber on all 4, but other than 10 years off my life based on my heart-rate, no damage.

Thanks Madza !

Squidward, you are right. Occam's razor holds true once again.

Actually the opposite.
I did not count the 2.5 tankfuls I have run with mods installed and active.
So far, using MY driving style, I have run 2 tanks on highway, and one half in city.
On the highway, where I generally run at 140-145kmh, I got just slightly better mileage than my previous tanks. About .5l/100 better.
In city driving, where I tend to rev higher more often, I got quite a bit better mileage, at around 1.5l/100 better.

As it is not a large enough sample, and as this study was on cars that are stock, i did not include my recent tankfuls.

I do not believe my mods will have a major impact on highway mileage, and for city mileage , while there is definite gain, that is dependant mostly on driving style.
The only areas where we leaned out the mixture was above 6,000rpm.
For this to be a significant factor you have to get on the gas and shift above 6,000 with some frequency.

If you drive more gently, and shift below that then i expect to see little difference in economy.

Exactly right. I ran one tankful on the highway, and kept rpm below 4,000 ( speed below 125kmh)
I got about 2L/100 better mileage than my usual speed of 140+kmh and 4,400rpm.

Another factor to consider on the highway driving is that just below 4,000rpm the secondary intake runners are opened, and fuel consumption will climb at an rpm range above that.

This car will make mediocre mileage when driven at speed limits, and with a gentle foot.

And horrible mileage when you go faster.

Norton: the link I quoted was found at www.fueleconomy.gov

Sorry I didn't include it with my post. That URL is on the window sticker in the bottom of the border that surrounds the MPG notice.

RodsterinFL: Based on the data provided, the correlation of .22 means that Octane has little to do with MPG. I tried a lot of different approaches in the regression analysis with respect to Octane because I know that this was a topic of much discussion. I could never achieve any result showing Octane measurably impacts MPG. So I cannot answer your question. From what I recall, I believe you were one of the major proponents of using 87 Octane and had originated a thread on this issue. Right??

canzoomer: Sorry. My bad for assuming your response was post engine mods.

newport8: Occam's razor Never heard that term before. Pretty funny. In case anyone is interested, here's a link for the definition, cartoon included: http://zebu.uoregon.edu/~js/glossary/occams_razor.html I guess for those people that think that the analysis showed ONLY what was obvious, then this is true.

In the statistical world, it's essentially leaving all those extra variables to your error term.

If you normalized MPG for % highway time and just plotted a simple histogram, I bet you'd get a standard bell curve. You might even get one without normalizing. I think the problem is that, no matter how precisely Mazda tries to build its rotary engines, there's going to be a some inevitable variation present, which will show up in a standard distribution of MPG, HP, or whatever. Some people will get lucky and get an engine that is at the top end of the curve. Others will be unlucky and get one at the bottom. But most people will get one at the mean, median and mode.

newport8: Yes, I agree with you about the normal distribution. Hopefully this inevitable variation in rotary engines would yield only a slight variation in MPG, given identical driving and other conditions. It's hard to assess though, because as you said, the Standard Error encompasses a slew of factors other than %Hwy and Driving Style.

It may seem obvious now, but there was protracted and heated debate when the first of us got our cars to look for other reasons in our different MPG results. The common culprit was ECU changes. We had no way to assess driving style until Norton put this together. STrange tho it may seem, it was not immediately obvious at the time.

Um, in reference to the above Squidwardian quote, it is the pretty (doggon) obvious factors, those very things, that cloud the original persuit of determining the not-so-obvious factors that also affect mpg.

VIN (build date) <<--- most sought-after factor
Total vehicle mileage
MT .vs. AT
Aero kit / rear spoiler
Strakes
Front / Rear rotary accents
Color
Marital status

I would love to see if distance traveled for daily commute is a significant factor. I have read several threads where a short trip in a cold environment will result in below average consumption. I travel 7 km all highway (except for a total of 10 city blocks with 3 stops). This was true, it would significantly skew the results since I would present as 90% highway but horrendous MPG. Ambient temperature (overnight and during travel) is another factor that should be investigated when trying to account for lower MPG. fimichael reports a drop of 2 L/100 km since temperatures have dropped below freezing.

I no longer have an 8, I returned it in September because of fuel consumption issues not because of lower HP. If Mazda can promise 12L/100 km hwy and around 10.5 city, I'll get another one. BTW it's not the cost that I mind, it's the fact that at 15L/100 km this car is less efficient than many SUV's.

So, buy an SUV. Since when was the 8 supposed to be an economy car anyway? I suppose an SUV with a lame power plant (typical, but there are exceptions) would have better mpg. Go for it!

Your short repeated highway useage is exactly the clouding of the issue that I was refering to. The pitfall of statistical analyses.

The question that I was asking, is it the short runs or cold temps or both. It would appear to be combination of the factors but the stats may show us that temp has more to do with it then distance. My current car (Integra) shows only a moderate difference in fuel consumption when doing the short stints and driving to Toronto and back (9.8L/100km vs 10.8L/km) while I see a drop of >1.5L/100km between summer and winter. The rotary may or may not follow this pattern.

Well, since you asked ;) Mazda says 9.2 L/100 km highway and 12.8 city. I never expected an econocar but 15L/100 km highway!!! My neighbours Pathfinder v6 4x4 is no beast but is no slouch either and gets better numbers. The best I've seen posted here is 10.5 highway but most are in the teens with some poor sod getting high teens. And yes it is possible to get decent fuel efficiency with a high reving, nimble sports car, ie S2k. The 8 is still the car that I want most but we all have to decide for ourselves what is acceptable. All I said was if Mazda can give me 12 hwy, I will take it, but 15 I will wait for something else. I was hoping that this thread was going bring a solution to my dilema but alas it looks like I will have to wait a little longer.

At least it brings an answer to your dilemma, but alas not the answer you were hoping for.

Someone (CZ?) posted that the stock ECU leans out in the 4k rpm region, so a remapped ECU wouldn't help MPG much unless retuned for lower than 4k rpms. So, where next for improved MPG? CAI? Larger rear tire radius? Higher differential ratio? Catbacks? Which ones? How?

As far as SUV's go I can say that the H2 I test drove for 2 days was ranging about 13.5 mpg with 850 miles on it. My RX-8 with 1,800 miles on it is still only getting 14-15.5 mpg. Both were driven in same conditions and terrain. So Racer X-8 are you suggesting that we should expect to have our cars pelted with rocks and acid by enviromentalists any time soon? And as a side note the mpg were not listed on the H2 because of its' weight class. I know that I am not competing with the H2 in its' weight class but it seems that I am in fuel consumption. Apparently the EPA standards were done for a car not driven in typical city driving conditions becuase, as I've read on the forum, most of the people posting about fuel economy are driving a good portion of the time in the city and not on the highway. I didn't tell Mazda what to post for mpg they did that all on their own. I just want them to live up to the standard they already set. Let me know if that is so wrong.

On a daily basis I do not have to get on the freeway to drive. I do drive roughly 45 mins to work. My car has always gotten 175 to 180 miles before te idiot light comes on. Roughly 14 mpg. It has never changed. Today I went roughly 276 mile before it came on. That is 14 city, 21 hwy. The suprising thing was that on the hwy i was never under 70, and was mostly over 90. The gas mileage sucks, but I was suprised at todays hwy mpg.

Holy resurrected threads, Batman!

The only thing surprising about your newly-achieved highway mileage is that it was as HIGH as it was, since you claim to be driving around at 90+.

It suprised me also! The car just seems to like to go fast.

I wonder what kind of cars and what kind of milage executives and CEO or the 8 big oil companies are getting? Any known stats?

Just a thought... My LR3 landrover weighs almost three tons with me driving and my RX-8 about 55% of that. The rover gets 14mpg and the Mazda 17mpg. Some how I seem happier with the LR3's milleage... though both are at about the EPA city range. On the highway the rover gets 17.5 (close to it's 18mpg rating, the Mazda get's 21-22 hwy - 3mpg short of its hwy rating. - I bet if sixth gear was just a little taller the MPG in real life would match the current EPA numbers. I'd like to turn 3000 RPM at 75MPH - not 3750.

I'm not really that upset about the milleage on the eight either. For the money I saved vs. other cars the effective miles per gallon is more like 22-28 mpg city instead of 17.

I get 22-24 on the highway with air running. Not sure about it off, its been blazing hot here.

Same here... Hot, that is. I beat the Monroney sticker in cooler months with no AC (I don't have the numbers in front of me, but I think my high was 25.5MPG, but even that used a LITTLE bit of AC for demisting) and now I'm right at the rated MPG, at least on the highway, even with the AC on. Ranges from 23.5-24.8. That high tank actually pushed me over 400mi on one tank, which is about as good as I'd ever expect from this car. Just slightly less range on one tank than my Mazda6S 5spd achieved on ITS high tank, but of course that car had a smaller tank.

For the record I do 72-77mph, depending upon the posted limit... I've got more to lose than just some points on my license and higher insurance if I get speeding tickets.

I must be doing something wrong....
 

My MPG is nowhere near the numbers bandied about here. I get about 16 mpg :( with about 80% rural driving. I haven't been driving the car hard either because I'm still in the break-in period. A/C is blasting all the time, though, because I can't stand the California heat. :crazy:

I hear a lot that the MPG improves with time. I'll be tracking my usage the next few months.