Assessing Quadradic Data

#1
I have a set of data that fits nicely to a quadratic equation
pubchart.png
Since the factors of a quadradic equation can be interpreted as Acceleration + Velocity + Location, I can characterize this data as containing an acceleration component. But this non-linear aspect of the data makes the use of average (and thus standard deviation and other tools that depend on average) of questionable merit.

What is the best practice for examining the spread of quadradic data?
 
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katxt

Active Member
#2
A quadratic model like this may fit the data but likely doesn't have a real world interpretation. Have you tried an exponential or power model, one of which may fit as well and mean something in the context of your project.
kat
 
#4
A quadratic model like this may fit the data but likely doesn't have a real world interpretation.
No. The acceleration factor is the result of percentage bonuses to production, as detailed in the link in the original post. Please stay on topic thank you.

Best answer so far has been to use residuals, the difference between formula estimate and actual data.
 
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Karabiner

TS Contributor
#7
I am not sure if I understand your goal here correctely.
What do you mean by "But this non-linear aspect of the data makes the use of average (and thus standard deviation and other tools that depend on average) of questionable merit." and for what reason do you want to examine the spread of quadradic data?
But maybe you already found your solution by using residuals. Is there any question left?

By the way, I cannot follow the claim that there's a nice fit. The regression weight for x² is just 0.008,
(compared with 2.1 for x), and in the range of the highest population, values are markedly overestimated
by the quadratic model.

With kind regards

Karabiner
 
#8
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hlsmith

Less is more. Stay pure. Stay poor.
#10
Stay on topic you all!

I would agree the model seems to be missing something, since you have those systematic little blips scattered across the data. Definitely a pattern there, so the underlying data function isn't quite identified.

What causes those blips? Not sure what it would do, but what happens when you transform the dependent variable (e.g. natural log)?
 

hlsmith

Less is more. Stay pure. Stay poor.
#11
P.S., Can you confirm these are data aren't breaking the independence assumption for linear regression? Tell us more about these data without sending s out in the ether. Thanks.
 
#12
for what reason do you want to examine the spread of quadradic data?
I just took a 1-year contract at an R&D lab on Mars. Big payday, hardly any deaths, nice bullet point on the resume, you know the drill. My main task is to operate some equipment that produces things. And there's a knob on the dashboard labelled "speed."

The outgoing guy who was training me left it set to 50%, figuring anything less and management would complain about production quotas, but anything more and he might be held responsible for breakdowns or something. And the user's manual wasn't much better: "attenuates the rotational velocity of the field effect pylon in the range of 4.5rpm to 7.8rpm" with links to pages for fuel consumption per rotation, pylon maintenance cycles, and mean time between failure.

But there's production quota bonuses that spend nicely in the caffeteria. Decisions, decisions.
 
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